• Largenton, Rodrigue
• Suquet, Pierre
• Michel, Jean-Claude

Abstract

The Nonuniform Transformation Field Analysis is a reduction technique introduced in the realm of Multiscale Problems in Nonlinear Solid Mechanics to achieve scale transition for materials exhibing a nonlinear behaviour. It is indeed well recognized that the nonlinearity introduces a strong coupling between the problems at the different scales which, in full rigor, remain coupled. To avoid the computational cost of the scale coupling, reduced models have been developed. To improve on the predictions of Transformation Field Analysis where the plastic strain field is assumed to be uniform in each domain, the authors have proposed another reduced model, called the Nonuniform Transformation Field Analysis, where the plastic strain fields follow shape functions which are not piecewise uniform. The model is presented for individual phases exhibiting an elastoviscoplastic behavior. A brief account on the reduction technique is given first. Then the time-integration of the model at the level of a macroscopic material point is performed by means of a numerical scheme. This reduced model is applied to structural problems. The implementation of the model in a Finite Element code is discussed. It is shown that the model predicts accurately the effective behavior of nonlinear composite materials with just a few internal variables. Another worth-noting feature of the method is that the local stress and strain fields can be determined simply by postprocessing the output of the structural (macroscopic) computation performed with the model.

Topics

• impedance spectroscopy
• polymer
• phase
• composite
• homogenization