Virtual element method for modeling the deformation of multiphase composites

In this paper, we study applications of the virtual element method (VEM) for simulating deformation multiphase composites. The VEM is a Galerkin approach that applicable to meshes consist arbitrarily-shaped polygonal and polyhedral (simple nonsimple) elements. VEM, basis functions are defined as solution local elliptic partial differential equation, never explicitly computed in implementation method. stiffness matrix each built by using projection operator internal work (bilinear form) it consists two terms: consistency term exactly (linear patch test satisfied) correction (ensures stability) orthogonal affine displacement fields has right scaling. simplifies mesh generation composite: stiff inclusion can be modeled single or element. Attributes highlighted through comparisons with Voronoi-cell lattice models, which provide discrete representations material structure. involve suite two-dimensional linear elastic problems: test, axisymmetric circular problem, three-phase composite. simulations demonstrate accuracy flexibility