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The fundamental problem of non-singular dislocations in the framework of the theory of gradient elasticity is presented in this work. Gradient elasticity of Helmholtz type and bi-Helmholtz type are used. A general theory of non-singular…
Universality in materials deformation is of intense interest: universal scaling relations if exist would bridge the gap from microscopic deformation to macroscopic response in a single material-independent fashion. While recent agreement of…
Dislocations play a key role in the understanding of many phenomena in solid state physics, materials science, crystallography and engineering. Dislocations are line defects producing distortions and self-stresses in an otherwise perfect…
When an amorphous solid is deformed homogeneously, the response exhibits heterogeneous plastic instabilities with localized cooperative rearrangement of cluster of particles. The heterogeneous behavior plays an important role in deciding…
Growth processes in many living organisms create thin, soft materials with an intrinsically hyperbolic geometry. These objects support novel types of mesoscopic defects - discontinuity lines for the second derivative and branch points -…
We show that there exists a universal mechanism of long-range soliton attraction in three-dimensional solids and, therefore, of discontinuity of any commensurate-incommensurate (C-IC) phase transition. This mechanism is due to the strain…
The transport of slightly deformable chiral objects in a uniform shear flow is investigated. Depending on the equilibrium configuration one finds up to four different asymptotic states that can be distinguished by a lateral drift velocity…
We study some properties of static spherically symmetric elastic bodies in general relativity using both analytical and numerical tools. The materials considered belong to the class of John elastic materials and reduce to perfect fluids…
A general expression for the strain energy of a homogeneous, isotropic, plane extensible elastica with an arbitrary undeformed configuration is derived. This energy constitutes the correct expression for one-dimensional models of polymers…
Point defects such as interstitials, vacancies, and impurities in otherwise perfect crystals induce complex displacement fields that are of long-range nature. In the present paper we study numerically the response of a two-dimensional…
In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as {\it linearization instability}, shows itself as…
A direct formulation of linear elasticity of cell complexes based on discrete exterior calculus is presented. The primary unknown are displacements, represented by primal vector-valued 0-cochain. Displacement differences and internal forces…
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a…
In linear elasticity, we decompose the elasticity tensor into two irreducible pieces with 15 and 6 independent components, respectively. The {\it vanishing} of the piece with 6 independent components corresponds to the Cauchy relations.…
A mechanical linkage is a mechanism made of rigid rods linked together by flexible joints, in which some vertices are fixed and others may move. The partial configuration space of a linkage is the set of all the possible positions of a…
The plasticity transition at the yield strength of a crystal typically signifies the tendency of dislocation defects towards relatively unrestricted motion. For an isolated dislocation the motion is in the slip plane with velocity…
Two classes of non-linear elastic materials are derived via two-dimensional homogenization. These materials are equivalent to a periodic grid of axially-deformable and axially-preloaded structural elements, subject to incremental…
We show that, in the athermal quasi-static deformation of amorphous materials, the onset of failure is accompanied by universal scalings associated with a \emph{divergence} of elastic constants. A normal mode analysis of the non-affine…
We experimentally, numerically and analytically explore the diffusive transport of active colloidal particles with sensory delay, navigating motility landscapes in which the self-propulsion speed depends on space. We show how the transport…
In this work, using the framework of (three-dimensional) Eshelbian dislocation mechanics, we derive the $J$-, $M$-, and $L$-integrals of a single (edge and screw) dislocation in isotropic elasticity as a limit of the $J$-, $M$-, and…