Explicit integration methods for constitutive equations of a mean-stress dependent elastoviscoplastic model: impact on structural finite element analyses

• Published in: Engineering with computers Vol. 37; no. 1; pp. 57 - 75
• Main Authors: Abdul-Hameed, Hemin, Roguet, Eléonore, Brusselle-Dupend, Nadège, Boulharts, Habiba, Cangémi, Laurent
• Format: Journal Article
• Language: English
• Published: London Springer London 01.01.2021; Springer Nature B.V; Springer Verlag
• Subjects: Accuracy; CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Classical Mechanics; Computer Science; Computer-Aided Engineering (CAD; Constitutive equations; Constitutive models; Constitutive relationships; Control; Convergence; Creep tests; Crystal structure; Crystallinity; Damping; Environmental Sciences; Finite element method; Math. Applications in Chemistry; Mathematical analysis; Mathematical and Computational Engineering; Mathematical models; Mechanical properties; Methods; Numerical integration; Numerical methods; Original Article; Physics; Polymers; Robustness (mathematics); Runge-Kutta method; Structural analysis; Systems Theory; Tensile tests; Polymer; Constitutive model; Structure analysis; Deformation behavior; Integration method; Viscoplasticity
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-019-00809-x

The strong dependent behavior of semi-crystalline polymers can lead to the use of simplified material laws in finite element structural calculations for reasons of robustness to the detriment of the quantitative response of the models. This work focuses on numerical integration methods as a solution to overcome the possible convergence and robustness limitations of mean-stress dependent elastoviscoplastic material laws, typical of the semi-crystalline polymers’ mechanical behavior. What is proposed here is a rational application of three explicit integration methods (fourth- and second-order Runge–Kutta method, a hybrid schema between Runge–Kutta, and Euler method) in engineering structural calculations, which provide a reliable solution for constitutive models of semi-crystalline polymer. These methods are examined for structure creep test and tensile test, in comparison with experimental data. The investigations have been done in terms of the stability toward convergence, the accuracy of results, the plastic consistency, and CPU time efficiency. This work, proposes an easy implementation of integration methods in any computational finite element code. It also provides a flexible modular implementation which is applicable to any different constitutive equations. An integration step sub-division technique is recommended. It is a powerful technique to improve the convergence of solution and accuracy of result by damping oscillation around stress Gauss point integration solution. The results obtained illustrate the effect of numerical integration schemas on structural analysis and provide an insight into select suitable method.