Related papers: A general criterion for solid instability and its …
This is the first of a series of three articles that treats fracture localization as a critical phenomenon. This first article establishes a statistical mechanics based on ensemble averages when fluctuations through time play no role in…
The hardness of materials plays an important role in material design. There are numerous experimental methods to measure the hardness of materials, but theoretical prediction of hardness is challenging. By investigating the correlation…
Recent step strain experiments in well-entangled polymeric liquids demonstrated a bulk fracture-like phenomenon. We have studied this instability using a modern version of the Doi-Edwards theory for entangled polymers, and we find close…
Strain localization is an instability phenomenon occurring in deformable solid materials which undergo dissipative deformation mechanisms. Such instability is characterized by the localization of the displacement or velocity fields in a…
We discuss the possibility that astrophysical accretion disks are dynamically unstable to non-axisymmetric disturbances with characteristic scales much smaller than the vertical scale height. The instability is studied using three methods:…
The temporal instability of stably stratified flow was investigated by analyzing the Taylor-Goldstein equation theoretically. According to this analysis, the stable stratification $N^2\geq0$ has a destabilization mechanism, and the flow…
We present analyses of crease-formation and stability criteria for incompressible hyperelastic solids. A generic singular perturbation over a laterally compressed half-space creates a far-field eigenmode of three energy-release angular…
The reliability of processes with moving elastic and isotropic material containing initial cracks is considered in terms of fracture. The material is modelled as a moving plate which is simply supported from two of its sides and subjected…
This paper addresses the stability of plane Couette flow in the presence of strong density and viscosity stratifications. It demonstrates the existence of a generalised inflection point that satisfies the generalised Fjortoft's criterion of…
Using the the concept of cracking we explore the influence of density fluctuations and local anisotropy have on the stability of local and non-local anisotropic matter configurations in general relativity. This concept, conceived to…
We develop a general stability analysis for objective structures, which constitute a far reaching generalization of crystal lattice systems. We show that these particle systems, although in general neither periodic nor space filling, allow…
We model the progressive maturation of a heterogeneous mass towards a gravity-driven instability, characterized by the competition between frictional sliding and tension cracking, using array of slider blocks on an inclined basal surface,…
We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…
A simple one-dimensional mechanical model is proposed for splitting instability in swollen membranes. The splitting instability occurs by ring constriction. The bifurcation can be both subcritical and supercritical, depending on the…
Liquid crystal elastomers (LCEs) are soft phase-changing solids that exhibit large reversible contractions upon heating, Goldstone-like soft modes and resultant microstructural instabilities. We heat a planar LCE slab to isotropic, clamp…
Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is,…
We discuss elastic tensegrity frameworks made from rigid bars and elastic cables, depending on many parameters. For any fixed parameter values, the stable equilibrium position of the framework is determined by minimizing an energy function…
In this paper we consider the inverse problem of determining a rigid inclusion inside a thin plate by applying a couple field at the boundary and by measuring the induced transversal displacement and its normal derivative at the boundary of…
Soft materials, such as liquids, polymers, foams, gels, colloids, granular materials, and most soft biological materials, play an important role in our daily lives. From a mechanical viewpoint, soft materials can easily achieve large…
We consider the forced surface quasi-geostrophic equation with supercritical dissipation. We show that linear instability for steady state solutions leads to their nonlinear instability. When the dissipation is given by a fractional…