An intelligent finite element method

Abstract

This paper presents a unified framework for constitutive modelling of complex materials in finite element analysis using evolutionary polynomial regression (EPR). EPR is a data-driven method based on evolutionary computing, aimed to search for polynomial structures representing a system. A procedure is presented for construction of EPR-based constitutive model (EPRCM) and its integration in finite element procedure. The main advantage of EPRCM over conventional and neural network-based constitutive models is that it provides the optimum structure for the material constitutive model representation as well as its parameters, directly from raw experimental (or field) data. It can learn nonlinear and complex material behaviour without any prior assumption on the constitutive relationship. The proposed approach provides a transparent relationship for the constitutive material model that can readily be incorporated in a finite element model. A procedure is presented for efficient training of EPR, computing the stiffness matrix using the trained EPR model and incorporation of the EPRCM in a commercial finite element code. The application of the developed EPR-based finite element method is illustrated through an example and advantages of the proposed method over conventional and neural network-based FE methods are highlighted