Abstract
We present a simple and robust implementation of the phase field fracture method in Abaqus. Unlike previous works, only a user material (UMAT) subroutine is used. This is achieved by exploiting the analogy between the phase field balance equation and heat transfer, which avoids the need for a user element mesh and enables taking advantage of Abaqus’ in-built features. A unified theoretical framework and its implementation are presented, suitable for any arbitrary choice of crack density function and fracture driving force. Specifically, the framework is exemplified with the so-called AT1, AT2 and phase field-cohesive zone models (PF-CZM). Both staggered and monolithic solution schemes are handled. We demonstrate the potential and robustness of this new implementation by addressing several paradigmatic 2D and 3D boundary value problems. The numerical examples show how the current implementation can be used to reproduce numerical and experimental results from the literature, and efficiently capture advanced features such as complex crack trajectories, crack nucleation from arbitrary sites and contact problems. The code developed is made freely available.
Highlights
We present a generalized theoretical and numerical framework that encapsulates what are arguably the three most popular phase field fracture models presented to date: (i) the so-called AT2 model [24], based on the Ambrosio and Tortorelli regularization of the Mumford-Shah functional [39], (ii) the AT1 model [40], which includes an elastic phase in the damage response, and (iii) the phase field-cohesive zone model phase field-cohesive zone models (PF-CZM) [41,42], aimed at providing an explicit connection to the material strength
The current stress-strain state is used to determine the driving force for fracture, H. Both C0 and σ0 are degraded using the current value of the phase field φ, which is passed to the subroutine by Abaqus, such that C = g(φ)C0 and σ = g(φ)σ0
We have presented a unified Abaqus implementation of the phase field fracture method
Summary
Variational phase field methods for fracture are enjoying a notable success [1,2]. Among many others, applications include shape memory alloys [3], glass laminates [4,5], hydrogen-embrittled alloys [6,7], dynamic fracture [8,9], fiber-reinforced composites [10,11,12,13], functionally graded materials [14,15,16], fatigue crack growth [17,18], and masonry structures [19]. The development of phase field fracture implementations in the commercial package Abaqus has received particular attention [32,33,34,35,36,37,38], due to its popularity in the solid mechanics community These works require the use of multiple user subroutines, most often including a user element (UEL) subroutine. The simple yet robust implementation presented is achieved by taking advantage of the analogy between the phase field evolution equation and heat transfer This greatly simplifies the use of Abaqus for conducting phase field fracture studies and enables taking advantage of the many in-built features provided by this commercial package.
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