Linearization and computation for large-strain visco-elasticity

DOI10.3934/mine.2023030arXiv2110.13728OpenAlexW3208525075MaRDI QIDQ6195570

Martin Kružík, Jan Valdman, Martin Jesenko, Patrick W. Dondl

Publication date: 14 March 2024

Published in: Mathematics in Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.13728

zbMATH Keywords

energy minimizationnumerical schemeKelvin-Voigt viscoelasticity

Mathematics Subject Classification ID

Nonlinear constitutive equations for materials with memory (74D10) PDEs in connection with mechanics of deformable solids (35Q74) Energy minimization in dynamical problems in solid mechanics (74H80)

Cites Work

• Quasistatic nonlinear viscoelasticity and gradient flows
• Physically unacceptable viscous stresses
• Linearized elasticity as \(\Gamma\)-limit of finite elasticity
• Numerical approximation of von Kármán viscoelastic plates
• Quasistatic viscoelasticity with self-contact at large strains
• A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence
• On Korn's first inequality with non-constant coefficients
• On the Passage from Nonlinear to Linearized Viscoelasticity
• An Approach to Nonlinear Viscoelasticity via Metric Gradient Flows
• Nonlinear problems of elasticity
• Direct methods in the calculus of variations

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