Efficient numerical implementation of pressure, time, and temperature superposition for elasto‐visco‐plastic material model by using a symbolic approach

Abstract

SUMMARYThis article is concerned with the finite element implementation of an elasto-visco-plastic constitutive model using a symbolic approach. The model combines the Knauss-Emri (KE) pressure, temperature, and time superposition principle in the implicit finite element scheme. The equation development and code generation was performed using the symbolic tool AceGen. The same symbolic system was applied to derive analytical sensitivities of the numerical model with respect to the material and shape parameters. To enable efficient numerical implementation of the KE model the convolution integrals were transformed into their respective incremental forms, so that radical improvements of code efficiency and computer storage requirements were achieved. The numerical examples derived for polyethylene terephthalate (PET) polymers demonstrate that symbolic systems can be applied to develop complex constitutive models capable of simulating material responses that are in good agreement with experimental measurements over a wide range of strain rates, temperatures, and loading conditions.