http://users.cecs.anu.edu.au/~Qinghua.Qin/publications/pap65E-EFM.pdf

BEM for crack-hole problems in thermopiezoelectric materials

Recent developments and applications of invariant integrals

The two-state conservation law is utilized, in conjunction with finite element analysis, to obtain the complete Williams eigenfunction series for elastic–plastic cracks, including the intensities not only for the inverse square root singularity and the T-stress but for the higher order singular and nonsingular terms as well. It is shown that the J-integral comprises only the contributions from the mutual interaction between all complementary pairs of the eigenfields. The same applies to the M-integral with a slightly different definition for the complementary pair. Particularly, it is found that the higher order singularities interact with the nonsingular higher order eigenfields to generate the extra configurational force, in addition to the energy release rate resulting from the inverse square root singularity. This additional J-value is associated with the translation of the plastic zone alone, with the crack tip being fixed. Numerical examples show that the effect of the higher order terms is negligible in terms of J when the plastic zone size is small, but that the higher order terms make a difference in the plastic zone configuration through the interaction between the singular and the nonsingular terms in the case of the large scale yielding.

The role of higher order eigenfields in elastic–plastic cracks

On the contribution of subinterface microcracks near the tip of an interface macrocrack to the J-integral in bimaterial solids

The problem of interactions between an inclusion and multiple cracks in a thermopiezoelectric solid is considered by boundary element method (BEM) in this paper. First of all, a BEM for the crack}inclusion problem is developed by way of potential variational principle, the concept of dislocation, and Green's function. In the BE model, the continuity condition of the interface between inclusion and matrix is satis"ed, a priori, by the Green's function, and not involved in the boundary element equations. This is then followed by expressing the stress and electric displacement (SED) and elastic displacements and electric potential (EDEP) in terms of polynomials of complex variables m t and m k in the transformed m-plane in order to simulate SED intensity factors by the BEM. The least-squares method incorporating the BE formulation can, then, be used to calculate SED intensity factors directly. Numerical results for a piezoelectric plate with one inclusion and a crack are presented to illustrate the application of the proposed formulation. Copyright ( 2000 John Wiley & Sons, Ltd.

/pdf/bem-for-crack-inclusion-problems-of-plane-2l1eeu01r9.pdf

Chen Yi-Heng

Papers

Interaction between a main-crack and a parallel micro-crack in an orthotropic plane elastic solid

Further investigation of Comninou's EEF for an interface crack with completely closed faces