4,597 research outputs found
Phase-field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy
Crack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic materials. Furthermore, when this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. This problem interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Here, we propose a variational phase-field model for strongly anisotropic fracture, which resorts to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture and reproduce strikingly well recent experimental observations.Peer ReviewedPostprint (author’s final draft
High-accuracy phase-field models for brittle fracture based on a new family of degradation functions
Phase-field approaches to fracture based on energy minimization principles
have been rapidly gaining popularity in recent years, and are particularly
well-suited for simulating crack initiation and growth in complex fracture
networks. In the phase-field framework, the surface energy associated with
crack formation is calculated by evaluating a functional defined in terms of a
scalar order parameter and its gradients, which in turn describe the fractures
in a diffuse sense following a prescribed regularization length scale. Imposing
stationarity of the total energy leads to a coupled system of partial
differential equations, one enforcing stress equilibrium and another governing
phase-field evolution. The two equations are coupled through an energy
degradation function that models the loss of stiffness in the bulk material as
it undergoes damage. In the present work, we introduce a new parametric family
of degradation functions aimed at increasing the accuracy of phase-field models
in predicting critical loads associated with crack nucleation as well as the
propagation of existing fractures. An additional goal is the preservation of
linear elastic response in the bulk material prior to fracture. Through the
analysis of several numerical examples, we demonstrate the superiority of the
proposed family of functions to the classical quadratic degradation function
that is used most often in the literature.Comment: 33 pages, 30 figure
An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS
We present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff–Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell’s mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith’s theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires C1-continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-α method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton–Raphson scheme. The interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching
Phase-field modelling of fracture in single crystal plasticity
We propose a phase-field model for ductile fracture in a single crystal within the kinematically linear
regime, by combining the theory of single crystal plasticity as formulated in Gurtin et al. (2010) and
the phase-field formulation for ductile fracture proposed by Ambati et al. (2015) . The model introduces
coupling between plasticity and fracture through the dependency of the so-called degradation function
from a scalar global measure of the accumulated plastic strain on all slip systems. A viscous regularization
is introduced both in the treatment of plasticity and in the phase-field evolution equation. Testing of
the model on two examples for face centred cubic single crystals indicates that fracture is predicted to
initiate and develop in the regions of the maximum accumulated plastic strain, which is in agreement
with phenomenological observations. A rotation of the crystallographic unit cell is shown to affect the
test results in terms of failure pattern and corresponding global and local response
Mixed displacement-pressure-phase field framework for finite strain fracture of nearly incompressible hyperelastic materials
The favored phase field method (PFM) has encountered challenges in the finite
strain fracture modeling of nearly or truly incompressible hyperelastic
materials. We identified that the underlying cause lies in the innate
contradiction between incompressibility and smeared crack opening. Drawing on
the stiffness-degradation idea in PFM, we resolved this contradiction through
loosening incompressible constraint of the damaged phase without affecting the
incompressibility of intact material. By modifying the perturbed Lagrangian
approach, we derived a novel mixed formulation. In numerical aspects, the
finite element discretization uses the classical Q1/P0 and high-order P2/P1
schemes, respectively. To ease the mesh distortion at large strains, an
adaptive mesh deletion technology is also developed. The validity and
robustness of the proposed mixed framework are corroborated by four
representative numerical examples. By comparing the performance of Q1/P0 and
P2/P1, we conclude that the Q1/P0 formulation is a better choice for finite
strain fracture in nearly incompressible cases. Moreover, the numerical
examples also show that the combination of the proposed framework and
methodology has vast potential in simulating complex peeling and tearing
problem
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