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

[Display omitted] •T-stresses of cracked 2D FGMs are evaluated with numerical manifold method.•Discontinuity and singularity of physical fields around the crack are well captured.•The T-stresses are computed by domain-independent interaction integral.•Our results are in nice agreement with the available reference solutions.•Main influencing factors on the T-stresses of the cracked FGMs are investigated. 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.