From microstructure-independent formulas for composite materials to rank-one convex, non-quasiconvex functions

DOI10.1007/s00205-017-1169-1zbMath1387.74096OpenAlexW2752438380MaRDI QIDQ1702101

Yury Grabovsky

Publication date: 28 February 2018

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-017-1169-1

Mathematics Subject Classification ID

Crystalline structure (74E15) Effective constitutive equations in solid mechanics (74Q15) Composite and mixture properties (74E30)

Related Items (9)

Numerical evidence towards a positive answer to Morrey's problem ⋮ Quasiconvexity, null Lagrangians, and Hardy space integrability under constant rank constraints ⋮ Automatic quasiconvexity of homogeneous isotropic rank-one convex integrands ⋮ A rank-one convex, nonpolyconvex isotropic function on with compact connected sublevel sets ⋮ Numerical approaches for investigating quasiconvexity in the context of Morrey's conjecture ⋮ Weak Lower Semicontinuity of Integral Functionals and Applications ⋮ An elementary proof of Marcellini Sbordone semicontinuity theorem ⋮ Exact relations for Green's functions in linear PDE and boundary field equalities: a generalization of conservation laws ⋮ Extremal rank-one convex integrands and a conjecture of Šverák

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• G-closure of some particular sets of admissible material characteristics for the problem of bending of thin elastic plates
• Thermal expansion of polycrystalline aggregates. I. Exact analysis
• Quasiconvexity and relaxation of nonconvex problems in the calculus of variations
• Multicomponent composites, electrical networks and new types of continued fraction. I
• Multicomponent composites, electrical networks and new types of continued fraction. II
• Variational bounds on the effective moduli of anisotropic composites
• Uniform fields and universal relations in piezoelectric composites
• Convexity conditions and existence theorems in nonlinear elasticity
• Exact relations for effective tensors of polycrystals. I: Necessary conditions
• Some more exact results concerning multifield moduli of two-phase composites
• On the existence of solutions to some problems of optimal design for bars and plates
• Elastic properties of reinforced solids: Some theoretical principles
• Quasi-convexity and the lower semicontinuity of multiple integrals
• Explicit relaxation of a variational problem in optimal design
• On uniform fields in heterogeneous media
• Exact Relations for Effective Conductivity of Fiber-Reinforced Conducting Composites with the Hall Effect via a General Theory
• Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion
• Optimal design and relaxation of variational problems, I
• Rank-one convexity does not imply quasiconvexity
• Exact relations between the thermoelectroelastic moduli of heterogeneous materials
• Exact relations for effective tensors of composites: Necessary conditions and sufficient conditions
• The Theory of Composites
• Composite Materials
• On characterizing the set of possible effective tensors of composites: The variational method and the translation method
• A Theorem on the Conductivity of a Composite Medium
• Algebra, Geometry, and Computations of Exact Relations for Effective Moduli of Composites

This page was built for publication: From microstructure-independent formulas for composite materials to rank-one convex, non-quasiconvex functions