Finite Cell Method implementation and validation of a nonlocal integral damage model

Abstract

In this paper, the Finite Cell Method is further developed for a nonlocal damage problem. This method is a combination of a fictitious domain approach with higher-order finite elements, adaptive integration, and weak enforcement of the non-conforming essential boundary conditions. The fictitious domain approach alleviates the urge for boundary conforming meshes that are usually time-consuming to be generated free of error in case of geometrically complex structures. The ductile damage constitutive model used is a thermodynamically consistent nonlocal theory of integral type in which the damage variable is integrated over the whole domain. The formulation is implemented in a high-order finite element package tailored for the Finite Cell Method. The experiments are performed on a test specimens made of the aluminum alloy AA-7075-T6 to validate the results of our numerical approach. A good agreement of the simulation and experimental testing has been achieved. The efficiency of the method is then investigated with a numerical study of a porous domain with a more complex geometry. Further it is demonstrated that the nonlocal damage model compared to the local models, studied earlier by the authors, performs better in terms of convergence and numerical stability.