The finite element implementation of 3D fractional viscoelastic constitutive models

• Published in: Finite elements in analysis and design Vol. 146; pp. 28 - 41
• Main Authors: Alotta, Gioacchino, Barrera, Olga, Cocks, Alan, Di Paola, Mario
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-07-2018; Elsevier BV
• Subjects: 3D constitutive models; Computer simulation; Constitutive equations; Constitutive models; Creep; Creep tests; Finite element analysis; Finite element method; Fractional viscoelasticity; Mathematical analysis; Mathematical models; Newton-Raphson method; Numerical modelling; Relaxation; Stress relaxation; Subroutines; Three dimensional imaging; Three dimensional models; Time dependence; Viscoelastic materials; Viscoelasticity; Fractional viscoelasticity; 3D constitutive models; Relaxation; Creep; Numerical modelling
• ISSN: 0168-874X; 1872-6925
• DOI: 10.1016/j.finel.2018.04.003

The aim of this paper is to present the implementation of 3D fractional viscoelastic constitutive theory presented in Alotta et al., 2016 [1]. Fractional viscoelastic models exactly reproduce the time dependent behaviour of real viscoelastic materials which exhibit a long “fading memory”. From an implementation point of view, this feature implies storing the stress/strain history throughout the simulations which may require a large amount of memory. We propose here a number of strategies to effectively limit the memory required. The form of the constitutive equations are summarized and the finite element implementation in a Newton-Raphson integration scheme is described in detail. The expressions that are needed to be coded in user-defined material subroutines for quasi static and dynamic implicit and explicit analysis (UMAT and VUMAT) in the commercial finite element software ABAQUS are readily provided. In order to demonstrate the accuracy of the numerical implementation we report a number of benchmark problems validated against analytical results. We have also analysed the behaviour of a viscoelastic plate with a hole in order to show the efficiency of these types of models. The source codes for the UMAT and VUMAT are provided as online supplements to this paper.
•Implementation of 3D fractional viscoelastic constitutive laws in a FE context.•The routines are suitable for both implicit and explicit integration schemes.•The models are implemented as user material subroutines in Abaqus (UMAT, VUMAT).•Stress/strain history needs to be accessed and stored during the calculation.•Strategies to effectively limit the amount of memory for large simulation.