6533b853fe1ef96bd12ad561

RESEARCH PRODUCT

The finite element implementation of 3D fractional viscoelastic constitutive models

Alan C.f. CocksOlga BarreraOlga BarreraMario Di PaolaGioacchino Alotta

subject

RelaxationComputer scienceSubroutineConstitutive equation3D constitutive models; Creep; Fractional viscoelasticity; Numerical modelling; Relaxation; Analysis; Engineering (all); Computer Graphics and Computer-Aided Design; Applied Mathematics02 engineering and technologyViscoelasticityStress (mechanics)Engineering (all)0203 mechanical engineeringFractional viscoelasticityApplied mathematicsLimit (mathematics)Applied MathematicsGeneral EngineeringAnalysiCreep021001 nanoscience & nanotechnologyComputer Graphics and Computer-Aided DesignFinite element method020303 mechanical engineering & transportsNumerical modellingBenchmark (computing)3D constitutive model0210 nano-technologyAnalysisQuasistatic process

description

Abstract 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.

yearjournalcountryeditionlanguage
2018-01-01
10.1016/j.finel.2018.04.003http://hdl.handle.net/10447/289615