Coupling recognition of the structure and parameters of non-linear constitutive material models using hybrid evolutionary algorithms

The structure of the non-linear constitutive models is a key to control non-linear behaviours of materials. Because the non-linear mechanical mechanism is not clearly understood in most cases, it is very difficult to assume the structure of the model in advance. The recognition of the structure of the model from experimental results can help understanding of the mechanism. This recognition is a dynamic search problem being highly multimodal, multi-variable with high order, and needing a large parameter space. How to obtain a global optimum solution is a key to this problem. In this paper, a hybrid evolutionary algorithm is proposed for coupling recognition of the structure of the non-linear constitutive material model and its coefficients in global space using global response information, e.g. load vs deflection data, obtained from the structural test. Genetic programming is used to recognize the structure of the non-linear stress–strain relationship without any assumption in advance and the genetic algorithm is then used to recognize its coefficients. The non-linear stress–strain relationship thus found can not only satisfy the dynamic change in its structure but also its variables and coefficients. Non-linear finite element analysis is used to transfer the load–deflection information to the stress–strain data. The potential of the proposed method is demonstrated by applying it to the macro-mechanical modelling of the non-linear behaviour of composite materials. A non-linear material model for the unidirectional ply is recognized by using experimental data of a lamina plate [(±45)6]s. The obtained non-linear constitutive model gave good predictions in coincidence with the non-linear behaviours of the [(±30)6]s, [(0/±45)3]s and [(0/±45)4]s plates. The results indicate that the coupling non-linear constitutive model of the structure and its coefficients can identify the model which the traditional constitutive model theory is unable to recognize