Related papers: Asymptotic rigidity of layered structures and its …

We derive an asymptotically consistent morphoelastic shell model to describe the finite deformations of biological tissues using the variational asymptotical method. Biological materials may exhibit remarkable compressibility when under…

This paper is concerned with the homogenization of Dirichlet problem of elliptic systems in a bounded, smooth domain of finite type. Both the coefficients of the elliptic operator and the Dirichlet boundary data are assumed to be periodic…

The response to a localized force provides a sensitive test for different models of stress transmission in granular solids. The elasto-plastic models traditionally used by engineers have been challenged by theoretical and experimental…

We analyse a system of partial differential equations describing the behaviour of an elastic plate with periodic moduli in the two planar directions, in the asymptotic regime when the period and the plate thickness are of the same order of…

When discretizing symmetric stress tensors in variational problems arising in continuum mechanics, one has to choose how to enforce the symmetry of the stress tensor: (i) strongly by requiring the discrete tensors to be pointwise symmetric…

Accurate asymptotic solutions are presented for axisymmetric deformation of thin layers constrained by either two rigid plates or two rigid spheres. Those solutions are developed using Saint-Venant's principle and the layer thinness as the…

We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic…

The transformation theory of optics and acoustics is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by…

This paper aims to study the convergence of adaptive finite element method for control constrained elliptic optimal control problems under $L^2$-norm. We prove the contraction property and quasi-optimal complexity for the $L^2$-norm errors…

This paper introduces the notion of weak rigidity to characterize a framework by pairwise inner products of inter-agent displacements. Compared to distance-based rigidity, weak rigidity requires fewer constrained edges in the graph to…

We study an atomistic model that describes the microscopic formation of material voids inside elastically stressed solids under an additional curvature regularization at the discrete level. Using a discrete-to-continuum analysis, by means…

We derive a hierarchy of plate theories for heterogeneous multilayers from three dimensional nonlinear elasticity by means of $\Gamma$-convergence. We allow for layers composed of different materials whose constitutive assumptions may vary…

A self-consistent model is developed to investigate attachment / detachment kinetics of two soft, deformable microspheres with irregular surface and coated with flexible binding ligands. The model highlights how the microscale binding…

We study elasticity of spontaneously orientationally-ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized for example by nematic elastomers and gels. We show that local heterogeneities and elastic…

The jamming transition, generally manifested by a rapid increase of rigidity under compression (i.e., compression hardening), is ubiquitous in amorphous materials. Here we study shear hardening in deeply annealed frictionless packings…

Using a geometric formalism of elasticity theory we develop a systematic theoretical method for controlling and manipulating the mechanical response of slender solids to external loads. We formally express global mechanical properties…

We consider a prototypical "stretching plus bending" functional of an elastic shell. The shell is modeled as a d-dimensional Riemannian manifold endowed, in addition to the metric, with a reference second fundamental form. The shell is…

While isotropic in-plane swelling problems for thin elastic sheets have been studied extensively in recent years, many shape-programmable materials, including nematic solids and 3D-printed structures, are anisotropic, as are most industrial…

We consider the cylindrical bending problem for an infinite plate as modelled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length scale effects in the sense that thinner…

We investigate the effective elastic properties of periodic dilute two-phase composites consisting of an homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply…