An ABAQUS toolbox for multiscale finite element computation

In this paper, we propose to implement, in the framework of a commercial finite element software, a computational multilevel finite element method for the modeling of composite materials and structures. In the present approach, the unknown constitutive relationship at the macroscale is obtained by solving a local finite element problem at the microscale. The main advantages of the proposed computational approach are that it can greatly save computer memory and CPU time, and it has good accuracy at the same time while it allows to easily building nonlinear behavior for high order mechanical theories to deal with problems which cannot be handled by classical multiscale or homogenization theories. The linear and the non-linear cases are introduced and implemented in ABAQUS. A Python script and user-defined FORTRAN subroutines have been developed for this purpose. Finally numerical results show that the method presented in this paper is effective and reliable.