Abaqus implementation of a large family of finite viscoelasticity models

• Published in: Finite elements in analysis and design Vol. 232; p. 104114
• Main Authors: Lefèvre, Victor, Sozio, Fabio, Lopez-Pamies, Oscar
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2024
• Subjects: Elastomers; Finite deformations; Hybrid finite elements; Rubber blends; Stable ODE solvers; Rubber blends; Hybrid finite elements; Finite deformations; Elastomers; Stable ODE solvers
• ISSN: 0168-874X
• DOI: 10.1016/j.finel.2024.104114

In this paper, we introduce an Abaqus UMAT subroutine for a family of constitutive models for the viscoelastic response of isotropic elastomers of any compressibility – including fully incompressible elastomers – undergoing finite deformations. The models can be chosen to account for a wide range of non-Gaussian elasticities, as well as for a wide range of nonlinear viscosities. From a mathematical point of view, the structure of the models is such that the viscous dissipation is characterized by an internal variable Cv, subject to the physically-based constraint detCv=1, that is solution of a nonlinear first-order ODE in time. This ODE is solved by means of an explicit Runge–Kutta scheme of high order capable of preserving the constraint detCv=1 identically. The accuracy and convergence of the code is demonstrated numerically by comparison with an exact solution for several of the Abaqus built-in hybrid finite elements, including the simplicial elements C3D4H and C3D10H and the hexahedral elements C3D8H and C3D20H. The last part of this paper is devoted to showcasing the capabilities of the code by deploying it to compute the homogenized response of a bicontinuous rubber blend. •An Abaqus UMAT subroutine is introduced for a family of finite viscoelasticity models.•The subroutine is based on hybrid finite elements and applies for materials with any compressibility, including fully incompressible materials.•The accuracy and convergence of the subroutine are demonstrated by direct comparison with an exact solution.•For demonstration purposes, the subroutine is deployed to compute the homogenized viscoelastic response of a bicontinuous rubber blend.