Concurrent multiresolution finite element: formulation and algorithmic aspects

A multiresolution concurrent theory for heterogenous materials is proposed with novel macro scale and micro scale constitutive laws that include the plastic yield function at different length scales. In contrast to the conventional plasticity, the plastic flow at the micro zone depends on the plastic strain gradient. The consistency condition at the macro and micro zones can result in a set of algebraic equations. Using appropriate boundary conditions, the finite element discretization was derived from a variational principle with the extra degrees of freedom for the micro zones. In collaboration with LSTC Inc, the degrees of freedom at the micro zone and their related history variables have been augmented in LS-DYNA. The 3D multiresolution theory has been implemented. Shear band propagation and the large scale simulation of a shear driven ductile fracture process were carried out. Our results show that the proposed multiresolution theory in combination with the parallel implementation into LS-DYNA can capture the effects of the microstructure on shear band propagation and allows for realistic modeling of ductile fracture process.