Related papers: A Co-rotational Virtual Element Method for 2D Elas…
The virtual element method (VEM) allows discretization of elasticity and plasticity problems with polygons in 2D and polyhedrals in 3D. The polygons (and polyhedrals) can have an arbitrary number of sides and can be concave or convex. These…
We present a Virtual Element Method (VEM) for possibly nonlinear elastic and inelastic problems, mainly focusing on a small deformation regime. The numerical scheme is based on a low-order approximation of the displacement field, as well as…
We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…
This work provides an efficient virtual element scheme for the modeling of nonlinear elastodynamics undergoing large deformations. The virtual element method (VEM) has been applied to various engineering problems such as elasto-plasticity,…
An introductory exposition of the virtual element method (VEM) is provided. The intent is to make this method more accessible to those unfamiliar with VEM. Familiarity with the finite element method for solving 2D linear elasticity problems…
The present paper is the second part of a twofold work, whose first part is reported in [3], concerning a newly developed Virtual Element Method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic…
This work presents a Virtual Element Method (VEM) formulation tailored for two-dimensional axisymmetric problems in linear elasticity. By exploiting the rotational symmetry of the geometry and loading conditions, the problem is reduced to a…
The present work deals with the formulation of a Virtual Element Method (VEM) for two dimensional structural problems. The contribution is split in two parts: in part I, the elastic problem is discussed, while in part II [3] the method is…
The Virtual Element Method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel hybrid VEM that integrates both conforming and nonconforming…
In this paper, we study applications of the virtual element method (VEM) for simulating the deformation of multiphase composites. The VEM is a Galerkin approach that is applicable to meshes that consist of arbitrarily-shaped polygonal and…
In the present work we generalize the curvilinear Virtual Element technology, introduced for a simple linear scalar problem in a previous work, to generic 2D solid mechanic problems in small deformations. Such generalization also includes…
This paper presents the Virtual Element Method (VEM) for the modeling of crack propagation in 2D within the context of linear elastic fracture mechanics (LEFM). By exploiting the advantage of mesh flexibility in the VEM, we establish an…
This paper devises a novel lowest-order conforming virtual element method (VEM) for planar linear elasticity with the pure displacement/traction boundary condition. The main trick is to view a generic polygon $K$ as a new one…
In the present paper we introduce a Virtual Element Method (VEM) for the approximate solution of general linear second order elliptic problems in mixed form, allowing for variable coefficients. We derive a theoretical convergence analysis…
It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the…
A robust $C^0$-continuous nonconforming virtual element method (VEM) is developed for a boundary value problem arising from strain gradient elasticity in two dimensions, with the family of polygonal meshes satisfying a very general…
The numerical approximation of 2D elasticity problems is considered, in the framework of the small strain theory and in connection with the mixed Hellinger-Reissner variational formulation. A low-order Virtual Element Method (VEM) with…
This paper presents two approaches: the virtual element method (VEM) and the stabilization-free virtual element method (SFVEM) for analyzing thermomechanical behavior in electronic packaging structures with geometric multi-scale features.…
In this thesis, a computational framework for microstructural modelling of transverse behaviour of heterogeneous materials is presented. The context of this research is part of the broad and active field of Computational Micromechanics,…
We consider the approximation of the 2D frictionless contact problem in elasticity using the Virtual Element Methods (VEMs). To overcome the volumetric locking phenomenon in the nearly incompressible case, we adopt a mixed…