Effective elastic moduli of two-dimensional solids with multiple cracks

Effective elastic moduli in solids with high density of cracks

We investigate the weakening of elastic materials through randomly distributed circles and cracks numerically and compare the results to predictions from homogenization theories. We find a good agreement for the case of randomly oriented cracks of equal length in an isotropic plane-strain medium for lower crack densities; for higher densities the material is weaker than predicted due to precurs...

Effective elastic moduli of two dimensional solids with distributed cohesive microcracks

Effective elastic properties of a defected solid with distributed cohesive micro-cracks are estimated based on homogenization of the Dugdale–Bilby–Cottrell–Swinden (Dugdale–BCS) type micro-cracks in a two dimensional elastic representative volume element (RVE). Since the cohesive micro-crack model mimics various realistic bond forces at micro-scale, a statistical average of cohesive defects can...

Two-parameter integral representation formula for the effective elastic moduli of two-phase composites

VII.D Two Dimensional Solids

The rotational invariance of energy is ensured by the implicit sum over the indices (i, j) in the above expression. In the Fourier representation, the energy depends on the quantities q, |u|, and (q · u) which are clearly independent of rotations. For other lattices, there are more elastic coefficients, since the energy should only be invariant under lattice rotations. For example, the symmetry...

VII.D Two Dimensional Solids

The rotational invariance of energy is ensured by the implicit sum over the indices (i, j) in the above expression. In the Fourier representation, the energy depends on the quan­ tities q , |u|, and (q · u) which are clearly independent of rotations. For other lattices, there are more elastic coefficients, since the energy should only be invariant under lattice rotations. For example, the symme...