A stabilized, nodal strain finite element method for small and large deformations: formulation, analysis, and impact on remeshing strategies
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.
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BibTeX
@misc{rossi2026stabilized,
title = {{A stabilized, nodal strain finite element method for small and large deformations: formulation, analysis, and impact on remeshing strategies}},
author = {Nestor Rossi and Ignacio Romero},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12893},
eprint = {2609.12893},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12893},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A stabilized, nodal strain finite element method for small and large deformations: formulation, analysis, and impact on remeshing strategies
AU - Nestor Rossi
AU - Ignacio Romero
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12893
UR - https://arxiv.org/abs/2609.12893
AB - 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.
ER -