Modeling the transient dynamic fracture and quasi-static crack growth in cracked functionally graded composites by the extended four-node gradient finite elements

Abstract

This paper presents numerical simulations of transient dynamic fracture behaviors and quasi-static crack growth in cracked functionally graded composites using the enhanced extended consecutive-interpolation quadrilateral element (XCQ4). The mechanical properties of functional composites are assumed to vary continuously in spatial coordinates. In terms of XCQ4 modeling, only one function of ramp type (either linear, quadratic or cubic order), alternatively to the usual four branch functions, is used as crack-tip enrichment, somewhat reducing the complexity in implementation. Another advantage of employing the ramp function, which is not derived from asymptotic solutions, lies in the less additional degrees of freedom (DOFs) required for the branch functions, saving the computational effort. The merits of the developed approach are demonstrated through our numerical experiments, which are devoted to both dynamic loading with stationary cracks and quasi-static crack growth simulation in FGMs composites. The accuracy of the developed model is verified by comparing the computed results with respect to reference solutions derived from analytical solution, other numerical methods, and experimental data.