A consistent algorithm for finite-strain visco-hyperelasticity and visco-plasticity of amorphous polymers

DOI10.1016/j.cma.2022.115528OpenAlexW4293317037WikidataQ113877826 ScholiaQ113877826MaRDI QIDQ2083152

M. Leite, M. Sardinha, M. F. Vaz, Pedro M. A. Areias, Timon Rabczuk

Publication date: 10 October 2022

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2022.115528

zbMATH Keywords

anisotropymatrix exponentialrate-dependencevisco-plasticityscaling and squaringvisco-hyperelasticityamorphous thermoplastics

Mathematics Subject Classification ID

Large-strain, rate-dependent theories of plasticity (74C20) Thermal effects in solid mechanics (74F05)

Uses Software

• Mathematica
• MATLAB expm
• HYPLAS
• GitHub

Cites Work

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• A thermo-mechanically-coupled large-deformation theory for amorphous polymers in a temperature range which spans their glass transition
• On constitutive modelling of porous neo-Hookean composites
• Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen
• A Cahn-Hilliard-type phase-field theory for species diffusion coupled with large elastic deformations: Application to phase-separating Li-ion electrode materials
• A thermo-mechanically coupled theory for large deformations of amorphous polymers. I: Formulation
• A thermo-mechanically coupled theory for large deformations of amorphous polymers. II: Applications
• The thermodynamics of elastic materials with heat conduction and viscosity
• Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory
• Computational inelasticity
• More explicit formulas for the matrix exponential
• A simple orthotropic finite elasto-plasticity model based on generalized stress-strain measures
• A theory of amorphous solids undergoing large deformations, with application to polymeric glasses.
• Exact expansions of arbitrary tensor functions \(\mathbf F(\mathbf A)\) and their derivatives.
• An introduction to continuum mechanics
• Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques
• A covariant formulation of anisotropic finite plasticity: theoretical developments
• Fully anisotropic hyperelasto-plasticity with exponential approximation by power series and scaling/squaring
• Closed-form matrix exponential and its application in finite-strain plasticity
• On the Development of Volumetric Strain Energy Functions
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• Numerical Computation of the Matrix Exponential with Accuracy Estimate
• The computation of the exponential and logarithmic mappings and their first and second linearizations
• GRADIENT ENHANCED DAMAGE FOR QUASI-BRITTLE MATERIALS
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• Computation of the matrix exponential and its derivatives by scaling and squaring
• A Course on Damage Mechanics
• New Scaling-Squaring Taylor Algorithms for Computing the Matrix Exponential
• Nonlinear Continuum Mechanics for Finite Element Analysis
• Elastic-Plastic Deformation at Finite Strains
• The exact derivative of the exponential of an unsymmetric tensor

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