%0 Journal Article
%D 2022
%T In vivo stiffness measurement of epidermis, dermis, and hypodermis using broadband Rayleigh-wave optical coherence elastography
%A Xu Feng
%A Li, Guo-Yang
%A Ramier, Antoine
%A Eltony, Amira M.
%A Seok-Hyun Yun
%K layered tissues
%K optical coherence elastography
%K Rayleigh surface wave
%K Skin
%K Stiffness
%X Traveling-wave optical coherence elastography (OCE) is a promising technique to measure the stiffness of biological tissues. While OCE has been applied to relatively homogeneous samples, tissues with significantly varying elasticity through depth pose a challenge, requiring depth-resolved measurement with sufficient resolution and accuracy. Here, we develop a broadband Rayleigh-wave OCE technique capable of measuring the elastic moduli of the 3 major skin layers (epidermis, dermis, and hypodermis) reliably by analyzing the dispersion of leaky Rayleigh surface waves over a wide frequency range of 0.1-10 kHz. We show that a previously unexplored, high frequency range of 4-10 kHz is critical to resolve the thin epidermis, while a low frequency range of 0.2-1 kHz is adequate to probe the dermis and deeper hypodermis. We develop a dual bilayer-based inverse model to determine the elastic moduli in all 3 layers and verify its high accuracy with finite element analysis and skin-mimicking phantoms. Finally, the technique is applied to measure the forearm skin of healthy volunteers. The Young's modulus of the epidermis (including the stratum corneum) is measured to be $\sim$ 4 MPa at 4-10 kHz, whereas Young's moduli of the dermis and hypodermis are about 40 and 15 kPa, respectively, at 0.2-1 kHz. Besides dermatologic applications, this method may be useful for the mechanical analysis of various other layered tissues with sub-mm depth resolution.
%8 jan
%G eng
%U https://arxiv.org/abs/2201.12258v1
%0 Journal Article
%D 2022
%T Non-destructive mapping of stress, strain and stiffness of thin elastically deformed materials
%A Li, Guo-Yang
%A Gower, Artur L.
%A Destrade, Michel
%A Seok-Hyun Yun
%X Knowing the stress within a soft material is of fundamental interest to basic research and practical applications, such as soft matter devices, biomaterial engineering, and medical sciences. However, it is challenging to measure stress fields in situ in a non-invasive way. It becomes even more difficult if the mechanical properties of the material are unknown or altered by the stress. Here we present a robust non-destructive technique capable of measuring in situ stress and strain in elastically deformed thin films without the need to know their material properties. The technique is based on measuring elastic wave speeds, and then using a universal dispersion curve we derived for Lamb wave to predict the local stress and strain. Using optical coherence tomography, we experimentally verified the method for a rubber sheet, a cling film, and the leather skin of a musical instrument.
%8 jan
%G eng
%U https://arxiv.org/abs/2201.01847v1
%0 Journal Article
%J IEEE Transactions on Medical Imaging
%D 2022
%T Arterial stiffness probed by dynamic ultrasound elastography characterizes waveform of blood pressure
%A Li, Guo-Yang
%A Jiang, Yuxuan
%A Zheng, Yang
%A Xu, Weiqiang
%A Zhang, Zhaoyi
%A Cao, Yanping
%K Arterial stiffness
%K Blood Pressure
%K Guided wave
%K In vivo experiment
%K Pulse wave
%K Ultrasound elastography
%X The clinical and economic burdens of cardiovascular diseases pose a global challenge. Growing evidence suggests an early assessment of arterial stiffness can provide insights into the pathogenesis of cardiovascular diseases. However, it remains difficult to quantitatively characterize local arterial stiffness in vivo. Here we utilize guided axial waves continuously excited and detected by ultrasound to probe local blood pressures and mechanical properties of common carotid arteries simultaneously. In a pilot study of 17 healthy volunteers, we observe a ~20% variation in the group velocities of the guided axial waves (5.16±0.55 m/s in systole and 4.31±0.49 m/s in diastole) induced by the variation of the blood pressures. A linear relationship between the square of group velocity and blood pressure is revealed by the experiments and finite element analysis, which enables us to measure the waveform of the blood pressures by the group velocities. Furthermore, we propose a wavelet analysis-based method to extract the dispersion relations of the guided axial waves. We then determined the shear modulus by fitting the dispersion relations in diastole with the leaky Lamb wave model. The average shear modulus of all the volunteers is 166.3±32.8 kPa. No gender differences are found. This study shows the group velocity and dispersion relation of the guided axial waves can be utilized to probe blood pressure and arterial stiffness locally in a noninvasive manner and thus promising for early diagnosis of cardiovascular diseases.
%B IEEE Transactions on Medical Imaging
%I Institute of Electrical and Electronics Engineers Inc.
%G eng
%R 10.1109/TMI.2022.3141613
%0 Journal Article
%J Journal of Biomechanics
%D 2021
%T AFM-based indentation method for measuring the relaxation property of living cells
%A Sheng, J.-Y.
%A Mo, C.
%A Li, G.-Y.
%A Zhao, H.-C.
%A Cao, Y.
%A Feng, X.-Q.
%K Atomic force microscope
%K Cell
%K Indentation relaxation test
%K Nanoindentation
%K Reduced relaxation modulus
%K Viscoelasticity
%X Probing the mechanical properties of cells is critical for understanding their deformation behaviors and biological functions. Although some methods have been proposed to characterize the elastic properties of cells, it is still difficult to measure their time-dependent properties. This paper investigates the use of atomic force microscope (AFM) to determine the reduced relaxation modulus of cells. In principle, AFM is hard to perform an indentation relaxation test that requires a constant indenter displacement during load relaxation, whereas the real AFM indenter displacement usually varies with time during relaxation due to the relatively small bending stiffness of its cantilever. We investigate this issue through a combined theoretical, computational, and experimental effort. A protocol relying on the choice of appropriate cantilever bending stiffness is proposed to perform an AFM-based indentation relaxation test of cells, which enables the measurement of reduced relaxation modulus with high accuracy. This protocol is first validated by performing nanoindentation relaxation tests on a soft material and by comparing the results with those from independent measurements. Then indentation tests of cartilage cells are conducted to demonstrate this method in determining time-dependent properties of living cells. Finally, the change in the viscoelasticity of MCF-7 cells under hyperthermia is investigated.
%B Journal of Biomechanics
%V 122
%G eng
%R 10.1016/j.jbiomech.2021.110444
%0 Journal Article
%D 2021
%T Supershear surface waves reveal prestress and anisotropy of soft materials
%A Li, Guo-Yang
%A Xu Feng
%A Ramier, Antoine
%A Seok-Hyun Yun
%X Surface waves play important roles in many fundamental and applied areas from seismic detection to material characterizations. Supershear surface waves with propagation speeds greater than bulk shear waves have recently been reported, but their properties are not well understood. In this Letter, we describe theoretical and experimental results on supershear surface waves in rubbery materials. We find that supershear surface waves can be supported in viscoelastic materials with no restriction on the shear quality factor. Interestingly, the effect of prestress on the speed of the supershear surface wave is opposite to that of the Rayleigh surface wave. Furthermore, anisotropy of material affects the supershear wave much more strongly than the Rayleigh surface wave. We offer heuristic interpretation as well as theoretical verification of our experimental observations. Our work points to the potential applications of supershear waves for characterizing the bulk mechanical properties of soft solid from the free surface.
%8 jul
%G eng
%U https://arxiv.org/abs/2107.11482v1
%0 Journal Article
%J Journal of the Mechanics and Physics of Solids
%D 2020
%T Backward Mach cone of shear waves induced by a moving force in soft anisotropic materials
%A Li, G.-Y.
%A Cao, Y.
%K Backward Mach cone
%K Elastic Cherenkov effect
%K Soft matter
%K Soft phononic crystals
%K Theoretical and finite element analysis
%X When a point force travels in a solid with a speed greater than the velocity of the elastic wave induced, the interfering elastic wave fronts will form a Mach cone. This phenomenon is called the elastic Cherenkov effect (ECE). In this study, the ECE in soft matter was investigated with emphasis on backward Mach cone formation. Phase diagrams were proposed based on the theoretical analysis to elucidate key features of the ECE in a wide material parameter space, including the critical conditions for the onset of backward Mach cones and the cone angles. Subsequently, finite element models were developed to validate the theoretical solutions. Our results show that backward Mach cones can be formed in some typical soft tissues under the described conditions, which is important for the use of the ECE in characterizing the mechanical properties of these soft tissues in vivo. Our method and results also illustrate that backward Mach cones can be generated in soft phononic crystals with periodic microstructures, indicating that they are promising material systems for studying the ECE in soft matter.
%B Journal of the Mechanics and Physics of Solids
%V 138
%G eng
%R 10.1016/j.jmps.2020.103896
%0 Journal Article
%J Extreme Mechanics Letters
%D 2020
%T Size effect in shear wave elastography of small solid tumors – A phantom study
%A Y. Zhang
%A Li, G.-Y.
%A Zhou, J.
%A Y. Zheng
%A Jiang, Y.-X.
%A Liu, Y.-L.
%A Zhang, L.-L.
%A Qian, L.-X.
%A Cao, Y.
%K Phantom experiments
%K Size effect
%K Soft matter composites
%K Solid tumors
%K Ultrasound shear wave elastography
%X Ultrasound shear wave elastography (USWE) enables us to quantitatively characterize the mechanical properties of solid tumors and is of clinical importance in differentiating malignant tumors from benign ones. However, limited by the resolution of USWE, it remains challenging in evaluating the elastic properties of tumors with small dimensions. Here we study the size effect in USWE of tumors via phantom experiments. Gelatin phantoms consisted of spherical inclusions and softer matrix were fabricated to model the tumors embedded in surrounding soft tissues. Our results show that elastic moduli E of the phantom tumors measured with conventional USWE are highly related to their diameters d (r > 0.96, P < 0.001). The elastic moduli of stiffer phantom tumors were heavily underestimated when the dimension of a tumor is smaller than 1.5 cm, indicating that the size effect should be considered in interpreting USWE of solid tumors. Based on dimension analysis and our phantom experiments, an empirical formula has been proposed to predict the size effect. The method and the results reported here may not only help quantitatively understand the size effect encountered in USWE of solid tumors, but also provide a promising approach to characterize the mechanical properties of soft matter composites in situ.
%B Extreme Mechanics Letters
%V 35
%G eng
%R 10.1016/j.eml.2020.100636
%0 Journal Article
%J Journal of the Acoustical Society of America
%D 2020
%T An ultrasonic method to measure stress without calibration: The angled shear wave method
%A Li, G.-Y.
%A Gower, A.L.
%A Destrade, M.
%X Measuring stress levels in loaded structures is crucial to assess and monitor structure health and to predict the length of remaining structural life. Many ultrasonic methods are able to accurately predict in-plane stresses inside a controlled laboratory environment but struggle to be robust outside, in a real-world setting. That is because these methods rely either on knowing beforehand the material constants (which are difficult to acquire) or require significant calibration for each specimen. This paper presents an ultrasonic method to evaluate the in-plane stress in situ directly, without knowing any material constants. The method is simple in principle, as it only requires measuring the speed of two angled shear waves. It is based on a formula that is exact for incompressible solids, such as soft gels or tissues, and is approximately true for compressible "hard"solids, such as steel and other metals. The formula is validated by finite element simulations, showing that it displays excellent accuracy, with a small error on the order of 1%.
%B Journal of the Acoustical Society of America
%V 148
%G eng
%N 6
%R 10.1121/10.0002959
%0 Journal Article
%J Extreme Mechanics Letters
%D 2019
%T Elastodiagnosis of diseases: A review
%A Cao, Y.
%A Y. Zheng
%A Li, G.-Y.
%A Jiang, Y.
%K Artery stiffening
%K Detecting cancers
%K Elastodiagnosis
%K Liver fibrosis
%K Magnetic resonance elastography
%K Ultrasound elastography
%X The occurrence and development of many diseases are accompanied by a change in the mechanical properties of the human body across different length scales. The word “elastodiagnosis” coined in this review paper indicates that the elastic cue, i.e., the variation in the elastic properties (including linear elastic, viscoelastic, hyperelastic, poroelastic properties and so on) of cells, tissues or organs, can be used in the diagnosis of a disease. This review is organized into sections based on the use of elastodiagnosis in different diseases, including monitoring the development of liver fibrosis, assessing artery stiffening, determining the stage of chronic kidney disease (CKD) and detecting cancers. Emphasis is given to the challenges involved in understanding and characterizing the variation in the mechanical properties of both healthy and diseased tissues, and future perspectives for improving and developing elastodiagnosis methods are discussed.
%B Extreme Mechanics Letters
%V 27
%G eng
%R 10.1016/j.eml.2019.01.009
%0 Journal Article
%J Acta Biomaterialia
%D 2019
%T Guided wave elastography of layered soft tissues
%A Li, G.-Y.
%A Y. Zheng
%A Jiang, Y.-X.
%A Z. Zhang
%A Cao, Y.
%K Elastography
%K Guided waves
%K Layered soft tissues
%K Phantom study
%K Skin
%X In vivo mechanical characterization of soft biological tissues has broad applications ranging from disease diagnosis to tissue engineering. Shear wave elastography based on the bulk wave theory has been widely used to measure the mechanical properties of soft tissues. Given that most soft tissues basically have layered structures, the dispersive feature of elastic waves should be considered when the thickness of the interested layer is comparable to or smaller than the wavelength. Bearing this fundamental issue in mind, we propose an ultrasound-based guided wave elastography (GWE) method to characterize the mechanical properties of layered soft tissues. The dispersion relations of guided waves in layered structures were derived first, and its explicit expression was achieved. An inverse approach based on the dispersion relation to characterize the mechanical properties of layered soft tissues was then established. Both finite element analysis (FEA) and phantom experiments were carried out to validate the new method. In vivo experiments on forearm skin demonstrate the usefulness of the present method in characterizing layered soft tissues. Statement of significance: Layered soft tissues and artificial soft materials are ubiquitous in both nature and engineering. Imaging their in vivo/in situ mechanical properties finds important applications and remains a great challenge to date. Here, we propose an ultrasound-based guided wave elastography method to in vivo/in situ characterize the elastic properties of layered soft materials. We validate the method via finite element analysis and phantom experiments and further demonstrate its usefulness in practice by performing in vivo measurements on forearm skins. Given that the dispersive feature of elastic waves in layered soft media is considered in our method, it provides the opportunity to assess the intrinsic elastic properties of an individual layer in a non-destructive manner as shown in our experiments.
%B Acta Biomaterialia
%V 84
%G eng
%R 10.1016/j.actbio.2018.12.002
%0 Journal Article
%J International Journal of Non-Linear Mechanics
%D 2019
%T Indentation creep tests to assess the viscoelastic properties of soft materials: Theory, method and experiment
%A Zhang, X.
%A Y. Zheng
%A Li, G.-Y.
%A Liu, Y.-L.
%A Cao, Y.
%K Experiments
%K finite element simulations
%K Portable indentation instrument
%K reduced creep function
%K Scaling law
%X Determining time-dependent mechanical properties of soft materials is essential in understanding their deformation behaviors under various stimuli. This paper investigates the use of indentation creep tests to measure the viscoelastic properties of soft materials at local areas. A simple scaling law between the reduced creep function and the creep displacement of the indenter is revealed in this paper based on a theoretical analysis. We show that the scaling relation can be used to interpret indentation creep tests of viscoelastic soft solids with arbitrary surface profile provided that the contact area does not change. Both numerical and practical experiments have been performed to validate the theory and the analytical solution. In our experiments, a low-cost portable indentation system is proposed to measure the reduced creep function. Our results show that the low-cost instrument and the analytical solution to interpret the experimental data reported here represent a useful testing method to deduce the intrinsic viscoelastic properties of soft materials in a non-destructive manner.
%B International Journal of Non-Linear Mechanics
%V 109
%G eng
%R 10.1016/j.ijnonlinmec.2018.12.005
%0 Journal Article
%J Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
%D 2019
%T Mechanical characterization of functionally graded soft materials with ultrasound elastography
%A Li, G.-Y.
%A Zhang, Z.-Y.
%A J. Qian
%A Y. Zheng
%A W. Liu
%A Wu, H.
%A Cao, Y.
%K Finite-element analysis
%K Functionally graded soft materials
%K Mechanical characterization
%K Phantom experiments
%K Shear wave elastography
%X Functionally graded soft materials (FGSMs) with microstructures and mechanical properties exhibiting gradients across a spatial volume to satisfy specific functions have received interests in recent years. How to characterize the mechanical properties of these FGSMs in vivo/in situ and/or in a non-destructive manner is a great challenge. This paper investigates the use of ultrasound elastography in the mechanical characterization of FGSMs. An efficient finite-element model was built to calculate the dispersion relation for surface waves in FGSMs. For FGSMs with large elastic gradients, the measured dispersion relation can be used to identify mechanical parameters. In the case where the elastic gradient is smaller than a certain critical value calculated here, our analysis on transient wave motion in FGSMs shows that the group velocities measured at different depths can infer the local mechanical properties. Experiments have been performed on polyvinyl alcohol (PVA) cryogel to demonstrate the usefulness of the method. Our analysis and the results may not only find broad applications in mechanical characterization of FGSMs but also facilitate the use of shear wave elastography in clinics because many diseases change the local elastic properties of soft tissues and lead to different material gradients.
%B Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
%V 377
%G eng
%N 2144
%R 10.1098/rsta.2018.0075
%0 Journal Article
%J Journal of Biomechanics
%D 2018
%T Effect of ligation on the viscoelastic properties of liver tissues
%A D. Liu
%A Li, G.-Y.
%A Su, C.
%A Y. Zheng
%A Jiang, Y.-X.
%A Qian, L.-X.
%A Cao, Y.
%K In vivo experiments
%K Indentation
%K Ligation
%K Liver
%K Viscoelasticity
%X It has been reported that ex vivo viscoelastic properties of liver tissues usually differ from those measured in in vivo state due to the reasons such as the effects of perfusion, temperature, and native pre-stress. Therefore, the development of an appropriate ex vivo protocol, which enables the measurement of liver mechanical properties close to those in vivo, is of great importance and has been pursued over the years. In this paper, we propose a simple protocol by ligating the liver when performing ex vivo indentation relaxation tests. Our results show that the viscoelastic kernel function, which measures the intrinsic time-dependent mechanical behavior of a viscoelastic material, determined with the present protocol can describe the in vivo viscoelasticity of liver tissues well in comparison with the ex vivo result measured on a liver without ligation and that obtained in vitro. The performance of the protocol reported here is similar to the ex vivo perfusion system developed by Kerdok et al. (2006). However, the present experimental set-up is much easier to realize.
%B Journal of Biomechanics
%V 76
%G eng
%R 10.1016/j.jbiomech.2018.05.018
%0 Journal Article
%J Journal of the Mechanical Behavior of Biomedical Materials
%D 2018
%T In vivo and ex vivo elastic properties of brain tissues measured with ultrasound elastography
%A Liu, Y.-L.
%A D. Liu
%A Xu, L.
%A Su, C.
%A Li, G.-Y.
%A Qian, L.-X.
%A Cao, Y.
%K Brain tissues
%K Effect of post-mortem interval
%K Elastic properties
%K In vivo and ex vivo measurements
%K Ultrasound elastography
%X Determining the mechanical properties of brain tissues is essential in the field of brain biomechanics. In this paper, we use ultrasound-based shear wave elastography to measure both in vivo and ex vivo elastic properties of brain tissues. Our results demonstrate that the shear modulus from in vivo measurements is about 47% higher than that given by the ex vivo measurements (p value = 0.0063). The change in ex vivo elastic properties within 60-min post-mortem is negligible. The results also show that within 60-min post-mortem and in a temperature range of 37–23 °C, the elastic properties of brain tissues approximately linearly depend on the temperature in both cooling and re-heating processes.
%B Journal of the Mechanical Behavior of Biomedical Materials
%V 83
%G eng
%R 10.1016/j.jmbbm.2018.04.017
%0 Journal Article
%J Journal of the Mechanics and Physics of Solids
%D 2018
%T Non-leaky modes and bandgaps of surface acoustic waves in wrinkled stiff-film/compliant-substrate bilayers
%A Li, G.-Y.
%A Xu, G.
%A Y. Zheng
%A Cao, Y.
%K Bandgaps
%K Metasurfaces
%K Non-leaky modes
%K Surface acoustic waves
%K Wrinkled bilayer
%X Surface acoustic wave (SAW) devices have found a wide variety of technical applications, including SAW filters, SAW resonators, microfluidic actuators, biosensors, flow measurement devices, and seismic wave shields. Stretchable/flexible electronic devices, such as sensory skins for robotics, structural health monitors, and wearable communication devices, have received considerable attention across different disciplines. Flexible SAW devices are essential building blocks for these applications, wherein piezoelectric films may need to be integrated with the compliant substrates. When piezoelectric films are much stiffer than soft substrates, SAWs are usually leaky and the devices incorporating them suffer from acoustic losses. In this study, the propagation of SAWs in a wrinkled bilayer system is investigated, and our analysis shows that non-leaky modes can be achieved by engineering stress patterns through surface wrinkles in the system. Our analysis also uncovers intriguing bandgaps (BGs) related to the SAWs in a wrinkled bilayer system; these are caused by periodic deformation patterns, which indicate that diverse wrinkling patterns could be used as metasurfaces for controlling the propagation of SAWs.
%B Journal of the Mechanics and Physics of Solids
%V 112
%G eng
%R 10.1016/j.jmps.2017.11.024
%0 Journal Article
%J Journal of the Acoustical Society of America
%D 2017
%T Assessing the mechanical properties of anisotropic soft tissues using guided wave elastography: Inverse method and numerical experiments
%A Li, G.-Y.
%A Cao, Y.
%X Determining the mechanical properties of soft biological tissues can be of great importance. For example, the microstructures of many soft tissues, such as those of the human Achilles tendon, have been identified as typical anisotropic materials. This paper proposes an inverse approach that uses guided wave elastography to determine the anisotropic elastic and hyperelastic parameters of thin-walled transversely isotropic biological soft tissues. This approach was developed from the theoretical solutions for the dispersion relations of guided waves, which were derived based on a constitutive model suitable for describing the deformation behavior of such tissues. The properties of these solutions were investigated; in particular, sensitivity to data errors was addressed by introducing the concept of the condition number. To further validate the proposed inverse approach, the guided wave elastography of thin-walled transversely isotropic soft tissues was investigated using numerical experiments. The results indicated that the four constitutive parameters (other than the tensile modulus along the direction of the fibers, EL) could be determined with a good level of accuracy using this method.
%B Journal of the Acoustical Society of America
%V 142
%G eng
%N 3
%R 10.1121/1.5002685
%0 Journal Article
%J Applied Physics Letters
%D 2017
%T Edge wrinkling of a soft ridge with gradient thickness
%A Y. Zhao
%A Shao, Z.-C.
%A Li, G.-Y.
%A Y. Zheng
%A Zhang, W.-Y.
%A B. Li
%A Cao, Y.
%A Feng, X.-Q.
%X We investigate the edge wrinkling of a soft ridge with gradient thickness under axial compression. Our experiments show that the wrinkling wavelength undergoes a considerable increase with increasing load. Simple scaling laws are derived based on an upper-bound analysis to predict the critical buckling conditions and the evolution of wrinkling wavelength during the post-buckling stage, and the results show good accordance with our finite element simulations and experiments. We also report a pattern transformation triggered by the edge wrinkling of soft ridge arrays. The results and method not only help understand the correlation between the growth and form observed in some natural systems but also inspire a strategy to fabricate advanced functional surfaces.
%B Applied Physics Letters
%V 110
%G eng
%N 23
%R 10.1063/1.4985009
%0 Journal Article
%J Journal of the Mechanics and Physics of Solids
%D 2017
%T Guided waves in pre-stressed hyperelastic plates and tubes: Application to the ultrasound elastography of thin-walled soft materials
%A Li, G.-Y.
%A He, Q.
%A Mangan, R.
%A Xu, G.
%A Mo, C.
%A J. Luo
%A Destrade, M.
%A Cao, Y.
%K finite element simulations
%K Fluid-loaded plates and tubes
%K Phantom gel experiments
%K Pre-stressed thin-walled soft biomaterials
%K Theoretical analysis
%K Ultrasound elastography
%X In vivo measurement of the mechanical properties of thin-walled soft tissues (e.g., mitral valve, artery and bladder) and in situ mechanical characterization of thin-walled artificial soft biomaterials in service are of great challenge and difficult to address via commonly used testing methods. Here we investigate the properties of guided waves generated by focused acoustic radiation force in immersed pre-stressed plates and tubes, and show that they can address this challenge. To this end, we carry out both (i) a theoretical analysis based on incremental wave motion in finite deformation theory and (ii) finite element simulations. Our analysis leads to a novel method based on the ultrasound elastography to image the elastic properties of pre-stressed thin-walled soft tissues and artificial soft materials in a non-destructive and non-invasive manner. To validate the theoretical and numerical solutions and demonstrate the usefulness of the corresponding method in practical measurements, we perform (iii) experiments on polyvinyl alcohol cryogel phantoms immersed in water, using the Verasonics V1 System equipped with a L10-5 transducer. Finally, potential clinical applications of the method have been discussed.
%B Journal of the Mechanics and Physics of Solids
%V 102
%G eng
%R 10.1016/j.jmps.2017.02.008
%0 Journal Article
%J Ultrasound in Medicine and Biology
%D 2017
%T An Inverse Method to Determine Arterial Stiffness with Guided Axial Waves
%A Li, G.-Y.
%A He, Q.
%A Jia, L.
%A He, P.
%A J. Luo
%A Cao, Y.
%K Arterial stiffness
%K Guided axial wave
%K Inverse method
%K Phantom experiments
%K Shear wave elastography method
%X Many cardiovascular diseases can alter arterial stiffness; therefore, measurement of arterial wall stiffness can provide valuable information for both diagnosis of such diseases in the clinic and evaluation of the effectiveness of relevant drugs. However, quantitative assessment of the in vivo elastic properties of arterial walls in a non-invasive manner remains a great challenge. In this study, we found that the elastic modulus of the arterial wall can be extracted from the dispersion curve of the guided axial wave (GAW) measured using the ultrasound elastography method. It is shown that the GAW in the arterial wall can be well described with the Lamb wave (LW) model when the frequency exceeds a critical value fc, whose explicit form is determined here based on dimensional analysis method and systematic finite-element simulations. Further, an inverse procedure is proposed to determine both fc and the elastic modulus of the arterial wall. Phantom experiments have been performed to validate the inverse method and illustrate its potential use in the clinic.
%B Ultrasound in Medicine and Biology
%V 43
%G eng
%N 2
%R 10.1016/j.ultrasmedbio.2016.10.006
%0 Journal Article
%J Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
%D 2017
%T Mechanics of ultrasound elastography
%A Li, G.-Y.
%A Cao, Y.
%K Shear wave
%K Soft tissues
%K Ultrasound elastography
%X Ultrasound elastography enables in vivo measurement of the mechanical properties of living soft tissues in a non-destructive and non-invasive manner and has attracted considerable interest for clinical use in recent years. Continuum mechanics plays an essential role in understanding and improving ultrasound-based elastography methods and is the main focus of this review. In particular, the mechanics theories involved in both static and dynamic elastography methods are surveyed. They may help understand the challenges in and opportunities for the practical applications of various ultrasound elastography methods to characterize the linear elastic, viscoelastic, anisotropic elastic and hyperelastic properties of both bulk and thin-walled soft materials, especially the in vivo characterization of biological soft tissues. 2017 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License.
%B Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
%V 473
%G eng
%N 2199
%R 10.1098/rspa.2016.0841
%0 Journal Article
%J Ultrasound in Medicine and Biology
%D 2017
%T Novel Method for Vessel Cross-Sectional Shear Wave Imaging
%A He, Q.
%A Li, G.-Y.
%A Lee, F.-F.
%A Q. Zhang
%A Cao, Y.
%A J. Luo
%K Circumferential
%K Cross section
%K Directional filter
%K Guided wave
%K Radial motion
%K Shear wave imaging
%K Vessel elastography
%X Many studies have investigated the applications of shear wave imaging (SWI) to vascular elastography, mainly on the longitudinal section of vessels. It is important to investigate SWI in the arterial cross section when evaluating anisotropy of the vessel wall or complete plaque composition. Here, we proposed a novel method based on the coordinate transformation and directional filter in the polar coordinate system to achieve vessel cross-sectional shear wave imaging. In particular, ultrasound radiofrequency data were transformed from the Cartesian to the polar coordinate system; the radial displacements were then estimated directly. Directional filtering was performed along the circumferential direction to filter out the reflected waves. The feasibility of the proposed vessel cross-sectional shear wave imaging method was investigated through phantom experiments and ex vivo and in vivo studies. Our results indicated that the dispersion relation of the shear wave (i.e., the guided circumferential wave) within the vessel can be measured via the present method, and the elastic modulus of the vessel can be determined.
%B Ultrasound in Medicine and Biology
%V 43
%G eng
%N 7
%R 10.1016/j.ultrasmedbio.2017.03.001
%0 Journal Article
%J Journal of the Mechanical Behavior of Biomedical Materials
%D 2017
%T Temperature-dependent elastic properties of brain tissues measured with the shear wave elastography method
%A Liu, Y.-L.
%A Li, G.-Y.
%A He, P.
%A Mao, Z.-Q.
%A Cao, Y.
%K Brain tissues
%K Shear wave elastography method
%K Temperature-dependent elastic properties
%X Determining the mechanical properties of brain tissues is essential in such cases as the surgery planning and surgical training using virtual reality based simulators, trauma research and the diagnosis of some diseases that alter the elastic properties of brain tissues. Here, we suggest a protocol to measure the temperature-dependent elastic properties of brain tissues in physiological saline using the shear wave elastography method. Experiments have been conducted on six porcine brains. Our results show that the shear moduli of brain tissues decrease approximately linearly with a slope of −0.041±0.006 kPa/°C when the temperature T increases from room temperature ($\sim$23 °C) to body temperature ($\sim$37 °C). A case study has been further conducted which shows that the shear moduli are insensitive to the temperature variation when T is in the range of 37 to 43 °C and will increase when T is higher than 43 °C. With the present experimental setup, temperature-dependent elastic properties of brain tissues can be measured in a simulated physiological environment and a non-destructive manner. Thus the method suggested here offers a unique tool for the mechanical characterization of brain tissues with potential applications in brain biomechanics research.
%B Journal of the Mechanical Behavior of Biomedical Materials
%V 65
%G eng
%R 10.1016/j.jmbbm.2016.09.026
%0 Journal Article
%J Extreme Mechanics Letters
%D 2017
%T Tissue-mimicking materials for elastography phantoms: A review
%A Cao, Y.
%A Li, G.-Y.
%A Zhang, X.
%A Liu, Y.-L.
%K Mechanical properties
%K Phantoms
%K Tissue-mimicking materials
%K Ultrasound elastography
%X Ultrasound imaging can generate real-time images and is a low-cost, safe, and mobile imaging modality, which has broad applications in clinical radiology. During the past decade, ultrasound-based elastography has emerged as a highly useful technique for characterizing the mechanical properties of living soft tissues. Tissue-mimicking phantoms play an essential role in the development, validation, and use of elastography methods. Phantoms with desired acoustic and mechanical properties that are stable over time and can be stored in a broad range of temperatures have been pursued over the years. In this paper, we provide a brief overview of the typical phantom materials reported in the literature; in particular, we discuss the progress made in recent years and the open issues that deserve further investigation.
%B Extreme Mechanics Letters
%V 17
%G eng
%R 10.1016/j.eml.2017.09.009
%0 Journal Article
%J Journal of Biomechanics
%D 2017
%T An ultrasound elastography method to determine the local stiffness of arteries with guided circumferential waves
%A Li, G.-Y.
%A He, Q.
%A Xu, G.
%A Jia, L.
%A J. Luo
%A Cao, Y.
%K Arterial stiffness
%K Finite Element Analysis
%K Guided circumferential wave
%K Inverse method
%K Shear wave elastography
%X Arterial stiffness is highly correlated with the functions of the artery and may serve as an important diagnostic criterion for some cardiovascular diseases. To date, it remains a challenge to quantitatively assess local arterial stiffness in a non-invasive manner. To address this challenge, we investigated the possibility of determining arterial stiffness using the guided circumferential wave (GCW) induced in the arterial wall by a focused acoustic radiation force. The theoretical model for the dispersion analysis of the GCW is presented, and a finite element model has been established to calculate the dispersion curve. Our results show that under described conditions, the dispersion relations of the GCW are basically independent of the curvature of the arterial wall and can be well-described using the Lamb wave (LW) model. Based on this conclusion, an inverse method is proposed to characterize the elastic modulus of artery. Both numerical experiments and phantom experiments had been performed to validate the proposed method. We show that our method can be applied to the cases in which the artery has local stenosis and/or the geometry of the artery cross-section is irregular; therefore, this method holds great potential for clinical use.
%B Journal of Biomechanics
%V 51
%G eng
%R 10.1016/j.jbiomech.2016.12.006
%0 Journal Article
%J Extreme Mechanics Letters
%D 2017
%T Wrinkling of a stiff film resting on a fiber-filled soft substrate and its potential application as tunable metamaterials
%A Y. Zheng
%A Li, G.-Y.
%A Cao, Y.
%A Feng, X.-Q.
%K Elastic wave
%K Soft metamaterial
%K Stiff-film/fiber-filled substrate bilayer
%K Stress patterns
%K Wrinkling
%X Mechanical self-assembly of ordered patterns via spontaneous buckling of thin-film/soft-substrate systems has received considerable interests in recent years. Here we study the wrinkling of a stiff film resting on a fiber-filled soft substrate. In particular, the effects of the cross-section dimension, spacing, and positions of fibers on the wrinkling patterns in the film/substrate bilayer system are investigated. We show that diverse wrinkling patterns, including sinusoidal wrinkling, period-doubling, period-tripling and mountain ridge modes, may occur at a small or moderate overall compression strain due to the inhomogeneous deformation in the substrate and they can be well controlled by tuning geometrical and physical parameters of the system. To illustrate the potential use of the wrinkling patterns revealed in this study, we investigate the elastic wave propagation in such a wrinkled bilayer using the Bloch wave theory. Our computational results show that diverse stress patterns generated in the soft composites give rise to a rich variety of band structures. Desired bandgaps of elastic waves can be achieved and tuned by simply designing the geometric parameters and controlling the external stimuli imposed on the soft metamaterials.
%B Extreme Mechanics Letters
%V 11
%G eng
%R 10.1016/j.eml.2016.12.002
%0 Journal Article
%J Soft Matter
%D 2016
%T Controlling elastic wave propagation in a soft bilayer system: Via wrinkling-induced stress patterns
%A Li, G.-Y.
%A Y. Zheng
%A Cao, Y.
%A Feng, X.-Q.
%A Zhang, W.
%X Compression of a film/substrate bilayer system with different surface/interfacial structures can lead to diverse buckling patterns including sinusoidal wrinkles, ridges, folds, creases and tilted sawteeth wrinkles. In this paper, we show that elastic wave band gaps in the film/substrate bilayer system largely depend on the wrinkling patterns. More interestingly, we find that different wrinkling patterns investigated here can coexist and evolve in one bilayer system and the elastic wave propagation behaviors can be controlled by manipulating the hybrid wrinkling patterns. Our analysis also reveals that the periodic stress pattern plays a dominant role in tuning the bandgap structures in comparison to geometrical patterns caused by surface instability. A careful investigation of the transmission spectra of the composite systems has validated the main findings given by the analysis based on the Bloch wave theory. Potential use of the method and materials reported here to gain wide attenuation frequency ranges and the design of nesting Fibonacci superlattices have been demonstrated.
%B Soft Matter
%V 12
%G eng
%N 18
%R 10.1039/c6sm00265j
%0 Journal Article
%J Journal of the Mechanics and Physics of Solids
%D 2016
%T Elastic Cherenkov effects in transversely isotropic soft materials-II: Ex vivo and in vivo experiments
%A Li, G.-Y.
%A He, Q.
%A Qian, L.-X.
%A Geng, H.
%A Liu, Y.
%A Yang, X.-Y.
%A J. Luo
%A Cao, Y.
%X In part I of this study, we investigated the elastic Cherenkov effect (ECE) in an incompressible transversely isotropic (TI) soft solid using a combined theoretical and computational approach, based on which an inverse method has been proposed to measure both the anisotropic and hyperelastic parameters of TI soft tissues. In this part, experiments were carried out to validate the inverse method and demonstrate its usefulness in practical measurements. We first performed ex vivo experiments on bovine skeletal muscles. Not only the shear moduli along and perpendicular to the direction of muscle fibers but also the elastic modulus EL and hyperelastic parameter c2 were determined. We next carried out tensile tests to determine EL, which was compared with the value obtained using the shear wave elastography method. Furthermore, we conducted in vivo experiments on the biceps brachii and gastrocnemius muscles of ten healthy volunteers. To the best of our knowledge, this study represents the first attempt to determine EL of human muscles using the dynamic elastography method and inverse analysis. The significance of our method and its potential for clinical use are discussed.
%B Journal of the Mechanics and Physics of Solids
%V 94
%G eng
%R 10.1016/j.jmps.2016.04.028
%0 Journal Article
%J Journal of the Mechanics and Physics of Solids
%D 2016
%T Elastic Cherenkov effects in transversely isotropic soft materials-I: Theoretical analysis, simulations and inverse method
%A Li, G.-Y.
%A Y. Zheng
%A Liu, Y.
%A Destrade, M.
%A Cao, Y.
%K Anisotropic soft materials
%K Dynamic elastography
%K Elastic Cherenkov effect (ECE)
%K Inverse method
%K Supersonic shear imaging (SSI) technique
%X A body force concentrated at a point and moving at a high speed can induce shear-wave Mach cones in dusty-plasma crystals or soft materials, as observed experimentally and named the elastic Cherenkov effect (ECE). The ECE in soft materials forms the basis of the supersonic shear imaging (SSI) technique, an ultrasound-based dynamic elastography method applied in clinics in recent years. Previous studies on the ECE in soft materials have focused on isotropic material models. In this paper, we investigate the existence and key features of the ECE in anisotropic soft media, by using both theoretical analysis and finite element (FE) simulations, and we apply the results to the non-invasive and non-destructive characterization of biological soft tissues. We also theoretically study the characteristics of the shear waves induced in a deformed hyperelastic anisotropic soft material by a source moving with high speed, considering that contact between the ultrasound probe and the soft tissue may lead to finite deformation. On the basis of our theoretical analysis and numerical simulations, we propose an inverse approach to infer both the anisotropic and hyperelastic parameters of incompressible transversely isotropic (TI) soft materials. Finally, we investigate the properties of the solutions to the inverse problem by deriving the condition numbers in analytical form and performing numerical experiments. In Part II of the paper, both ex vivo and in vivo experiments are conducted to demonstrate the applicability of the inverse method in practical use.
%B Journal of the Mechanics and Physics of Solids
%V 96
%G eng
%R 10.1016/j.jmps.2016.05.023
%0 Journal Article
%J Extreme Mechanics Letters
%D 2016
%T Tunable defect mode in a soft wrinkled bilayer system
%A Li, G.-Y.
%A Y. Zheng
%A Cao, Y.
%K Elastic wave control
%K Soft metamaterial
%K Tunable defect mode
%K Wrinkled bilayer system
%X Here we study the defect mode in a wrinkled soft bilayer induced by a local geometrical defect introduced into the system. We show that the band gap of the studied composite system depends on the wrinkling-induced stress pattern and is not sensitive to the compression strain $ε$ in the given loading range. However, the frequency of the defect mode apparently varies with $ε$. This interesting phenomenon enables us to widely tune the spatial extension of the defect mode from highly localized to completely extended by simply controlling the imposed external load. Our strategy to create a tunable defect mode in a soft layered composite is simple and straightforward and may find such broad applications as the development of advanced soft metamaterials and corresponding devices.
%B Extreme Mechanics Letters
%V 9
%G eng
%R 10.1016/j.eml.2016.06.005
%0 Journal Article
%J Medical Image Analysis
%D 2015
%T Characterization of the nonlinear elastic properties of soft tissues using the supersonic shear imaging (SSI) technique: Inverse method, ex vivo and in vivo experiments
%A Jiang, Y.
%A Li, G.-Y.
%A Qian, L.-X.
%A Hu, X.-D.
%A D. Liu
%A Liang, S.
%A Cao, Y.
%K Clinical diagnosis
%K Dynamic elastography
%K In vivo experiments
%K Stressed hyperelastic soft tissues
%K supersonic shear imaging
%X Dynamic elastography has become a new clinical tool in recent years to characterize the elastic properties of soft tissues in vivo, which are important for the disease diagnosis, e.g., the detection of breast and thyroid cancer and liver fibrosis. This paper investigates the supersonic shear imaging (SSI) method commercialized in recent years with the purpose to determine the nonlinear elastic properties based on this promising technique. Particularly, we explore the propagation of the shear wave induced by the acoustic radiation force in a stressed hyperelastic soft tissue described via the Demiray-Fung model. Based on the elastodynamics theory, an analytical solution correlating the wave speed with the hyperelastic parameters of soft tissues is first derived. Then an inverse approach is established to determine the hyperelastic parameters of biological soft tissues based on the measured wave speeds at different stretch ratios. The property of the inverse method, e.g., the existence, uniqueness and stability of the solution, has been investigated. Numerical experiments based on finite element simulations and the experiments conducted on the phantom and pig livers have been employed to validate the new method. Experiments performed on the human breast tissue and human heel fat pads have demonstrated the capability of the proposed method for measuring the in vivo nonlinear elastic properties of soft tissues. Generalization of the inverse analysis to other material models and the implication of the results reported here for clinical diagnosis have been discussed.
%B Medical Image Analysis
%V 20
%G eng
%N 1
%R 10.1016/j.media.2014.10.010
%0 Journal Article
%J Medical Physics
%D 2015
%T Determining the in vivo elastic properties of dermis layer of human skin using the supersonic shear imaging technique and inverse analysis
%A Luo, C.-C.
%A Qian, L.-X.
%A Li, G.-Y.
%A Jiang, Y.
%A Liang, S.
%A Cao, Y.
%K dermis layer
%K finite element simulations
%K Human skin
%K in vivo measurement
%K supersonic shear imaging
%X Purpose: Human skin consists of several layers including epidermis, dermis, and hypodermis. The determination of the in vivo mechanical properties of an individual skin layer represents a great challenge to date. In this study, the authors explore the use of the supersonic shear imaging (SSI) technique and inverse analysis to determine the in vivo elastic properties of the dermis layer of human skin. Methods: The measurements are conducted on the volar forearms and dorsal forearms of 18 healthy volunteers (nine females and nine males) using the SSI technique that gives the velocities of the shear wave generated by the acoustic force. Finite element analysis is carried out to simulate the propagation of the shear wave in the multilayer soft media and the results are used to interpret the experimental data and deduce the shear modulus of the dermis layer. Results: The shear moduli of the skin dermis layer obtained for the 18 healthy volunteers exhibit significant anisotropy. A standard statistical analysis demonstrates the differences between sexes. Conclusions: This study demonstrates that the SSI technique together with the inverse analysis represents a useful tool to characterize the in vivo elastic properties of human skin.
%B Medical Physics
%V 42
%G eng
%N 7
%R 10.1118/1.4922133
%0 Journal Article
%J Journal of the Mechanics and Physics of Solids
%D 2015
%T Effect of lateral dimension on the surface wrinkling of a thin film on compliant substrate induced by differential growth/swelling
%A Y. Zhao
%A Han, X.
%A G. Li
%A Lu, C.
%A Cao, Y.
%A Feng, X.-Q.
%A H. Gao
%K Differential growth/swelling
%K Lateral dimension of thin film
%K Wrinkling patterns
%X Surface wrinkling in thin films on compliant substrates is of considerable interest for applications involving surface patterning, smart adhesion, liquid/cell shaping, particle assembly, design of flexible electronic devices, as well as mechanical characterization of thin film systems. When the in-plane size of the system is infinite, the critical wrinkling strain is known to be governed by the moduli ratio between the film and substrate. Here we show a surprising result that the lateral dimension of the film can play a critical role in the occurrence of surface wrinkling. The basic phenomenon was established through selective UV/Ozone (UVO) exposure of a strain-free PDMS slab via composite copper grids with different meshes, followed by treatment using mixed ethanol/glycerol solvents with different volume fractions of ethanol. To understand the physics behind the experimental observations, finite element (FE) simulations were performed to establish an analytical expression for the distribution of shear tractions at the film-substrate interface. Subsequent theoretical analysis leads to closed-form predictions for the critical growth/swelling strain for the onset of wrinkling. Our analysis reveals that the occurrence of surface wrinkling and post-wrinkling pattern evolution can be controlled by tuning the lateral size of the thin film for a given moduli ratio. These results may find broad applications in preventing surface wrinkling, creating desired surface patterns, evaluating the interfacial shear strength of a film/substrate system and designing flexible electronic devices.
%B Journal of the Mechanics and Physics of Solids
%V 83
%G eng
%R 10.1016/j.jmps.2015.06.003
%0 Journal Article
%J Biomechanics and Modeling in Mechanobiology
%D 2015
%T Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis
%A Jiang, Y.
%A G. Li
%A Qian, L.-X.
%A Liang, S.
%A Destrade, M.
%A Cao, Y.
%K Brain tissue
%K Elastic and hyperelastic properties
%K Inverse method
%K Supersonic shear wave imaging technique
%X We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus $μ$0 varies from 1.8 to 3.2 kPa, the stiffening parameter b of the hyperelastic Demiray–Fung model from 0.13 to 0.73, and the third- (A) and fourth-order (D) constants of weakly nonlinear elasticity from -1.3 to -20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired t test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.
%B Biomechanics and Modeling in Mechanobiology
%V 14
%G eng
%N 5
%R 10.1007/s10237-015-0658-0
%0 Journal Article
%J Journal of Applied Mechanics, Transactions ASME
%D 2014
%T Determination of the reduced creep function of viscoelastic compliant materials using pipette aspiration method
%A Cao, Y.-P.
%A Li, G.-Y.
%A Zhang, M.-G.
%A Feng, X.-Q.
%K analytical analysis
%K finite element simulations
%K pipette aspiration test
%K reduced creep function
%X Determining the mechanical properties of soft matter across different length scales is of great importance in understanding the deformation behavior of compliant materials under various stimuli. A pipette aspiration test is a promising tool for such a purpose. A key challenge in the use of this method is to develop explicit expressions of the relationship between experimental responses and material properties particularly when the tested sample has irregular geometry. A simple scaling relation between the reduced creep function and the aspiration length is revealed in this paper by performing a theoretical analysis on the aspiration creep tests of viscoelastic soft solids with arbitrary surface profile. Numerical experiments have been performed on the tested materials with different geometries to validate the theoretical solution. In order to incorporate the effects of the rise time of the creep pressure, an analytical solution is further derived based on the generalized Maxwell model, which relates the parameters in reduced creep function to the aspiration length. Its usefulness is demonstrated through a numerical example and the analysis of the experimental data from literature. The analytical solutions reported here proved to be independent of the geometric parameters of the system under described conditions. Therefore, they may not only provide insight into the deformation behavior of soft materials in aspiration creep tests but also facilitate the use of this testing method to deduce the intrinsic creep/relaxation properties of viscoelastic compliant materials. © 2014 by ASME.
%B Journal of Applied Mechanics, Transactions ASME
%V 81
%G eng
%N 7
%R 10.1115/1.4027159
%0 Journal Article
%J Journal of the Mechanics and Physics of Solids
%D 2014
%T Pipette aspiration of hyperelastic compliant materials: Theoretical analysis, simulations and experiments
%A Zhang, M.-G.
%A Cao, Y.-P.
%A Li, G.-Y.
%A Feng, X.-Q.
%K Dimensional analysis
%K Finite element method
%K Hyperelastic compliant materials
%K Inverse problem
%K Pipette aspiration method
%X This paper explores the pipette aspiration test of hyperelastic compliant materials. Explicit expressions of the relationship between the imposed pressure and the aspiration length are developed, which serve as fundamental relations to deduce the material parameters from experimental responses. Four commonly used hyperelastic constitutive models, e.g. neo-Hookean, Mooney-Rivlin, Fung, and Arruda-Boyce models, are investigated. Through dimensional analysis and nonlinear finite element simulations, we establish the relations between the experimental responses and the constitutive parameters of hyperelastic materials in explicit form, upon which inverse approaches for determining the hyperelastic properties of materials are developed. The reliability of the results given by the proposed methods has been verified both theoretically and numerically. Experiments have been carried out on an elastomer (polydimethylsiloxane, 1:50) and porcine liver to validate the applicability of the inverse approaches in practical measurements. © 2014 Elsevier Ltd.
%B Journal of the Mechanics and Physics of Solids
%V 68
%G eng
%N 1
%R 10.1016/j.jmps.2014.03.012
%0 Journal Article
%J Biomechanics and Modeling in Mechanobiology
%D 2014
%T Spherical indentation method for determining the constitutive parameters of hyperelastic soft materials
%A Zhang, M.-G.
%A Cao, Y.-P.
%A Li, G.-Y.
%A Feng, X.-Q.
%K Dimensional analysis
%K Finite element method
%K Hyperelastic soft materials
%K Inverse problem
%K Spherical indentation
%X A comprehensive study on the spherical indentation of hyperelastic soft materials is carried out through combined theoretical, computational, and experimental efforts. Four widely used hyperelastic constitutive models are studied, including neo-Hookean, Mooney-Rivlin, Fung, and Arruda-Boyce models. Through dimensional analysis and finite element simulations, we establish the explicit relations between the indentation loads at given indentation depths and the constitutive parameters of materials. Based on the obtained results, the applicability of Hertzian solution to the measurement of the initial shear modulus of hyperelastic materials is examined. Furthermore, from the viewpoint of inverse problems, the possibility to measure some other properties of a hyperelastic material using spherical indentation tests, e.g., locking stretch, is addressed by considering the existence, uniqueness, and stability of the solution. Experiments have been performed on polydimethylsiloxane to validate the conclusions drawn from our theoretical analysis. The results reported in this study should help identify the extent to which the mechanical properties of hyperelastic materials could be measured from spherical indentation tests. © 2013 Springer-Verlag Berlin Heidelberg.
%B Biomechanics and Modeling in Mechanobiology
%V 13
%G eng
%N 1
%R 10.1007/s10237-013-0481-4