A stabilized, nodal strain finite element method for small and large deformations: formulation, analysis, and impact on remeshing strategies
Year: 2026
Type: preprint
Abstract: We present in this article the discretization of small and finite strain mechanics using variationally consistent, stabilized, nodal strain finite element formulations. We prove that these methods derive from a mixed variational principle that uses different meshes for the primal and dual variables. We demonstrate that, for both mechanical problems, nodal strain finite elements can be written as pure primal formulations with assumed strain operators. The stabilization terms are shown to be necessary and a new, general class of stabilizing functions is proposed for the finite strain regime. The ensuing formulations can be interpreted as pure particle methods because all kinematic and material information is stored at the nodes. This point of view explains the favorable properties of nodal strain methods when employed in problems that require frequent remeshing and involve inelastic materials. In these cases, the diffusion of internal variables is kept to a minimum. The numerical examples presented validate the claims.
Source: arXiv (Cornell University)
Authors: Rossi, Nestor, Romero, Ignacio
Institutions: IMDEA Materials, Universidad Politécnica de Madrid
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212727203