Nonlinear viscoelastic analysis based on dual neural networks

Abstract

Due to the complexity of materials, the mechanical analysis of viscoelastic problems becomes relatively difficult, so it has been widely concerned by scholars. Although the linear viscoelastic theory has been improved, there are still a lot of problems to be solved in the study of nonlinear theory and effective numerical methods. In this paper, the nonlinear viscoelastic problem is solved by the viscoelastic correspondence principle. In order to construct the nonlinear viscoelastic constitutive relation, the method of solving the elastic mechanics problem with dual neural network is presented, and the instantaneous stress and strain components in the nonlinear viscoelastic constitutive relation are calculated. Aiming at the problem that unknown parameters in the relaxation modulus fitting model are difficult to obtain, a custom neural network fitting method is introduced to fit the relaxation modulus. Dual neural network integral method is used to solve the integral problem in viscoelastic constitutive relation, the present stress and strain of a class of nonlinear viscoelastic materials are obtained, and the nonlinear viscoelastic problem is solved. Numerical examples show that the proposed method is an efficient and high-precision method for solving nonlinear viscoelastic problems.