Helmholtz-type nonlocal regularization of anisotropic multi-surface elastoplasticity at finite deformations

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Contributors

Abstract

Wood exhibits strongly anisotropic inelastic behavior governed by its microstructural organization, resulting in pronounced sensitivity with respect to the local stress state under heterogeneous loading. Conventional continuum formulations based on local internal variables are prone to pathological strain localization, in which deformation collapses into element-scale bands, leading to mesh-dependent responses and non-objective energy distribution. To address this limitation, a nonlocal enhancement of an anisotropic multi-surface elastoplastic model is proposed using a Helmholtz-type regularization of driving variables constructed from plastic consistency parameters. In contrast to strain-based nonlocal plasticity approaches, the proposed formulation acts directly on the algorithmic variables governing the activation of individual yield mechanisms. This enables the incorporation of nonlocal effects into the return-mapping framework while preserving the constitutive structure and the separation of deformation modes, without introducing kinematic degrees of freedom into the mechanical equilibrium problem.The performance of the proposed approach is demonstrated through benchmark and structural simulations. In contrast to the local formulations, the regularized model yields mesh-insensitive inelastic fields and a convergent structural response under mesh refinement. Parameter studies highlight the roles of the internal length scale, penalty, and degradation parameters in controlling the spatial distribution of inelastic deformation and the post-peak response. The formulation is further demonstrated in a three-point bending simulation of spruce wood, including contact interaction, where relative root-mean-square (RMS) errors below 1% are obtained for the global force response across the considered discretizations. In addition, the relative RMS error of the accumulated internal energy decreases from approximately 13% on coarse meshes to below 2% under refinement. These results demonstrate that the proposed approach provides a robust and computationally efficient framework, enabling direct control of the interaction between competing inelastic mechanisms while reducing mesh sensitivity and improving the consistency of internal energy evolution.

Details

Original languageEnglish
Article number114184
Number of pages19
JournalInternational journal of solids and structures
Volume339
Publication statusPublished - 1 Oct 2026
Peer-reviewedYes

External IDs

ORCID /0009-0007-8311-5725/work/222763679

Keywords

Keywords

  • Finite deformations, Finite element methods, Nonlocal anisotropic plasticity, Wood material