On the Passage from Nonlinear to Linearized Viscoelasticity

DOI10.1137/17M1131428zbMath1393.74019arXiv1705.06438WikidataQ129386572 ScholiaQ129386572MaRDI QIDQ4580416

Martin Kružík, Manuel Friedrich

Publication date: 15 August 2018

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.06438

zbMATH Keywords

viscoelasticity\(\Gamma\)-convergenceminimizing movementscurves of maximal slopedissipative distancemetric gradient flows

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Methods involving semicontinuity and convergence; relaxation (49J45) Linear constitutive equations for materials with memory (74D05) Nonlinear constitutive equations for materials with memory (74D10) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items

Gradient Polyconvexity and Modeling of Shape Memory Alloys ⋮ Pressure live loads and the variational derivation of linear elasticity ⋮ Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture ⋮ One-dimensional viscoelastic von Kármán theories derived from nonlinear thin-walled beams ⋮ Linearization and computation for large-strain visco-elasticity ⋮ Numerical approximation of von Kármán viscoelastic plates ⋮ Homogenization in BV of a model for layered composites in finite crystal plasticity ⋮ Two-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitions ⋮ Separately global solutions to rate-independent processes in large-strain inelasticity ⋮ Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons ⋮ Thermoviscoelasticity in Kelvin-Voigt rheology at large strains ⋮ Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials ⋮ Nonlinear and linearized models in thermoviscoelasticity

Cites Work

• Quasistatic nonlinear viscoelasticity and gradient flows
• Minimizing movements along a sequence of functionals and curves of maximal slope
• Local minimization, variational evolution and \(\Gamma\)-convergence
• An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem
• Gamma-convergence of gradient flows on Hilbert and metric spaces and applications
• Thermoviscoelasticity in Kelvin-Voigt rheology at large strains
• Linear \(\Gamma \)-limits of multiwell energies in nonlinear elasticity theory
• Elastic materials with couple-stresses
• Null Lagrangians, weak continuity, and variational problems of arbitrary order
• Thermodynamics of non-simple elastic materials
• Convexity conditions and existence theorems in nonlinear elasticity
• Physically unacceptable viscous stresses
• An introduction to \(\Gamma\)-convergence
• Weak solutions for a class of nonlinear systems of viscoelasticity
• Linearized elasticity as \(\Gamma\)-limit of finite elasticity
• Theories of elasticity with couple-stress
• On the thermodynamics of non-simple elastic materials with two temperatures
• Rate-independent elastoplasticity at finite strains and its numerical approximation
• PASSING TO THE LIMIT IN MAXIMAL SLOPE CURVES: FROM A REGULARIZED PERONA–MALIK EQUATION TO THE TOTAL VARIATION FLOW
• Injective weak solutions in second-gradient nonlinear elasticity
• Gamma-convergence of gradient flows with applications to Ginzburg-Landau
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• An Approach to Nonlinear Viscoelasticity via Metric Gradient Flows
• Contact interactions, stress and material symmetry
• On the heat flow on metric measure spaces: existence, uniqueness and stability
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item