Some Model Problems of Polycrystal PLasticity with Deficient Basic Crystals

DOI10.1137/S0036139997320019zbMath0932.74012MaRDI QIDQ4237233

T. D. Little, Robert V. Kohn

Publication date: 31 March 1999

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

plane stressductile behaviournonlinear homogenizationantiplane sheartranslation methodcompensated compactness methodlimit loadsBishop-Hill-Taylor boundcheckerboard microstructuresgeometry-independent bounds on effective yield setlinear comparison methodrigid behaviourSachs bound

Mathematics Subject Classification ID

Bounds on effective properties in solid mechanics (74Q20) Crystalline structure (74E15) Composite and mixture properties (74E30) Statistical mechanics of crystals (82D25) Plastic materials, materials of stress-rate and internal-variable type (74C99)

Related Items (22)

Bounds for nonlinear composites via iterated homogenization ⋮ Second-order theory for the effective behavior and field fluctuations in viscoplastic polycrystals ⋮ Homogenization of layered materials with rigid components in single-slip finite crystal plasticity ⋮ Mathematical model and analysis of the strength of particle reinforced ideally plastic composites ⋮ On the asymptotic behavior of variable exponent power-law functionals and applications ⋮ A symmetric fully optimized second‐order method for nonlinear homogenization ⋮ Lower semicontinuity and relaxation of nonlocal \(L^\infty\)-functionals ⋮ Criteria for guaranteed breakdown in two-phase inhomogeneous bodies ⋮ On the interplay of anisotropy and geometry for polycrystals in single‐slip crystal plasticity ⋮ Bounds for nonlinear composite conductors via the translation method ⋮ Bounding the current in nonlinear conducting composites ⋮ Linear comparison estimates for the effective resistivity of three-dimensional nonlinear polycrystals ⋮ Variational self-consistent estimates for cubic viscoplastic polycrystals: The effects of grain anisotropy and shape. ⋮ A model problem concerning recoverable strains of shape-memory polycrystals ⋮ \(\Gamma \)-convergence of power-law functionals with variable exponents ⋮ Stress-induced phase transformations in shape-memory polycrystals ⋮ HOMOGENIZATION OF L^∞ FUNCTIONALS ⋮ A variational characterization of the effective yield set for ionic polycrystals ⋮ Homogenization of the nonlinear Kelvin-Voigt model of viscoelasticity and of the Prager model of plasticity ⋮ Multiphase Conductors Realizing Aleksandrov's Mean ⋮ Improved bounds for the yield stress of a model polycrystalline material ⋮ Second‐order and affine estimates for the behavior of viscous polycrystals

This page was built for publication: Some Model Problems of Polycrystal PLasticity with Deficient Basic Crystals