Interaction integrals for fracture analysis of functionally graded piezoelectric materials

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Transient thermal shock fracture analysis of functionally graded piezoelectric materials by the extended finite element method (2014, methodology): “The thermal stress intensity factors and the electrical displacement intensity factor can be evaluated through a judicious choice of the auxiliary fields in computing I and solving the corresponding simultaneous equations using the components of the generalized Irwin matrix Y (Rao and Kuna, 2008; Bu”