A new adaptive multiscale method for the nonlinear fracture simulation of heterogeneous materials is proposed. The two major sources of error in the finite element simulation are discretisation and modelling errors. In the failure problems, the discretisation error increases due to the strain localisation which is also a source for the error in the homogenisation of the underlying micro-structure. In this paper, the discretisation error is controlled by an adaptive mesh refinement procedure following the Zienkiewicz-Zhu technique, and the modelling error, which is the resultant of homogenisation of micro-structure, is controlled by replacing the macroscopic model with the underlying heterogeneous micro-structure. The scale adaptation criterion which is based on an error indicator for homogenisation proposed by[1] is employed for our nonlinear fracture problem. The control of both discretisation and homogenisation errors is the main feature of the proposed multiscale method.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.