Numerical Implementation of a Cohesive Zone Element Coupled with Continuum Damage Mechanics Volume Elements

Abstract

ABSTRACT: The objective of this paper is to develop a two-dimensional Cohesive Element Model (CZM) coupled with a Continuum Damage Mechanics (CDM) model. The novel cohesive element model allows expressing the separation criterion in terms of the damage tensor used in the CDM model implemented in the neighboring volume elements. Above a critical damage value, debonding triggers. The residual tensile and shearing strength of the CZM follow a linear softening law. The proposed model was calibrated against published triaxial compression tests conducted on shale. Single-cohesive zone tests highlight that the proposed approach allows simulation of hardening during damage propagation followed by softening and failure. The model predicts different strengths in tension and compression and different stiffnesses and strengths for different confinements. A boundary-value problem was solved by using a mesh with embedded cohesive zones at all interfaces. It is shown that the 2D model can predict realistic stress/strain curves, stress and strain fields, and fracture patterns for biaxial compression tests. The advantage of the proposed approach is that it can be used to simulate diffuse damage followed by localized fracture with a smooth transfer of field variables between the finite and cohesive elements. 1 INTRODUCTION Simulating fracture propagation from the inception of microscopic cracks to the localization of macroscopic fractures remains a challenge. To date, finite element modeling approaches based on Continuum Damage Mechanics (CDM) and Cohesive Zone Models (CZM) emerge as the most widely used approaches. The goal of this study is to couple both, in order to take advantage of the benefits that each technique can bring. In CDM, sets micro-cracks are represented by a damage tensor, which is modeled as an internal variable within the framework of thermodynamic irreversible processes. Stiffness and strength decrease as damage accumulates. CDM models can be formulated based on phenomenological principles (Xu and Arson, 2014) or micromechanics principles (Jin and Arson, 2017). Exhaustive reviews of damage rock mechanics are available in (Arson and Gatmiri, 2008; Arson, 2020).