Three Dimensional CS-FEM Phase-Field Modeling Technique for Brittle Fracture in Elastic Solids

Sauradeep Bhowmick,Gui-Rong Liu

doi:10.3390/app8122488

Sauradeep Bhowmick, Gui-Rong Liu

Open Access

https://doi.org/10.3390/app8122488

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Journal: Applied sciences	Publication Date: Dec 4, 2018
Citations: 23	License type: CC BY 4.0

Affiliation: University of Cincinnati

Abstract

The cell based smoothed finite element method (CS-FEM) was integrated with the phase-field technique to model brittle fracture in 3D elastic solids. The CS-FEM was used to model the mechanics behavior and the phase-field method was used for diffuse fracture modeling technique where the damage in a system was quantified by a scalar variable. The integrated CS-FEM phase-field approach provides an efficient technique to model complex crack topologies in three dimensions. The detailed formulation of our combined method is provided. It was implemented in the commercial software ABAQUS using its user-element (UEL) and user-material (UMAT) subroutines. The coupled system of equations were solved in a staggered fashion using the in-built non-linear Newton–Raphson solver in ABAQUS. Eight node hexahedral (H8) elements with eight smoothing domains were coded in CS-FEM. Several representative numerical examples are presented to demonstrate the capability of the method. We also discuss some of its limitations.

Highlights

In the past decade, Liu et al [1,2] generalized the gradient smoothing approach in meshfree method [3] and proposed the smoothed finite element method(S-FEM) to overcome some of the inherent shortcomings of the classical finite element method(FEM) such as overly stiff behavior, sensitivity to mesh distortions, and stress inaccuracy
We present several numerical examples to validate the accuracy of the 3D-CSFEM-phase field method for linear elastic brittle fracture and to discuss some shortcomings of the implementation in ABAQUS
The cell based smoothed finite element method (CS-FEM)-H8 element is implemented in the commercial platform of ABAQUS

Summary

Introduction

Liu et al [1,2] generalized the gradient smoothing approach in meshfree method [3] and proposed the smoothed finite element method(S-FEM) to overcome some of the inherent shortcomings of the classical finite element method(FEM) such as overly stiff behavior, sensitivity to mesh distortions, and stress inaccuracy. The SFEM combines the FEM with the traditional meshfree methods in producing more accurate results with higher efficiency [1,2]. It uses the base mesh of the FEM and reconstructs the strain field using the gradient smoothing technique. The node based smoothing domains (NS-FEM) produce upper bound solutions for force driven problems [7]

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