Kelvin decomposition for nonlinear hyperelastic modeling in large deformation

DOI10.2140/memocs.2021.9.337OpenAlexW4225361487MaRDI QIDQ2107569

Mathias Brieu, Annie Morch, Jean-François Witz, Boris Desmorat, Rodrigue Desmorat

Publication date: 2 December 2022

Published in: Mathematics and Mechanics of Complex Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/memocs.2021.9.337

zbMATH Keywords

anisotropysecond Piola-Kirchhoff stressGreen-Lagrange straingeneralized Odgen materialgeneralized Saint Venant-Kirchhoff materialHooke tensorLagrangian finite strain measure

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Anisotropy in solid mechanics (74E10)

Cites Work

• Unnamed Item
• Geometry of logarithmic strain measures in solid mechanics
• On the use of the Bingham statistical distribution in microsphere-based constitutive models for arterial tissue
• Non-quadratic Kelvin modes based plasticity criteria for anisotropic materials
• A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials
• A simple framework for full-network hyperelasticity and anisotropic damage
• Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling
• The exponentiated Hencky-logarithmic strain energy. I: Constitutive issues and rank-one convexity
• A new constitutive theory for fiber-reinforced incompressible nonlinearly elastic solids
• On Hooke's law
• Symmetry classes for elasticity tensors
• A multidimensional anisotropic strength criterion based on Kelvin modes
• A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function
• Micromechanics based framework with second-order damage tensors
• The exponentiated Hencky energy: anisotropic extension and case studies
• Hyperelastic energy densities for soft biological tissues: a review
• Observation and modeling of the anisotropic visco-hyperelastic behavior of a rubberlike material
• A note on the decomposition of tensors into traceless symmetric tensors
• A micro-macro approach to rubber-like materials. I: The non-affine micro-sphere model of rubber elasticity
• Coordinate-free characterization of the symmetry classes of elasticity tensors
• A non-Gaussian theory for rubber in biaxial strain. I. Mechanical properties
• Fourth-rank tensors of the thirty-two crystal classes: multiplication tables
• Methodical fitting for mathematical models of rubber-like materials
• Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids
• Large elastic deformations of isotropic materials IV. further developments of the general theory
• Some remarks on the compressed matrix representation of symmetric second-order and fourth-order tensors
• Physically based strain invariant set for materials exhibiting transversely isotropic behavior

This page was built for publication: Kelvin decomposition for nonlinear hyperelastic modeling in large deformation