arXiv subjects

Andrea Panteghini

Publications and source records attributed to Andrea Panteghini.

4 recordsLinked to original sources

arXiv2026

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 modifying the stress update algorithm or consistent tangent operator. A key feature of the framework is the strict separation of dissipative and energetic mechanisms: all dissipation is confined to the macro-continuum, while the micro-continuum contributes only through linear elastic terms associated with the director field. As a result, the constitutive structure of the elastoplastic model is preserved, and existing models can be employed as black-box components. 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 parameter. The formulation is easy to implement within standard finite element frameworks, requiring only additional linear contributions to the residual and tangent operators. The performance of the approach is assessed through benchmark problems involving shallow foundations on soil, a demanding test due to complex and unstable localization mechanisms. Both Tresca and Matsuoka-Nakai plasticity models are considered, including cases with highly unstable post-peak responses. Numerical results show convergence of load-displacement responses, dissipated energy and shear-band patterns upon mesh refinement, even in the presence of nonlinear interacting localization processes. These findings demonstrate a robust and physically consistent approach for the analysis of strain localization in softening plasticity.

math.NA↗

arXiv2023

A closed form exact formulation of the spectral representation of a second-order symmetric tensor and of its derivatives

The spectral decomposition of a symmetric, second-order tensor is widely adopted in many fields of Computational Mechanics. As an example, in elasto-plasticity under large strain and rotations, given the Cauchy deformation tensor, it is a fundamental step to compute the logarithmic strain tensor. Recently, this approach has been also adopted in small-strain isotropic plasticity to reconstruct the stress tensor as a function of its eigenvalues, allowing the formulation of predictor-corrector return algorithms in the invariants space. These algorithms not only reduce the number of unknowns at the constitutive level, but also allow the correct handling of stress states in which the plastic normals are undefined, thus ensuring a better convergence with respect to the standard approach. While the eigenvalues of a symmetric, second-order tensor can be simply computed as a function of the tensor invariants, the computation of its eigenbasis can be more difficult, especially when two or more eigenvalues are coincident. Moreover, when a Newton-Rhapson algorithm is adopted to solve nonlinear problems in Computational Mechanics, also the tensorial derivatives of the eigenbasis, whose computation is still more complicate, are required to assemble the tangent matrix. A simple and comprehensive method is presented, which can be adopted to compute a closed form representation of a second-order tensor, as well as their derivatives with respect to the tensor itself, allowing a simpler implementation of spectral decomposition of a tensor in Computational Mechanics applications.

cs.CE↗

arXiv2021

A micropolar isotropic plasticity formulation for non associated flow rule and softening featuring multiple classical yield criteria. Part II -- FE integration and applications

A Finite Element procedure based on a full implicit backward Euler predictor/corrector scheme for the Cosserat continuum is here presented. Since this is based on invariants of the stress and couple stress tensors and on the spectral decomposition of the former, considerable benefits are achieved. The integration requires the solution of a single equation in a single unknown, which is a considerable improvement as compared to the system of seven or four equations required by other approaches available in the literature for the Cauchy medium. The scheme also allows for a very efficient treatment of the singularity which affects the apex of most of the existing yield and plastic potential surfaces. Moreover, no complications arise when some of the principal stresses coincide. The algorithm has been implemented in a proprietary Finite Element program, and used for the constitutive model proposed in part I of this paper. Numerical analyses have been conducted to simulate a biaxial compression test and a shallow strip footing resting on a Tresca, Mohr-Coulomb, Matsuoka-Nakai and Lade-Duncan soil. The benefits of the Cosserat continuum over the Cauchy/Maxwell medium are discussed considering mesh refinement, non-associated flow and softening behaviour.

math.NA↗

arXiv2021

A micropolar isotropic plasticity formulation for non-associated flow rule and softening featuring multiple classical yield criteria Part I -- Theory

The Cosserat continuum is used in this paper to regularize the ill-posed governing equations of the Cauchy/Maxwell continuum. Most available constitutive models adopt yield and plastic potential surfaces with a circular deviatoric section. This is a too crude an approximation which hinders the application of the Cosserat continuum into practice, particularly in the geotechnical domain. An elasto-plastic constitutive model for the linear formulation of the Cosserat continuum is here presented, which features non-associated flow and hardening/softening behaviour, whilst linear hyper-elasticity is adopted to reproduce the recoverable response. For the formulation of the yield and plastic potential functions, a definition of the \textit{equivalent von Mises stress} is used which is based on Hencky's interpretation of the von Mises criterion and also on the theory of representations. The dependency on the Lode's angle of both the yield and plastic potential functions is introduced through the adoption of a recently proposed \textit{Generalized classical} criterion, which rigorously defines most of the classical yield and failure criteria.

math.NA↗