HOMOGENIZATION IN GRADIENT PLASTICITY

DOI10.1142/S0218202511005520zbMath1233.35017MaRDI QIDQ3098845

Hauke Hanke

Publication date: 18 November 2011

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

elasto-plasticity\(\Gamma\)-convergencetwo-scale convergencefolding and unfoldingrate-independent systems

Mathematics Subject Classification ID

Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) (74C05) Effective constitutive equations in solid mechanics (74Q15) Methods involving semicontinuity and convergence; relaxation (49J45) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (13)

Stochastic two-scale convergence and Young measures ⋮ Stochastic homogenization of plasticity equations ⋮ Variational Approaches and Methods for Dissipative Material Models with Multiple Scales ⋮ Existence, numerical convergence and evolutionary relaxation for a rate-independent phase-transformation model ⋮ A homogenization result in finite plasticity ⋮ A phase-field damage model based on evolving microstructure ⋮ Two-scale homogenization of nonlinear reaction-diffusion systems with slow diffusion ⋮ Homogenization for dislocation based gradient visco-plasticity ⋮ Corrector Estimates for a Thermodiffusion Model with Weak Thermal Coupling ⋮ Pulses in FitzHugh--Nagumo Systems with Rapidly Oscillating Coefficients ⋮ Stochastic Unfolding and Homogenization of Spring Network Models ⋮ On static and evolutionary homogenization in crystal plasticity for stratified composites ⋮ Deriving amplitude equations via evolutionary \(\Gamma\)-convergence

Cites Work

• Unnamed Item
• Two-scale convergence of some integral functionals
• Plasticity. Mathematical theory and numerical analysis
• Energetic formulation of multiplicative elasto-plasticity using dissipation distances
• Periodic unfolding and homogenization
• Existence results for energetic models for rate-independent systems
• Homogenization of nonlinear integrals via the periodic unfolding method
• \(\Gamma\)-limits and relaxations for rate-independent evolutionary problems
• EXISTENCE AND UNIQUENESS RESULTS FOR A CLASS OF RATE-INDEPENDENT HYSTERESIS PROBLEMS
• Homogenization and Two-Scale Convergence
• A General Convergence Result for a Functional Related to the Theory of Homogenization
• Two-Scale Homogenization for Evolutionary Variational Inequalities via the Energetic Formulation
• Homogenization of Quasiconvex Integrals via the Periodic Unfolding Method

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