A novel boundary element formulation for anisotropic fracture mechanics

Abstract

A novel boundary element formulation for two-dimensional fracture mechanics is presented in this work. The formulation is based on the derivation of a supplementary boundary integral equation to be used in combination with the classic displacement boundary integral equation to solve anisotropic fracture mechanics problems via a single-region approach. The formulation is built starting from the observation that the displacement field for an anisotropic domain can be represented as the superposition of a vector field, whose components satisfy a suitably defined anisotropic Laplace equation, and the gradient of the Airy stress function. The supplementary boundary integral equation is then obtained using such representation into the integral expression of the aforementioned Laplace equation and employing the relationship between the stress function gradient and the boundary tractions. The supplementary equation neither requires the computation of hyper-singular integrals nor does it introduce additional variables for the problem, as it involves boundary displacements and tractions only. Numerical results are obtained for both uncracked and cracked bodies and show the accuracy and potential of the proposed approach.

Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods

“…The considered orthotropic solid is a FCC Copper crystal [58] with density ρ = 8.92 and non-zero elastic constants c 11 = 168, c 12 = 121, c 44 = 75. In 2D, the constitutive behavior of the considered anisotropic solid represents the in-plane behavior of a multilayered composite material [59] with density ρ = 1.…”

Modelling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods

“…The considered orthotropic solid is a FCC Copper crystal [52] with density ρ = 8.92 and non-zero elastic constants c 11 = 168, c 12 = 121, c 44 = 75. In 2D, the constitutive behavior of the considered anisotropic solid represents the in-plane behavior of a multilayered composite material [53] with density ρ = 1.…”

A Ritz model for damage analysis in variable angle tow composite plates

“…FEM's accuracy is strongly related to the suitable quality of the generated mesh that, in the case of VAT laminates, due to the variation of the in-plane and through-the-thickness properties, generally indices a high number of mesh elements, thus leading to high computational efforts [4,5]. To overcome such issues, and possibly speed up the analysis still retaining a high level of accuracy, different numerical techniques have been proposed as alternative to FEM, such as boundary elements methods [6,7,8] or mesh-less techniques [9]; in this context, the Ritz method, which may be seen as a global mesh-less technique, has been often shown effective for the analysis of classical, laminated and VAT composite structures [10,11,12,13].…”