Nonlinear homogenization method for practical applications

The homogenization method applied to nonlinear problems is discussed from practical point view. The conventional procedure of the asymptotic homogenization method for linear elasticity problems is directly extended to nonlinear problems by using rate formulation of the updated Lagrangian scheme. Analysis is made for a composite material whose constituents reveal elastoplasticity character as well as finite deformation in which a local periodicity can be assumed. The updating scheme also enables us to utilize the microscopic stress field, which is obtained in a localization process, to judge, for example, plastic failure. Several computational features in the incremental solution method are investigated to examine the feasibility of the nonlinear homogenization method in practical applications. Numerical examples verify the formulation and provide some insight into practical applications. Some brief remarks are made on large deformation of a periodic unit cell and on computing costs in global-local simultaneous computations. The expensive cost in the computation requires us to propose a new approach to large scale problems. Here the nonlinear homogenization solutions are used as experimental data and construct the macroscopic constitutive relations.