ABSTRACT
The micro-scale problem in the global-local computations, which is based on the nonlinear homogenization theory, has been interpreted as providing a constitutive (stress–strain) relationship to the macroscale problem of the overall structure. This study uses this interpretation to carry out three-dimensional micro-scale analysis of a granular medium to evaluate the macroscopic failure surface, which is one of the important items for the constitutive theory. This paper starts by giving an overview of global-local modeling, and shows that the micro-scale problem provides a constitutive relationship to the macro-scale problem. Next, we apply three-dimensional micro-scale analysis of idealized granular materials to evaluate and examine failure surfaces. By the numerical experiments, we obtained the following main conclusions about the failure surface on p-q plane and π plane: The failure surface on p-q plane can be expressed by two straight lines opened in the compression direction on p-axis. The shape of failure surface obtained by the simulations on π plane looks like a Japanese rice ball.
