Kirigami skins make a simple soft actuator crawl
A. Rafsanjani, Y. Zhang, B. Liu, S. M. Rubinstein, and K. Bertoldi. 2/21/2018. “Kirigami skins make a simple soft actuator crawl.” Science Robotics, 3, 15, Pp. eaar7555. Publisher's VersionAbstract

Bioinspired soft machines made of highly deformable materials are enabling a variety of innovative applications, yet their locomotion typically requires several actuators that are independently activated. We harnessed kirigami principles to significantly enhance the crawling capability of a soft actuator. We designed highly stretchable kirigami surfaces in which mechanical instabilities induce a transformation from flat sheets to 3D-textured surfaces akin to the scaled skin of snakes. First, we showed that this transformation was accompanied by a dramatic change in the frictional properties of the surfaces. Then, we demonstrated that, when wrapped around an extending soft actuator, the buckling-induced directional frictional properties of these surfaces enabled the system to efficiently crawl.

Durable Bistable Auxetics Made of Rigid Solids
X. Shang, L. Liu, A. Rafsanjani, and D. Pasini. 2/14/2018. “Durable Bistable Auxetics Made of Rigid Solids.” Journal of Materials Research, Focus Issue: Architected Materials, 33, 3, Pp. 300-308. Publisher's VersionAbstract
Bistable Auxetic Metamaterials (BAMs) are a class of monolithic perforated periodic structures with negative Poisson’s ratio. Under tension, a BAM can expand and reach a second state of equilibrium through a globally large shape transformation that is ensured by the flexibility of its elastomeric base material. However, if made from a rigid polymer, or metal, BAM ceases to function due to the inevitable rupture of its ligaments. The goal of this work is to extend the unique functionality of the original kirigami architecture of BAM to a rigid solid base material. We use experiments and numerical simulations to assess performance, bistability and durability of rigid BAMs at 10,000 cycles. Geometric maps are presented to elucidate the role of the main descriptors of BAM architecture. The proposed design enables the realization of BAM from a large palette of materials, including elastic-perfectly plastic materials and potentially brittle materials.
On the design of porous structures with enhanced fatigue life
F. Javid, J. Liu, A. Rafsanjani, M. Schaenzer, M. Q. Pham, D. Backman, S. Yandt, M. C. Innes, C. Booth-Morrison, M. Gerendas, T. Scarinci, A. Shanian, and K. Bertoldi. 10/2017. “On the design of porous structures with enhanced fatigue life.” Extreme Mechanics Letters, 16, Pp. 13-17. Publisher's VersionAbstract
Many components of gas turbines, including the combustion liners, ducts, casings and sealing structures, comprise metallic sheets perforated with arrays of circular cooling holes. These parts are highly prone to fatigue failure due to the stresses induced by temperature variations during operation. Here, we demonstrate both experimentally and numerically that the fatigue life of these porous components can be greatly enhanced by carefully designing the pores’ shape. In particular, we show that while the fatigue life of a metallic sheet with a square array of conventional circular cooling holes is <100k cycles, by replacing the pores with novel orthogonal S-shaped holes the life of the structure increases up to more than one million cycles. This is because the S-shaped pores introduce a soft mode of deformation based on rotation of the domains between neighboring holes that significantly affect the stress distribution and crack propagation in the structure.
Buckling-Induced Kirigami
A. Rafsanjani and K. Bertoldi. 2/24/2017. “Buckling-Induced Kirigami.” Physical Review Letters, 118, Pp. 084301. Publisher's VersionAbstract

We investigate the mechanical response of thin sheets perforated with a square array of mutually orthogonal cuts, which leaves a network of squares connected by small ligaments. Our combined analytical, experimental and numerical results indicate that under uniaxial tension the ligaments buckle out-of-plane, inducing the formation of 3D patterns whose morphology is controlled by the load direction. We also find that by largely stretching the buckled perforated sheets, plastic strains develop in the ligaments. This gives rise to the formation of kirigami sheets comprising periodic distribution of cuts and permanent folds. As such, the proposed buckling-induced pop-up strategy points to a simple route for manufacturing complex morphable structures out of flat perforated sheets.

Bistable Auxetic Mechanical Metamaterials Inspired by Ancient Geometric Motifs
A. Rafsanjani and D. Pasini. 12/2016. “Bistable Auxetic Mechanical Metamaterials Inspired by Ancient Geometric Motifs.” Extreme Mechanics Letters, 9, Pp. 291-296. Publisher's VersionAbstract

Auxetic materials become thicker rather than thinner when stretched, exhibiting an unusual negative Poisson’s ratio well suited for designing shape transforming metamaterials. Current auxetic designs, however, are often monostable and cannot maintain the transformed shape upon load removal. Here, inspired by ancient geometric motifs arranged in square and triangular grids, we introduce a class of switchable architected materials exhibiting simultaneous auxeticity and structural bistability. The material concept is experimentally realized by perforating various cut motifs into a sheet of rubber, thus creating a network of rotating units connected with compliant hinges. The metamaterial performance is assessed through mechanical testing and accurately predicted by a coherent set of finite element simulations. A discussion on a rich set of mechanical phenomena follows to shed light on the main design principles governing bistable auxetics.

[available on arXiv]

Watch a video about this work on Vimeo!

A US Patent (US2017/0362414A1) is filed for Bistable Auxetics and we are actively seeking commercialization opportunities.

Featured in PhysicsWorld MagazineAPS NewsBBC NewsAhmad's interview with BBC NewshourBBC Newsroom report, NewScientist, PhysicsWorld, Creators, Science, McGill TribuneSmithsonian Magazine, PNAS

Hierarchies of Plant Stiffness
V. Brulé, A. Rafsanjani, D. Pasini, and T. L. Western. 9/2016. “Hierarchies of Plant Stiffness.” Plant Science, 250, Pp. 79-96. Publisher's VersionAbstract

Plants must meet mechanical as well as physiological and reproductive requirements for survival. Management of internal and external stresses is achieved through their unique hierarchical architecture. Stiffness is determined by a combination of morphological (geometrical) and compositional variables that vary across multiple length scales ranging from the whole plant to organ, tissue, cell and cell wall levels. These parameters include, among others, organ diameter, tissue organization, cell size, density and turgor pressure, and the thickness and composition of cell walls. These structural parameters and their consequences on plant stiffness are reviewed in the context of work on stems of the genetic reference plant Arabidopsis thaliana (Arabidopsis), and the suitability of Arabidopsis as a model system for consistent investigation of factors controlling plant stiffness is put forward. Moving beyond Arabidopsis, the presence of morphological parameters causing stiffness gradients across length-scales leads to beneficial emergent properties such as increased load-bearing capacity and reversible actuation. Tailoring of plant stiffness for old and new purposes in agriculture and forestry can be achieved through bioengineering based on the knowledge of the morphological and compositional parameters of plant stiffness in combination with gene identification through the use of genetics.

Hydro-Responsive Curling of the Resurrection Plant Selaginella lepidophylla
A. Rafsanjani, V. Brulé, T. L. Western, and D. Pasini. 2015. “Hydro-Responsive Curling of the Resurrection Plant Selaginella lepidophylla.” Scientific Reports, 5, Pp. 8064. Publisher's VersionAbstract

The spirally arranged stems of the spikemoss Selaginella lepidophylla, an ancient resurrection plant, compactly curl into a nest-ball shape upon dehydration. Due to its spiral phyllotaxy, older outer stems on the plant interlace and envelope the younger inner stems forming the plant centre. Stem curling is a morphological mechanism that limits photoinhibitory and thermal damages the plant might experience in arid environments. Here, we investigate the distinct conformational changes of outer and inner stems of S. lepidophylla triggered by dehydration. Outer stems bend into circular rings in a relatively short period of desiccation, whereas inner stems curl slowly into spirals due to hydro-actuated strain gradient along their length. This arrangement eases both the tight packing of the plant during desiccation and its fast opening upon rehydration. The insights gained from this work shed light on the hydro-responsive movements in plants and might contribute to the development of deployable structures with remarkable shape transformations in response to environmental stimuli.

A. Rafsanjani, D. Derome, and J. Carmeliet. 2015. “Poromechanical modeling of moisture induced swelling anisotropy in cellular tissues of softwoods.” RSC Advances, 5, 5, Pp. 3560-3566. Publisher's VersionAbstract

Experimental studies reveal that softwoods exhibit different swelling patterns at the cellular scale depending on the position of the tracheid cells within the growth ring. Thin-walled earlywood cells show anisotropic swelling behavior while the swelling of thick-walled bulky latewood cells is generally isotropic. A poromechanical model is developed to explore the anisotropic swelling behavior of softwoods at the cellular scale. The general description for the macroscopically observable free swelling strain of cellular tissues is derived by upscaling the constitutive equations of a double porosity medium which is found to be dependent on stiffness, Biot coefficient, Biot modulus and the geometry of the cells. The effective poroelastic constants of earlywood and latewood cells are computed from a periodic honeycomb unit cell by means of an efficient finite-element-based computational upscaling scheme. The estimated swelling coefficients compare well with experimental measurements. It is found that the anisotropy in swelling behavior of wood cells can be related to the anisotropy of elastic properties at the cell wall level and the geometry of the cells. The proposed poromechanical model provides a physically relevant description of swelling behavior which originates from the coupled interaction of water and solid phases within the porous cell walls of softwoods.

Snapping Mechanical Metamaterials under Tension
A. Rafsanjani, A. Akbarzadeh, and D. Pasini. 2015. “Snapping Mechanical Metamaterials under Tension.” Advanced Materials, 27, 39, Pp. 5931–5935. Publisher's VersionAbstract

A snapping mechanical metamaterial is designed, which exhibits a sequential snap-through behavior under tension. The tensile response of this mechanical metamaterial can be altered by tuning the architecture of the snapping segments to achieve a range of nonlinear mechanical responses, including monotonic, S-shaped, plateau, and non-monotonic snap-through behavior.

A. Patera, K. Jefimovs, A. Rafsanjani, F. Voisard, R. Mokso, D. Derome, and J. Carmeliet. 2014. “Micro-Scale Restraint Methodology for Humidity Induced Swelling Investigated by Phase Contrast X-Ray Tomography.” Experimental Mechanics, 54, 7, Pp. 1215-1226. Publisher's VersionAbstract

A new methodology for restraining the swelling of spruce wood samples in the micrometre range is developed and presented. We show that the restraining device successfully prevents the free swelling of wood during moisture adsorption, thus modifying significantly the anisotropy of swelling and provoking the intended collapse and large deformations of the wood cells at the edges of the sample in contact with the restraining device. The device consists in a slotted cube designed to restrain swelling and is made of PMMA manufactured by laser ablation. The sample undergoing the restraining experiment is imaged with high-resolution synchrotron radiation phase contrast X-Ray Tomographic Microscopy. The deformation of the restraining device itself is only approximately 2 μm with respect to a 500 μm width in cubes containing latewood samples and half of that in the case of cubes containing earlywood.

Hygroscopic swelling and shrinkage of latewood cell wall micropillars reveal ultrastructural anisotropy
A. Rafsanjani, M. Stiefel, K. Jefimovs, R. Mokso, D. Derome, and J. Carmeliet. 2014. “Hygroscopic swelling and shrinkage of latewood cell wall micropillars reveal ultrastructural anisotropy.” Journal of The Royal Society Interface, 11, 95, Pp. 20140126. Publisher's VersionAbstract

We document the hygroscopic swelling and shrinkage of the central and the thickest secondary cell wall layer of wood (named S2) in response to changes in environmental humidity using synchrotron radiation-based phase contrast X-ray tomographic nanoscopy. The S2 layer is a natural fibre-reinforced nano-composite polymer and is strongly reactive to water. Using focused ion beam, micropillars with a cross section of few micrometres are fabricated from the S2 layer of the latewood cell walls of Norway spruce softwood. The thin neighbouring cell wall layers are removed to prevent hindering or restraining of moisture-induced deformation during swelling or shrinkage. The proposed experiment intended to get further insights into the microscopic origin of the anisotropic hygro-expansion of wood. It is found that the swelling/shrinkage strains are highly anisotropic in the transverse plane of the cell wall, larger in the normal than in the direction parallel to the cell wall's thickness. This ultrastructural anisotropy may be due to the concentric lamellation of the cellulose microfibrils as the role of the cellulose microfibril angle in the transverse swelling anisotropy is negligible. The volumetric swelling of the cell wall material is found to be substantially larger than the one of wood tissues within the growth ring and wood samples made of several growth rings. The hierarchical configuration in wood optimally increases its dimensional stability in response to a humid environment with higher scales of complexity.

Swelling of Wood Tissue: Interactions at the Cellular Scale
D. Derome, J. Carmeliet, A. Rafsanjani, A. Patera, and R. A. Guyer. 2014. “Swelling of Wood Tissue: Interactions at the Cellular Scale.” In Nonlinear Elasticity and Hysteresis: Fluid-Solid Coupling in Porous Media, Pp. 153-170. Wiley‐VCH Verlag GmbH & Co. KGaA. Publisher's VersionAbstract

The swelling behavior is of interest as the locus of the nice interaction of moisture and mechanical behavior. We take wood as our model material. Although, moisture behavior is known to be hysteretic in terms of relative humidity, we demonstrate that it is not hysteresis in terms of moisture content and take this as an opportunity to look for a full description of this moisture/mechanical interaction. Investigations by phase contrast synchrotron X-ray microtomography and by hygro-elastic modeling allows to see the strong effects of porosity and cellular geometry on the anisotropy of swelling. We end with a few observations on moisture-induced shape memory.

D. Derome, A. Rafsanjani, S. Hering, M. Dressler, A. Patera, C. Lanvermann, M. Sedighi-Gilani, F. K. Wittel, P. Niemz, and J. Carmeliet. 2013. “The role of water in the behavior of wood.” Journal of Building Physics, 36, 4, Pp. 398-421. Publisher's VersionAbstract

Wood, due to its biological origin, has the capacity to interact with water. Sorption/desorption of moisture is accompanied with swelling/shrinkage and softening/hardening of its stiffness. The correct prediction of the behavior of wood components undergoing environmental loading requires that the moisture behavior and mechanical behavior of wood are considered in a coupled manner. We propose a comprehensive framework using a fully coupled poromechanical approach, where its multiscale implementation provides the capacity to take into account, directly, the exact geometry of the wood cellular structure, using computational homogenization. A hierarchical model is used to take into account the subcellular composite-like organization of the material. Such advanced modeling requires high-resolution experimental data for the appropriate determination of inputs and for its validation. High-resolution x-ray tomography, digital image correlation, and neutron imaging are presented as valuable methods to provide the required information.

A. Rafsanjani, D. Derome, and J. Carmeliet. 2013. “Micromechanics investigation of hygro-elastic behavior of cellular materials with multi-layered cell walls.” Composite Structures, 95, Pp. 607-611. Publisher's VersionAbstract

In this paper, the hygro-elastic behavior of two-dimensional periodic honeycombs composed of multi-layered cell walls is investigated using a computational micromechanics approach. Detailed numerical results for the effective hygro-expansion coefficients and the elastic moduli of honeycombs are obtained. The influence of the arrangement of the cell wall layers and the geometrical parameters of the honeycombs on the effective hygro-elastic properties is examined. Limiting cases are considered, and the validity of the model is established by comparison with the analytical solutions available in the existing literature. The obtained results suggest that the layered architecture of the cell wall enhances the anisotropy in swelling behavior of honeycombs with irregular configuration which is reflected in their transverse hygro-expansion coefficients while regular honeycombs show isotropic behavior. The proposed model explains the complex thermo-hygro-mechanical behavior of natural cellular materials and provides a predictive tool for bio-mimetic material design.

Multiscale analysis of free swelling of Norway spruce
A. Rafsanjani, C. Lanvermann, P. Niemz, J. Carmeliet, and D. Derome. 2013. “Multiscale analysis of free swelling of Norway spruce.” Composites Part A: Applied Science and Manufacturing, 54, Pp. 70-78. Publisher's VersionAbstract

The swelling of the hierarchical cellular structure of wood can be properly predicted when both the cellular and the growth ring scales are taken into account. In this study, a multiscale computational upscaling finite element model is utilized for the estimation of the free swelling behavior of Norway spruce softwood. The microstructural information, e.g. the geometry of the wood cells, the local density and the microfibril angle across the growth rings is the input of the lower scale cellular model. The elastic properties and the swelling coefficients within the growth ring are estimated using a periodic honeycomb unit cell model. Based on this model, the transverse anisotropy in the swelling behavior of softwood at timber or growth ring level is then predicted. Comparison of simulation results with experimental measurements obtained using digital image correlation shows very good agreement.

Multiscale poroelastic model: bridging the gap from cellular to macroscopic scale
A. Rafsanjani. 2013. “Multiscale poroelastic model: bridging the gap from cellular to macroscopic scale.” ETH Zürich (20821). Publisher's VersionAbstract

Many biological and engineering materials are essentially porous or cellular, a feature which provides them with a low density and high strength and toughness.  The deformation of cellular materials in response to environmental stimuli such as changes in relative humidity is of practical interest to evaluate the durability of materials in different working conditions. In this thesis, the hygro-mechanical behavior of hierarchical cellular materials is investigated using a multiscale computational framework. Attention is focused on softwoods but the proposed model is general and can be applied to other cellular materials. In wood, the interaction of the moisture and mechanical behavior is best observed in swelling. The complicated hierarchical architecture of wood introduces a strong geometric anisotropy which is reflected in the anisotropy of its mechanical and swelling behavior. A two-step computational upscaling method is utilized to devise a finite element model for the estimation of swelling behavior of softwoods. Starting from the cellular scale which represents the underlying structure of the growth ring scale, an efficient scheme is developed for the estimation of the hygro-elastic properties of periodic honeycombs as a model for the cellular structure of wood. Predicted results are found to be comparable to experimental data at both cellular scale and growth ring level. A poromechanical approach is also presented as an alternative formulation for the estimation of the effective swelling coefficients of cellular materials. The computational approach proposed in this thesis provides a predictive tool for revealing the structure-property relations of biological and engineering cellular materials and can also be used for the design of new functional cellular materials with tailorable swelling properties. 

A. Rafsanjani, D. Derome, R. A. Guyer, and J. Carmeliet. 2013. “Swelling of cellular solids: From conventional to re-entrant honeycombs.” Applied Physics Letters, 102, Pp. 211907. Publisher's VersionAbstract

We find that, in two-dimensional periodic cellular solids, the hygro-expansion properties of the cell wall and the geometrical configurations of the lattice determine the effective swelling behavior of the medium. In this letter, we present the associated phase diagram for the swelling anisotropy of conventional and re-entrant honeycomb morphologies. The presented results are obtained numerically from a finite element based computational upscaling scheme. We show how the pattern of anisotropy in swelling behavior of cellular materials reverses when swelling is more important across or along the cell walls.

D. Derome, A. Rafsanjani, A. Patera, R. A. Guyer, and J. Carmeliet. 2012. “Hygromorphic behaviour of cellular material: hysteretic swelling and shrinkage of wood probed by phase contrast X-ray tomography.” Philosophical Magazine, 92, 28-30, Pp. 3680-3698. Publisher's VersionAbstract

Wood is a hygromorphic material, meaning it responds to changes in environmental humidity by changing its geometry. Its cellular biological structure swells during wetting and shrinks during drying. The origin of the moisture-induced deformation lies at the sub-cellular scale. The cell wall can be considered a composite material with stiff cellulose fibrils acting as reinforcement embedded in a hemicellulose/lignin matrix. The bulk of the cellulose fibrils, forming 50% of the cell wall, are oriented longitudinally, forming long-pitched helices. Both components of cell wall matrix are displaying swelling. Moisture sorption and, to a lesser degree, swelling/shrinkage are known to be hysteretic. We quantify the affine strains during the swelling and shrinkage using high resolution images obtained by phase contrast synchrotron X-ray tomography of wood samples of different porosities. The reversibility of the swelling/shrinkage is found for samples with controlled moisture sorption history. The deformation is more hysteretic for high than for low density samples. Swelling/shrinkage due to ad/desorption of water vapour displays also a non-affine component. The reversibility of the swelling/shrinkage indicates that the material has a structural capacity to show a persistent cellular geometry for a given moisture state and a structural composition that allows for moisture-induced transitional states. A collection of qualitative observations of small subsets of cells during swelling/shrinkage is further studied by simulating the observed behaviour. An anisotropic swelling coefficient of the cell wall is found to emerge and its origin is linked to the anisotropy of the cellulose fibrils arrangement in cell wall layers.

Computational up-scaling of anisotropic swelling and mechanical behavior of hierarchical cellular materials
A. Rafsanjani, D. Derome, F. K. Wittel, and J. Carmeliet. 2012. “Computational up-scaling of anisotropic swelling and mechanical behavior of hierarchical cellular materials.” Composites Science and Technology, 72, Pp. 744–751. Publisher's VersionAbstract

The hygro-mechanical behavior of a hierarchical cellular material, i.e. growth rings of softwood is investigated using a two-scale micro-mechanics model based on a computational homogenization technique. The lower scale considers the individual wood cells of varying geometry and dimensions. Honeycomb unit cells with periodic boundary conditions are utilized to calculate the mechanical properties and swelling coefficients of wood cells. Using the cellular scale results, the anisotropy in mechanical and swelling behavior of a growth ring in transverse directions is investigated. Predicted results are found to be comparable to experimental data. It is found that the orthotropic swelling properties of the cell wall in thin-walled earlywood cells produce anisotropic swelling behavior while, in thick latewood cells, this anisotropy vanishes. The proposed approach provides the ability to consider the complex microstructure when predicting the effective mechanical and swelling properties of softwood.

The role of geometrical disorder on swelling anisotropy of cellular solids
A. Rafsanjani, D. Derome, and J. Carmeliet. 2012. “The role of geometrical disorder on swelling anisotropy of cellular solids.” Mechanics of Materials, 55, Pp. 49-59. Publisher's VersionAbstract

The anisotropic swelling behavior of two-dimensional cellular solids is investigated using computational upscaling of periodic honeycombs and compared with direct finite element simulations of real cellular structure of wood as a complex cellular material. In both models, the anisotropy of the cell wall material has been taken into account. The real structure model is used for inverse determination of swelling coefficients of the wood cell wall by comparing the simulation results to free swelling experimental data. The obtained results reveal that the cell walls swell to a much less extent along the cell wall than in the thickness direction. A systematic study is carried out to investigate the influence of geometrical disorder on swelling properties. It is found that periodic symmetric honeycombs provide the upper bound for anisotropic swelling ratio, while disorder in arrangement of the cellular structure reduces the swelling anisotropy.