Related papers: Elastic theory of unconstrained non-Euclidean plat…
The isothermal quasistatic (i.e.\ acceleration neglected) hardening-free plasticity at large strains is considered, based on the standard multiplicative decomposition of the total strain and the isochoric plastic distortion. The Eulerian…
Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties of…
Nonlinear elastic theory studies the elastic constants of a material (such as Young's modulus or bulk modulus) as a power series in the applied load. The inverse bulk modulus K, for example depends on the compression P: $ {1/ K(P)} = c_0 +…
Initially stressed plates are widely used in modern fabrication techniques, such as additive manufacturing and UV lithography, for their tunable morphology by application of external stimuli. In this work, we propose a formal asymptotic…
We study the dynamical regime of wave turbulence of a vibrated thin elastic plate based on experimental and numerical observations. We focus our study to the strongly non linear regime described in a previous letter by N. Yokoyama & M.…
The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming…
We study the non-rigidity of Euclidean $t$-designs, namely we study when Euclidean designs (in particular certain tight Euclidean designs) can be deformed keeping the property of being Euclidean $t$-designs. We show that certain tight…
A homogeneous elastic solid, bounded by a flat surface in its unstressed configuration, undergoes a finite strain when in frictionless contact against a rigid and rectilinear constraint, ending with a rounded or sharp corner, in a…
We present a general and systematic theory of non-equilibrium dynamics of multi-component fluid membranes, in general, and membranes containing transmembrane proteins, in particular. Developed based on a minimal number of principles of…
We reformulate the theory of polycrystalline plasticity, in externally driven, nonequilibrium situations, by writing equations of motion for the flow of energy and entropy associated with dislocations. Within this general framework, and…
When subjected to specific prestresses, continuum elastic shells can exhibit geometric zero modes: complex motions that require vanishing elastic energy to excite, enabling them to be driven by weak and generic energy inputs. Despite recent…
We consider the steady-state analysis of a pinned elastic plate lying on the free surface of a thin viscous fluid, forced by the motion of a bottom substrate moving at constant speed. A mathematical model incorporating elasticity,…
Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility…
We study elastic ribbons subject to large, tensile pre-stress confined to a central region within the cross-section. These ribbons can buckle spontaneously to form helical shapes, featuring regions of alternating chirality (phases) that are…
This paper derives a finite-strain plate theory consistent with the principle of stationary three-dimensional (3-D) potential energy under general loadings with a third-order error. Staring from the 3-D nonlinear elasticity (with both…
In this article, we unravel an intimate relationship between two seemingly unrelated concepts: elasticity, that defines the local relations between stress and strain of deformable bodies, and topology that classifies their global shape.…
The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the…
We derive a von K\'arm\'an plate theory from a three-dimensional quasistatic nonlinear model for nonsimple thermoviscoelastic materials in the Kelvin-Voigt rheology, in which the elastic and the viscous stress tensor comply with a frame…
This paper presents a theory for the behaviour of isotropic-hardening/softening elastoplastic materials that do not have a preferred reference configuration. In spite of important differences, many ingredients of classical plasticity are…
A number of boundary problems in multidimensional elasticity theory are solved. The solutions can be treated as the simplest cosmological models. Some specific properties of the solutions and experimental consequences of the theory are…