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Dynamic crack analysis in piezoelectric solids with nonlinear electrical and mechanical boundary conditions by a time-domain BEM. (English) Zbl 1230.74211
Summary: This paper presents advanced transient dynamic crack analysis in two-dimensional, homogeneous and linear piezoelectric solids using non-linear mechanical and electrical crack-face boundary conditions. Stationary cracks in infinite and finite piezoelectric solids subjected to impact loadings are considered. For this purpose a time-domain boundary element method (TDBEM) is developed. A Galerkin-method is implemented for the spatial discretization, while a collocation method is applied for the temporal discretization. An explicit time-stepping scheme is obtained to compute the unknown boundary data including the generalized crack-opening-displacements (CODs) numerically. An iterative solution algorithm is developed to consider the non-linear semi-permeable electrical crack-face boundary conditions. Furthermore, an additional iteration scheme for crack-face contact analysis is implemented at time-steps when a physically meaningless crack-face intersection occurs. Several numerical examples are presented and discussed to show the effects of the electrical crack-face boundary conditions on the dynamic intensity factors.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
74R10 Brittle fracture
74F15 Electromagnetic effects in solid mechanics
74H35 Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics
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