Strain localization in softening plasticity without modifying standard constitutive models: A deformable Cosserat approach

This paper presents a formulation for strain localization in softening plasticity based on a deformable Cosserat model. The approach enables the direct use of standard elastoplastic constitutive models formulated for a classical Cauchy continuum, without any modification of the stress update algorithm or the local material consistent tangent operator provided by the underlying constitutive routine. The key feature of the proposed framework is a strict separation between dissipative and energetic mechanisms: all dissipation is confined to the macro-continuum, while the micro-continuum contributes exclusively through linear elastic terms associated with the director field. As a result, the constitutive structure of the underlying elastoplastic model is preserved, and any standard small deformation, thermodynamically consistent constitutive model can be employed as a black-box stress-update module. The internal length scale arises naturally from the micro-continuum and governs the development, interaction, and selection of localization patterns, rather than acting as a diffusive or artificial parameter. The formulation is straightforward to implement within standard finite element frameworks: the local constitutive integration is left unchanged, while the global residual vector and tangent matrix are augmented by the additional linear contributions associated with the director field. The performance of the proposed approach is assessed through benchmark problems involving shallow foundations on soil, which represent a particularly demanding test due to the onset of complex, interacting, and unstable localization mechanisms. Both Tresca and Matsuoka–Nakai plasticity models are considered, including cases exhibiting highly unstable post-peak responses. Numerical results show that load–displacement responses, dissipated energy, and shear-band patterns converge upon mesh refinement, even in the presence of strongly nonlinear and interacting localization processes. These findings indicate that the proposed framework provides a promising route for mesh-objective analyses of strain localization in softening plasticity, while preserving the constitutive structure of the underlying elastoplastic model.