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

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 functional are assumed to vary continuously spatial coordinates. In terms XCQ4 modeling, only one function ramp type (either linear, quadratic or cubic order), alternatively usual four branch functions, is used as crack-tip enrichment, somewhat reducing complexity implementation. Another advantage employing function, which not derived from asymptotic solutions, lies less additional degrees freedom (DOFs) required for saving computational effort. merits developed approach demonstrated through our experiments, devoted both loading with stationary cracks simulation FGMs composites. accuracy model verified by comparing computed results respect reference solutions analytical solution, other methods, experimental data.