On the finite element analysis of inverse problems in fracture mechanics

This paper presents a numerical study of inverse parameter identification p roblems in fracture mechanics. Inverse methodology is applied to the detect ion of subsurface cracks and to the study of propagating cracks. The proced ure for detecting subsurface cracks combines the finite element method with a sequential quadratic programming algorithm to solve for the unknown geom etric parameters associated with the internal flaw. The procedure utilizes finite element substructuring capabilities in order to minimize the process ing and solution time for practical problems. The finite element method and non-linear optimization are also used in determining the direction a crack will propagate in a heterogeneous planar domain. This procedure involves d etermining the direction that produces the maximum strain energy release fo r a given increment of crack growth. The procedure is applied to several nu merical examples. The results of these numerical studies coincide with theo retical predictions and experimentally observed crack behavior.