CONCURRENT ATOMISTIC-CONTINUUM MODEL FOR DEVELOPING SELF-CONSISTENT ELASTIC CONSTITUTIVE MODELING OF CRYSTALLINE SOLIDS WITH CRACKS

Damage of materials inherently involves coupling of deformation and failure mechanisms at multiple length and time scales. This paper develops self-consistent elastic constitutive relations of crystalline materials containing atomistic scale cracks, from observations made in a concurrent multi-scale simulation system coupling atomistic and continuum domain models. The self-consistent constitutive model incorporates both nonlinearity and nonlocality to account for atomic level interactions and deformation mechanisms, especially near crack tips. Atomistic modeling in the concurrent model is done using molecular dynamics (MD), while the continuum modeling is done using a crystal elasticity finite element (FE) analysis code. The atomistic-continuum coupling is achieved by enforcing geometric compatibility and force equilibrium in an interface region. The constitutive model is calibrated by comparing with the results of MD predictions in the concurrent model. For validation, the crack tip stress field is investigated using both the coupled concurrent model and a FE model with the constitutive law. The self-consistent model exhibits excellent accuracy and enhanced efficiency in comparison with pure MD and concurrent model results.