Related papers: Structured Deformations in Linearized Elasticity
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
Granular elasticity, an elasticity theory useful for calculating static stress distribution in granular media, is generalized to the dynamic case by including the plastic contribution of the strain. A complete hydrodynamic theory is derived…
This paper presents a pure complementary energy variational method for solving anti-plane shear problem in finite elasticity. Based on the canonical duality-triality theory developed by the author, the nonlinear/nonconex partial…
We study three-dimensional deformations of thin inextensible elastic rods with non-vanishing spontaneous curvature and torsion. In addition to the usual description in terms of curvature and torsion which considers only the configuration of…
A large family of deployable filamentary structures can be built by connecting two elastic rods along their length. The resulting structure has interesting shapes that can be stabilized by tuning the material properties of each rod. To…
The elastic behavior of materials operating in the linear regime is constrained, by definition, to operations that are linear in the imposed deformation. Though the nonlinear regime holds promise for new functionality, the design in this…
Starting from a two-dimensional theory of magneto-elasticity for fiber-reinforced magnetic elastomers we carry out a rigorous dimension reduction to derive a rod model that describes a thin magneto-elastic strip undergoing planar…
We develop a nonlinear generalisation of the causal linear thermodynamics of bulk viscosity, incorporating positivity of the entropy production rate and the effective specific entropy. The theory is applied to viscous fluid inflation (which…
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
Exact equations describing flexoelectric deformation in solids, derived previously within the framework of a continuum media theory, are partial differential equations of the fourth order. They are too complex to be used in the cases…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
Explicit expressions, for efficient application in engineering practice, are derived for generalized displacements and stresses in simply supported multi-layered wide plates and beams subjected to steady-state thermal and mechanical…
In complex crystals close to melting or at finite temperatures, different types of defects are ubiquitous and their role becomes relevant in the mechanical response of these solids. Conventional elasticity theory fails to provide a…
We derive a class of two-dimensional shell energies for thin elastic bodies exhibiting small-length scale effects modeled via strain-gradient elasticity. Building on the final author's earlier work on plate models, the kinetic and stored…
The formation energy of a solid surface can be extracted from slab calculations if the bulk energy per atom is known. It has been pointed out previously that the resulting surface energy will diverge with slab thickness if the bulk energy…
Continuum elasticity is a powerful tool applicable in a broad range of physical systems and phenomena. Yet, understanding how and on what scales material disorder may lead to the breakdown of continuum elasticity is not fully understood. We…
We propose a one-dimensional, nonconvex elastic constitutive model with higher gradients that can predict spontaneous fracture at a critical load via a bifurcation analysis. It overcomes the problem of discontinuous deformations without…
We propose a new peridynamic formulation with shear deformation for linear elastic solid. The key idea lies in subtracting the rigid body rotation part from the total deformation. Based on the strain energy equivalence between classic local…
This work focuses on the bearing rigidity theory, namely the branch of knowledge investigating the structural properties necessary for multi-element systems to preserve the inter-units bearings when exposed to deformations. The original…
Continuum strain energy functions are developed for soft biological tissues that possess long fibrillar components. The treatment is based on the model of an elastica, which is our fine scale model, and is homogenized in a simple fashion to…