Related papers: Elastic interactions between 2D geometric defects
A collision of a rubber rod to a hard floor is regarded as a simple example of obstacle problems for elastic material. In this article we have proposed a new mathematical model for the collision phenomenon by applying beam equations with…
Evaluating accessible conformational space is computationally expensive and thermal motions are partly neglected in computer models of molecular interactions. This produces error into the estimates of binding strength. We introduce a method…
The response of many materials to applied forces and boundary constraints depends upon internal geometric changes at multiple submacroscopic levels. Hierarchical structured deformations provide a mathematical setting for the description of…
A theory and computational method are provided for the calculation of lipid membranes elastic parameters, which overcomes the difficulties of the existing approaches and can be applied not only to single-component but also to…
We introduce a pure--stress formulation of the elasticity eigenvalue problem with mixed boundary conditions. We propose an H(div)-based discontinuous Galerkin method that imposes strongly the symmetry of the stress for the discretization of…
A consistent treatment of the coupling of surface energy and elasticity within the multi-phase- field framework is presented. The model accurately reproduces stress distribution in a number of analytically tractable, yet non-trivial, cases…
We formulate and discuss the relationship between polyhedral stress functions and internally self-equilibrated frameworks in 2D, and a two-mesh technique for the prediction of the stress field associated with such systems. We generalize…
We consider hyperelastic problems and their numerical solution using a conforming finite element discretization and iterative linearization algorithms. For these problems, we present equilibrated, weakly symmetric, $H(\rm{div)}$-conforming…
Compression experiments are widely used to study the mechanical properties of materials at micro- and nanoscale. However, the conventional engineering stress measurement method used in these experiments neglects to account for the…
We consider the influence of elasticity and anisotropic surface energy on the energy-minimizing shape of a two-dimensional void under biaxial loading. In particular, we consider void shapes with corners for which the strain energy density…
When the elastic properties of structured materials become direction-dependent, the number of their descriptors increases. For example, in two-dimensions, the anisotropic behavior of materials is described by up to 6 independent elastic…
Using a geometric formalism of elasticity theory we develop a systematic theoretical method for controlling and manipulating the mechanical response of slender solids to external loads. We formally express global mechanical properties…
Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…
We investigate the spatial correlations of microscopic stresses in soft particulate gels, using 2D and 3D numerical simulations. We use a recently developed theoretical framework predicting the analytical form of stress-stress correlations…
The calculation of the stress field around an arbitrarily shaped crack in an infinite two-dimensional elastic medium is a mathematically daunting problem. With the exception of few exactly soluble crack shapes the available results are…
The paper presents two-scale numerical algorithms for stress-strain analysis of porous media featured by self-contact at pore level. The porosity is constituted as a periodic lattice generated by a representative cell consisting of elastic…
We develop an analytical model of adhesive wear between two unlubricated rough surfaces, forming micro-contacts under normal load. The model is based on an energy balance and a crack initiation criteria. We apply the model to the problem of…
The incompatibility of linearized piecewise smooth strain field, arising out of volumetric and surface densities of topological defects and metric anomalies, is investigated. First, general forms of compatibility equations are derived for a…
The dependence of the elastic tensor on the equilibrium stress is investigated theoretically. Using ideas from finite-elasticity, it is first shown that both the equilibrium stress and elastic tensor are given uniquely in terms of the…
We present the formulation for finding the distribution of eigenstrains, i.e. the sources of residual stress, from a set of measurements of residual elastic strain (e.g. by diffraction), or residual stress, or stress redistribution, or…