Otimização bayesiana aplicada à identificação de parâmetros constitutivos de um modelo elasto-viscoplástico

Abstract

The increasing use of polymers as engineering materials has driven the development of advanced constitutive models capable of accurately describing their mechanical behavior under different loading conditions. Among these materials, high-density polyethylene (HDPE) stands out due to its favorable mechanical properties, thermal stability, and chemical resistance. To properly represent its behavior, it is essential not only to employ robust constitutive models but also to adopt effective strategies for the identification of constitutive parameters. In this context, the first part of this work proposes an implicit elasto-viscoplastic constitutive model formulated for large deformations and based on the definition of internal variables to describe the evolution of viscoplastic strain. The verification and validation of the model were carried out through numerical simulations of a notched specimen subjected to tensile loading, with the results compared to experimental data available in the literature. The numerical results showed strong agreement with the experimental data, thereby validating the proposed formulation. In order to improve the model response in the elastic regime, the constitutive formulation was further modified by coupling it with a proposed pseudo-viscoelastic model, in which Young’s modulus depends on the strain rate. In the second part of the work, a methodology for constitutive parameter identification was developed using data from multiple mechanical experiments. The problem was formulated as a multi-objective optimization problem, and a global solution strategy was adopted. Two optimisation methods were applied and their results compared: Particle Swarm Optimisation (PSO) and Bayesian Optimisation (BO), both combined with the Nelder–Mead (NM) method. For this purpose, results from uniaxial tensile tests performed on dumbbell and notched specimens at three different strain rates were used. The identification results for the dumbbell specimen indicate that the hybrid approach combining BO with NM achieved higher efficiency in parameter identification and lower computational cost compared to the hybrid PSO-based approach. With the modified model, an improved agreement between numerical and experimental curves was obtained. When parameter identification was performed for the notched specimen, a set of parameters different from that obtained for the smooth specimen was found, highlighting the lack of uniqueness in the solution. Therefore, a combined identification considering both specimens was carried out in order to obtain a unique set of parameters that is physically consistent with the experimental results. Finally, through a sensitivity analysis based on Bayesian inference, the relative influence of the constitutive parameters on the model response was assessed. Overall, the results demonstrate that Bayesian Optimization is a promising tool for the identification of parameters in elasto-viscoplastic constitutive models based on multiple experiments, due to its high computational efficiency.