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.

The finite element implementation of 3D fractional viscoelastic constitutive models

Alotta, Gioacchino;
2018-01-01

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.
2018
3D constitutive models; Creep; Fractional viscoelasticity; Numerical modelling; Relaxation; Analysis; Engineering (all); Computer Graphics and Computer-Aided Design; Applied Mathematics
File in questo prodotto:
File Dimensione Formato  
Alo_Bar_DiP_Coc 2018 Postprint.pdf

Open Access dal 02/07/2022

Tipologia: Documento in Post-print
Licenza: Creative commons
Dimensione 2.77 MB
Formato Adobe PDF
2.77 MB Adobe PDF Visualizza/Apri
Alotta_2018_ Finite Element_editor.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 2.4 MB
Formato Adobe PDF
2.4 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/47172
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 36
  • ???jsp.display-item.citation.isi??? 28
social impact