A Unified Abaqus Implementation of the Phase Field Fracture Method Using Only a User Material Subroutine

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.

Phase-field fracture irreversibility using the slack variable approach

“…the centre of the pin. Furthermore, [23] opted for l = 0.1 [mm], in this manuscript as well as in [48], l = 0.25 [mm]. Finally, from Figure 8b, it observed that the final phase-field fracture topology does match the experimentally observed fracture patterns in Figure 7.…”

“…Figure 8a presents the load-displacement curves obtained using the Lagrange Multiplier Method and the Penalty method, along with those from the literature [23,48]. The curves corresponding to the Lagrange Multiplier Method and the Penalty method coincide, and predict peak loads close to those obtained in [23] and [48]. However, the load-displacement curves are significantly different from [23].…”

A general framework for decomposing the phase field fracture driving force, particularised to a Drucker–Prager failure surface

“…As described in Appendix C, we take advantage of the analogy between the phase field evolution law and the heat transfer equation to implement the model into the finite element package ABAQUS using solely a user-material subroutine (UMAT) (see Refs. [36,37]). Maurini [33], where a Drucker-Prager failure surface was also adopted.…”

Thermodynamically consistent linear-gradient damage model in Abaqus

“…Recently, Navidtehrani et al [52] proposed a clever technique to use Abaqus's coupled thermal-stress analysis module to solve the phase-field fracture problem in a single UMAT code. There are promising solutions [67,53] in the literature to replace the quadratic phase-field representation with a linear function and an energy threshold. However, a thermodynamically consistent scheme has yet to be proposed in the finite element code Abaqus (see the discussion on existing models).…”