T-stress evaluation for multiple cracks in FGMs by the numerical manifold method and the interaction integral

Abstract

The numerical manifold method (NMM) is superior in discontinuous analysis, benefiting from its bi-cover systems, i.e., the mathematical cover and the physical cover. In this work, the NMM is devoted to compute the T-stress for two-dimensional functionally graded materials (FGMs) with multiple cracks. The displacement field for cracked FGMs is firstly solved by the NMM and then the related T-stress is evaluated in the NMM postprocessing via the interaction integral method. Two typical examples are firstly tested to verify the accuracy of the proposed method and the domain-independence of the interaction integral, and then another three cases are examined to reveal the effects of material gradients, crack geometries and boundary conditions on the T-stress.