An efficient finite strain constitutive model for amorphous thermoplastics: Fully implicit computational implementation and optimization-based parameter calibration. (June 2023) - Ferreira, Bernardo P.; Carvalho Alves, A. Francisca; Andrade Pires, F.M.
Highlights: A novel visco-elastic visco-plastic constitutive model is consistently formulated. Well-established rheological elements are judiciously combined. An implicit integration scheme is derived, leading to a highly efficient algorithm. A new unsupervised two-stage optimization-based calibration strategy is developed. Close agreement with experimental and numerical results from the literature. Abstract: In this paper, a new visco-elastic visco-plastic (three-dimensional) constitutive model is consistently formulated under isothermal conditions to describe the nonlinear behavior of thermoplastic polymers at finite strains. The constitutive equations include three well-established rheological elements to have well-defined parametric behavior and capture the experimental response. In particular, a visco-elastic generalized Maxwell element, a visco-plastic Eyring dashpot, and a plasticity-induced (nonlinear) hardening element are selected and consistently combined. A fully implicit integration algorithm is derived, and highly efficient implementation is obtained by simplifying the system of equations to a single (scalar) nonlinear residual equation. A new two-stage optimization-based calibration procedure is developed to identify the material parameters in a completely unsupervised way. The constitutive model is validated against results available in the literature for polycarbonate, accounting for temperature and strain rate dependencies. The results show the efficiency of the overall numerical strategy and demonstrate that quadratic convergence rates are attained. Despite the strongly nonlinear finite strain response, it is possible to observe an excellent agreement for all stages of deformation.