Shape design optimization of dynamic crack propagation using peridynamics

Abstract

Crack generation tends to be prevented in most of design problems but taking advantages of cracks with some flaw acceptability could provide better design margin in practical problems. To develop a crack control strategy, we propose a shape design optimization method using an adjoint shape sensitivity based on a peridynamics theory that does not require crack propagation path a priori and thus is advantageous for the problems in which the discontinuity initiates, propagates, and interacts dynamically. The adjoint design sensitivity analysis (DSA) method based on the peridynamics is developed for dynamic crack propagations in brittle materials, including the successive branching of cracks. For a performance measure of stretch between the designated points at final time, the design sensitivity with respect to the design parameters is derived to be used in the shape design optimization. Numerical examples are demonstrated to verify the accuracy of the developed design sensitivity to show excellent agreement with finite differencing for all the shape design variables. Also, the proposed DSA method works very well in the shape design optimization applications of creating or avoiding cracks in a specified region.