Data driven approach in multiphysics framework: Application to coupled electro-mechanical problems

Abstract

Solving coupled multiphysics problems using finite elements and conventional modeling approach requires building, from coupled finite element formulation often in the same code, the monophysical operators and the multiphysics coupling operators. In this work the data driven, model-free computational approach is fitted in the multiphysics framework adapted for ‘smart’ materials. Thus, in this work we ought to expand the phase space and propose a new norm for the distance based data driven solver adapted to the problem at hands. Given the good material database which naturally encodes the coupling interactions, we show that proposed application of data driven approach enables to avoid the coupling tangent terms altogether. In other words, the data driven approach permits to decouple the different ‘physics’ and to manage the coupling from the data. We illustrate the performance and robustness of the approach on two examples related to lattice model composed of planar, piezoelectric truss network and of finite element discretized linear piezoelectric solids. The numerical tests show good convergence properties related to the number of data points, as well as the choice of material and weighting parameters.