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Biological cells sense and respond to mechanical forces, but how such a mechanosensing proccess takes place in a nonlinear inhomogeneous fibrous matrix remains unknown. We show that cells in a fibrous matrix induce deformation fields that…
We investigate the crumpling of a sheet as it is repeatedly crushed onto itself by rolling it into a cylinder and twisting it axially while allowing the end-to-end length to evolve freely. As deduced from its plastic deformations, the sheet…
Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as a important paradigm for relating these…
Biological membranes are elastic media in which the presence of a transmembrane protein leads to local bilayer deformation. The energetics of deformation allow two membrane proteins in close proximity to influence each other's equilibrium…
The pinning of an inhomogeneous elastic medium by a disordered substrate is studied analytically and numerically. The static and dynamic properties of a $D$-dimensional system are shown to be equivalent to those of the well known problem of…
Previous research on semiflexible polymers including cytoskeletal networks in cells has suggested the existence of distinct regimes of elastic response, in which the strain field is either uniform (affine) or non-uniform (non-affine) under…
The fluctuations of two-dimensional extended objects membranes is a rich and exciting field with many solid results and a wide range of open issues. We review the distinct universality classes of membranes, determined by the local order,…
Many biological and engineering materials have nonperiodic microstructures for which classical periodic homogenization results do not apply. Certain nonperiodic microstructures may be approximated by locally periodic microstructures for…
This study investigates the coupled deformation and flow behavior of thin, hyper-elastic, porous membranes subjected to pressure loading. Using bulge test experiments, optical deformation measurements, and flow rate characterization, we…
In this paper we consider nonlinearly elastic, frame-indifferent, and singularly perturbed two-well models for materials undergoing solid-solid phase transitions in any space dimensions, and we perform a simultaneous passage to…
We propose nonlinear semi-discrete and discrete models for the elastic energy induced by a finite systems of edge dislocations in two dimensions. Within the dilute regime, we analyze the asymptotic behavior of the nonlinear elastic energy,…
We use a minimal model for a dense suspension undergoing thickening and thinning to investigate microstructural changes in 2d simulations. Our simulations show that in steady flow the contact network contains distinct building blocks which…
We connect the theories of the deformation of elastic surfaces and phase surfaces arising in the description of almost periodic patterns. In particular, we show parallels between asymptotic expansions for the energy of elastic surfaces in…
Slow dynamic nonlinearity is widely observed in brittle materials with complex heterogeneous or cracked microstructures. It is seen in rocks, concrete and cracked glass blocks. Unconsolidated structures show the behavior as well: aggregates…
Initially straight slender elastic rods with geometrically constrained ends buckle and form stable two-dimensional shapes when compressed by bringing the ends together. It is also known that beyond a critical value of the pre-stress,…
Active cell-junction remodeling is important for tissue morphogenesis, yet its underlying physics is not understood. We study a mechanical model that describes junctions as dynamic active force dipoles. Their instability can trigger cell…
The resonance modes and the related effects to the transmission of elastic waves in a two dimensional phononic crystal formed by periodic arrangements of a two blocks unit cell in one direction are studied. The unit cell consists of two…
Fractal is an intriguing geometry with self-similarity and non-integer dimensions, the elastic-wave topological phase based on fractal structures has not been revealed up to now. In this work, elastic-wave higher-order topological states in…
A thin flat rectangular plate supported on its edges and subjected to in-plane loading exhibits stable post-buckling behaviour. However, the introduction of a nonlinear (softening) elastic foundation may cause the response to become…
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…