Complete Elasticity Solution to the Stress Problem in a Planar Grained Structure

DOI10.1177/108128659900400402zbMath1001.74550OpenAlexW2125209450MaRDI QIDQ4528207

Shmuel Vigdergauz

Publication date: 19 December 2002

Published in: Mathematics and Mechanics of Solids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1177/108128659900400402

Mathematics Subject Classification ID

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

Related Items (8)

Planar grained structures with multiple inclusions in a periodic cell: Elastostatic solution and its potential applications ⋮ Criteria for guaranteed breakdown in two-phase inhomogeneous bodies ⋮ Stress-smoothing holes in an elastic plate: The triangular checkerboard lattice of low symmetry ⋮ A generalization of the equi-stress principle in optimizing the mechanical performance of two-dimensional grained composites ⋮ New Results on the Poisson Ratio Behavior in Matrix-Inclusion Planar Composites ⋮ Stress-smoothing holes in an elastic plate: From the square lattice to the checkerboard ⋮ Optimal shape of a grain or a fibre cross-section in a two-phase composite ⋮ Complex variable boundary integral equations for perforated infinite planes

Cites Work

• Unnamed Item
• A hole in a plate, optimal for its biaxial extension - compression
• Inverse problems of the plane theory of elasticity
• An integral equation method for elastostatics of periodic composites
• Microstructures minimizing the energy of a two-phase elastic composite in two space dimensions. II: The Vigdergauz microstructure
• On the numerical evaluation of elastostatic fields in locally isotropic two-dimensional composites
• On the theory of elastic nonhomogeneous media with a regular structure
• Invariant properties of the stress in plane elasticity and equivalence classes of composites
• Effective properties of composite materials containing voids
• Optimal bounds on the effective behavior of a mixture of two well-ordered elastic materials
• Rhombic lattice of equi-stress inclusions in an elastic plate

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