On the modeling of cavitation and yielding in rubber-toughened amorphous polymers: Fully implicit implementation and optimization-based calibration

Abstract

In the present contribution, a finite strain visco-elastic visco-plastic (three-dimensional) constitutive model is proposed to predict the nonlinear response of neat, porous and rubber-toughened amorphous polymers. In this context, a well-known nucleation law is modified and coupled with a nucleation criterion to suppress nucleation under compression and shear loadings, as well as to identify its material parameters directly. The growth of both the nucleated and initial voids is ruled by a modified version of the Gurson’s potential, ensuring the coherence in the energy dissipation between the macro and microscales. The post-yield strain hardening of the material is modeled with the well-established eight-chain model. A fully implicit integration algorithm is formulated under the infinitesimal strains functional format, and both constitutive state update and consistent tangent modulus are properly established. A three-stage optimization-based calibration procedure is designed to identify the model’s material parameters efficiently. This decoupled calibration strategy is only possible due to the well-defined influence of the model’s material parameters in the numerical response. The predictive capability of the proposed constitutive model is validated against literature results for polycarbonate and three rubber-filled polycarbonate blends. Moreover, the numerical response of the model is assessed under different triaxial states and is further compared with the homogenized response of a Representative Volume Element of the voided-amorphous polymer microstructure. The results highlight that the model can capture the typical behavior of amorphous polymers, namely yield stress, strain-softening and strain hardening under different loading conditions, as well as the decrease of stress associated with the increase of the void volume fraction. The additional numerical analyses conducted, validated some constitutive assumptions. The efficiency of the calibration procedure and the overall numerical strategy is also demonstrated.