Related papers: A group theoretical approach to elasticity under c…
We extend the theory of structured deformations to the setting of linearized elasticity by providing an integral representation for the underlying energy that features bulk and surface contributions. Our derivation is obtained both via a…
We report a method for describing plasticity in a broad class of amorphous materials. The method is based on nonlinear (geometric) deformation theory allowing the separation of the plastic deformation from the general deformation tensor.…
Budiansky's nonlinear shell theory is particularized to a 2D setting, and thereupon generalized to a fully nonlinear, statically and kinematically exact, theory of strain-gradient elasticity of beams. The governing equations are displayed…
A general nonlinear theory for the elasticity of pre-stressed single crystals is presented. Various types of elastic moduli are defined, their importance is determined, and relationships between them are presented. In particular, B moduli…
Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz-Mindlin effective medium theories (EMT) of contact…
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…
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…
Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…
Group theory is used in many textbooks of contemporary physics. However, electromagnetic community often considers group theory as an "exotic" tool. Graduate and postgraduate textbooks on electromagnetics and electrodynamics usually do not…
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced as invariants…
In this paper we consider and compare special classes of static theories of gradient elasticity, nonlocal elasticity, gradient micropolar elasticity and nonlocal micropolar elasticity with only one gradient coefficient. Equilibrium…
We give a brief overview of the current state of the study of the deformation theory of Kleinian groups. The topics covered include the definition of the deformation space of a Kleinian group and of several important subspaces; a discussion…
A state-based peridynamic formulation for linear elastic shells is presented. The emphasis is on introducing, possibly for the first time, a general surface based peridynamic model to represent the deformation characteristics of structures…
We consider the problem of satisfaction of boundary conditions when the generalized stress vector is given on the surfaces for elastic plates and shells. This problem was open also both for refined theories in the wide sense and…
In the present paper we investigate the mechanics of systems of affinely-rigid bodies, i.e., bodies rigid in the sense of affine geometry. Certain physical applications are possible in modelling of molecular crystals, granular media, and…
The strain-energy formulation of nonlinear elasticity can be extended to the case of significant compression by modulating suitable strain energy terms by a function of relative volume. For isotropic materials this can be accomplished by…
For construction of the general theory it is necessary, first of all, to refuse from traditional performance of the elastic theory of field, within the framework of which the static processes with commutative quantities are described only.…
"Granular elasticity," useful for calculating static stress distributions in granular media, is generalized by including the effects of slowly moving, deformed grains. The result is a hydrodynamic theory for granular solids that agrees well…