A phase field approach to fracture for hyperelastic and visco-hyperelastic materials applied to pre-stressed cylindrical structures

Abstract

In this investigation, the mechanical modeling of nonlinear visco-hyperelastic residually stressed materials obtained from an invariant-based constitutive energy framework is coupled with the phase field approach to fracture. The main target regards the extension of the phase field method to simulate pre-stressed cylindrical structures subjected to monotonic axial pulling load upon failure. This formulation is incorporated into a numerical procedure using the Finite Element Method (FEM), in particular, it is implemented in the commercial FE package ABAQUS as a user subroutine UMAT. Results suggest the dependence of the mechanical behavior and the crack pattern of these structures on not only viscous parameters like the relaxation time and the displacement rate, but also on the strength of the residual stress field, which in turn depends on geometrical characteristics of the cylindrical structure such as the radius or the length. A range of solutions related to crack propagation is shown for different cylindrical structures, from azimuthal crack propagation to axial one. The proposed framework aims to provide an extended application for the already-defined visco-hyperelastic formulation by the inclusion of residual stresses.

Keywords:

• Residual stress
• phase field
• viscoelasticity
• hyperelasticity
• finite element method
• cylindrical structures

Acknowledgements

AVG would like to acknowledge the financial support from Erasmus + funding (Project 2020-1-IT02-KA103-078114) for his visiting time in University of Seville during the period 15th June–15th September 2021.

JR is grateful to Consejería de Economía y Conocimiento, Junta de Andalucía, and European Regional Development Fund (Project P20-00595).

MP would like to acknowledge the financial support from the Italian Ministry of Education, University and Research (MIUR) to the research project of relevant national interest (PRIN 2017) “XFAST-SIMS: Extra fast and accurate simulation of complex structural systems” (MUR: 20173C478N).

All the authors would like to acknowledge Prof. E. Martínez-Pañeda (Imperial College, United Kingdom) for the fruitful discussions and his kind guidance of the implementation of the phase field method as unified user-material subroutine in ABAQUS.

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Notes

1 This is required since previous versions of ABAQUS 2019 do not compute properly the volumetric heat generation.