A node-based uniform strain virtual element method for elastoplastic solids

TL;DR

This work extends the node-based uniform strain virtual element method (NVEM) to small-strain elastoplastic solids to address volumetric locking under near-incompressibility. By averaging strains at nodes from surrounding linearly precise virtual elements and sampling the weak form at nodal locations, the method associates all state and history-dependent variables with nodes, enabling Newton-based solves without remapping of internal variables. A deviatoric-only stabilization (D-recipe) and a von Mises plasticity model with mixed isotropic/kinematic hardening provide a robust, locking-free framework that yields accurate results in benchmark elastoplastic problems, closely matching the locking-free FEM Q9 B-bar solution. The results demonstrate that NVEM can accurately solve elastoplastic problems with linearly precise virtual elements while avoiding volumetric locking, with potential benefits for remeshing scenarios in larger deformation analyses; future work includes extending to large strains with remeshing.

Abstract

A recently proposed node-based uniform strain virtual element method (NVEM) is here extended to small strain elastoplastic solids. In the proposed method, the strain is averaged at the nodes from the strain of surrounding linearly precise virtual elements using a generalization to virtual elements of the node-based uniform strain approach for finite elements. The averaged strain is then used to sample the weak form at the nodes of the mesh leading to a method in which all the field variables, including state and history-dependent variables, are related to the nodes and thus they are tracked only at these locations during the nonlinear computations. Through various elastoplastic benchmark problems, we demonstrate that the NVEM is locking-free while enabling linearly precise virtual elements to solve elastoplastic solids with accuracy.

Figures (23)

• Figure 1: Schematic representation of a polygonal element of $N_E^V=7$ edges
• Figure 2: Nodal patch $\mathcal{T}_I$ (shaded elements) formed by the virtual elements that are connected to node $I$
• Figure 3: Thick-walled cylinder problem. (a) Geometry and boundary conditions, and (b) mesh used for benchmarking the VEM, NVEM, FEM Q4 and FEM Q9 B-bar approaches
• Figure 4: Radial displacement at points $A$ ($u_A$) and $B$ ($u_B$) due to the applied internal pressure in steps for the thick-walled cylinder problem. (a) Compressible case ($\nu=0.3$), and (b) nearly incompressible case ($\nu=0.4999$)
• Figure 5: Plots of the total displacement field solution in mm at the last load step for the nearly incompressible thick-walled cylinder problem ($\nu=0.4999$). (a) FEM Q4, (b) FEM Q9 B-bar, (c) VEM, and (d) NVEM