# Phase-field modeling of fracture for quasi-brittle materials

## TL;DR

This paper develops a phase-field model for fracture in quasi-brittle materials that incorporates a damage threshold, providing a more realistic representation of crack initiation and growth compared to traditional models.

## Contribution

It introduces a new phase-field fracture model with a damage threshold, systematically formulated within a variational framework and validated through 2D and 3D benchmark simulations.

## Key findings

- The model ensures an elastic stage before damage initiation.
- Good agreement with existing literature demonstrates the model's validity.
- Inclusion of a damage threshold improves fracture prediction accuracy.

## Abstract

This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack topology. Within the computational mechanics community, several studies have treated the issue of modeling fracture using phase fields. Most of these studies have used an approach that implies the lack of a damage threshold. We herein explore an alternative model that includes a damage threshold and study how it compares with the most popular approach. The formulation is systematically explained within a rigorous variational framework. Subsequently, we present the corresponding three-dimensional finite element discretization that leads to a straightforward numerical implementation. Benchmark simulations in two dimensions and three dimensions are then presented. The results show that while an elastic stage and a damage threshold are ensured by the present model, good agreement with the results reported in the literature can be obtained, where such features are generally absent.