Related papers: Stress-stress correlations in two-dimensional amor…
In the recent years, much attention has been devoted to the inhomogeneous nature of the mechanical response at the nano-scale in disordered solids. Clearly, the elastic heterogeneities that have been characterized in this context are…
This review is on the phase field modelling studies in elastic stress effects on microstructural instabilities. We will focus primarily on four elastic stress driven instabilities: (i) Spinodal phase separation; (ii) Particle splitting;…
The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which…
The purpose of the present article is to make a model using analytical equations, based on elasticity theory of continuous media for small deformations, with the aim of completely characterizing the material in their mechanical properties…
The three-dimensional elastic-plastic deformation is considered. The catastrophe theory underlies the construction of this process model. It was shown that the variety of stable states consists on elastic states and can be depicted as a…
The mechanical, structural and functional properties of crystals are determined by their defects and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect…
Elastic theory of ring-(or cylinder-)shaped crystals is constructed and the generation of edge dislocations due to geometrical frustration caused by the bending is studied. The analogy to superconducting (or superfluid) vortex state is…
We present the foundations of a projective geometric theory of elasticity, as well as outline a few possible application possibilities. We give the description of the Cauchy stress and infinitesimal strain tensors compatible with coordinate…
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…
Usual introductions of the concept of motion are not well adapted to a subsequent, strictly tensorial, theory of elasticity. The consideration of arbitrary coordinate systems for the representation of both, the points in the laboratory, and…
A paradigm for the study of wrinkling in elastic sheet is the Lam\'{e} configuration, in which azimuthal wrinkles form in an annular sheet subjected to tensile loads at both edges. Since wrinkles are spatially extended, this instability…
A question of some fundamental importance is whether a given assembly of frictional granules (say sand or powder) will exhibit stress autocorrelations with long-range anisotropic decay as determined by the elastic Green's function. In…
Simulation studies of the atomic shear stress in the local potential energy minima (inherent structures) are reported for binary liquid mixtures in 2D and 3D. These inherent structure stresses are fundamental to slow stress relaxation and…
We develop a theory of anomalous elasticity in disordered two-dimensional flexible materials with orthorhombic crystal symmetry. Similar to the clean case, we predict existence of infinitely many flat phases with anisotropic bending…
The slow flow of amorphous solids exhibits striking heterogeneities: swift localised particle rearrangements take place in the midst of a more or less homogeneously deforming medium. Recently, experimental as well as numerical work has…
This paper analyzes the stress distribution in a two-dimensional elastic disk under diametric loading, with a focus on enhancing the understanding of concrete and rock materials' mechanical behavior. The study revisits the Brazilian test…
Progress is reported on several questions that bedevil understanding of granular systems: (i) are the stress equations elliptic, parabolic or hyperbolic? (ii) how can the often-observed force chains be predicted from a first-principles…
The dynamics of defect excitations in crystalline solids is necessary to understand the macroscopic low-energy properties of elastic media. We use fracton-elasticity duality to systematically study the defect dynamics and interactions in…
Stress transmission inside three dimensional granular packings is investigated using computer simulations. Localized force perturbation techniques are implemented for frictionless and frictional shallow, ordered, granular arrays confined by…
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…