Identifying the crack path for the phase field approach to fracture with non-maximum suppression

A new continuous-discontinuous strategy for the computational modeling of crack propagation within the context of phase-field models of fracture is presented. The method is designed to introduce and update a sharp crack surface within an evolving damage band and to enhance the kinematics of the finite element approximation accordingly. The proposed approach relies on three key elements. First, we propose the use of a crack length functional to provide a trigger for initiating a continuous to discontinuous transition. Next, the crack path identification is addressed by introducing the concept of an auxiliary damage field that varies with an extension of the sharp crack surface. The sharp crack surface is extended through an optimization algorithm, in which the difference between the auxiliary field and the actual damage field stemming from the phase-field framework is minimized. Finally, a strong discontinuity is inserted in the wake of the diffuse crack tip with the extended finite element method, completing the continuous to discontinuous transition. Several benchmark problems in two-dimensional quasi-static fracture mechanics are presented to demonstrate the accuracy and robustness of the method. KEYWORDS crack propagation, finite elements, optimization, phase-field approach, X-FEM Int J Numer Methods Eng. 2018;116:1-20.wileyonlinelibrary.com/journal/nme

“…A solution for the damage field, with a sharp crack centered at x =0, is found multiplying with

\frac{normald d}{normald x}

and making use of the fact that the stress is constant, to obtain

\frac{d}{normald x} ([], \frac{G_{c} d^{2}}{2 l} - \frac{σ^{2}}{2 E {false(1 - d false)}^{2}} - \frac{1}{2} {((), \frac{normald d}{normald x})}^{2} G_{c} l) = 0 .

For a fully developed crack, ie, σ = 0, and by applying boundary conditions d (0)=1 and d ( ∞ )=0, we find

d false(x false) = \exp ((), - \frac{false| x false|}{l})

d_{Γ} false(boldx, normalΓ false) : boldx \mapsto \exp ((), - \frac{dist false(boldx, normalΓ false)}{l}),

where

dist false(boldx, normalΓ false) ≔ \inf_{x^{*} \in normalΓ} false| boldx - x^{*} false|

is the minimal distance from x to Γ.…”

Section: The Phase‐field Approach To Brittle Fracturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An optimization‐based phase‐field method for continuous‐discontinuous crack propagation

Geelen

Liu

Dolbow

et al. 2018

“…Another global approach is that of Geelen et al: in the context of a continuous‐discontinuous phase‐field model, the crack is located by fitting two fields, ie, the mechanical damage phase‐field and a geometrical auxiliary damage field, which can be regarded as a diffuse representation of the discontinuity. This fitting is carried out by solving a minimization problem …”

Section: Model Formulationmentioning

confidence: 99%

A continuous‐discontinuous model for crack branching

Tamayo-Mas

Feliu‐Fabà

Casado‐Antolin

et al. 2019

Summary A new continuous‐discontinuous model for fracture that accounts for crack branching in a natural manner is presented. It combines a gradient‐enhanced damage model based on nonlocal displacements to describe diffuse cracks and the extended finite element method (X‐FEM) for sharp cracks. Its most distinct feature is a global crack tracking strategy based on the geometrical notion of medial axis: the sharp crack propagates following the direction dictated by the medial axis of a damage isoline. This means that, if the damage field branches, the medial axis automatically detects this bifurcation, and a branching sharp crack is thus easily obtained. In contrast to other existing models, no special crack‐tip criteria are required to trigger branching. Complex crack patterns may also be described with this approach, since the X‐FEM enrichment of the displacement field can be recursively applied by adding one extra term at each branching event. The proposed approach is also equipped with a crack‐fluid pressure, a relevant feature in applications such as hydraulic fracturing or leakage‐related events. The capabilities of the model to handle propagation and branching of cracks are illustrated by means of different two‐dimensional numerical examples.

A phase‐field method for modeling cracks with frictional contact

Fei

Choo

2019

We introduce a phase-field method for continuous modeling of cracks with frictional contacts. Compared with standard discrete methods for frictional contacts, the phase-field method has two attractive features: (1) it can represent arbitrary crack geometry without an explicit function or basis enrichment, and (2) it does not require an algorithm for imposing contact constraints. The first feature, which is common in phase-field models of fracture, is attained by regularizing a sharp interface geometry using a surface density functional. The second feature, which is a unique advantage for contact problems, is achieved by a new approach that calculates the stress tensor in the regularized interface region depending on the contact condition of the interface. Particularly, under a slip condition, this approach updates stress components in the slip direction using a standard contact constitutive law, while making other stress components compatible with stress in the bulk region to ensure non-penetrating deformation in other directions. We verify the proposed phase-field method using stationary interface problems simulated by discrete methods in the literature. Subsequently, by allowing the phase field to evolve according to brittle fracture theory, we demonstrate the proposed method's capability for modeling crack growth with frictional contact.