Gradient Damage Models and Their Use to Approximate Brittle Fracture
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In this paper, a variational approach to brittle fracture approximates the crack evolution in an elastic solid through the use of gradient damage models, and a stability criterion in terms of the positivity of the second derivative of the total energy under the unilateral constraint induced by the irreversibility of damage is introduced.Abstract:
In its numerical implementation, the variational approach to brittle fracture approximates the crack evolution in an elastic solid through the use of gradient damage models. In this article, we first formulate the quasi-static evolution problem for a general class of such damage models. Then, we introduce a stability criterion in terms of the positivity of the second derivative of the total energy under the unilateral constraint induced by the irreversibility of damage. These concepts are applied in the particular setting of a one-dimensional traction test. We construct homogeneous as well as localized damage solutions in a closed form and illustrate the concepts of loss of stability, of scale effects, of damage localization, and of structural failure. Considering several specific constitutive models, stressread more
Citations
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A phase-field description of dynamic brittle fracture
TL;DR: It is shown that the combination of the phase-field model and local adaptive refinement provides an effective method for simulating fracture in three dimensions.
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A unified phase-field theory for the mechanics of damage and quasi-brittle failure
TL;DR: In this paper, a unified phase-field theory for the mechanics of damage and quasi-brittle failure is proposed within the framework of thermodynamics, where the crack phase field and its gradient are introduced to regularize the sharp crack topology in a purely geometric context.
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Phase field modeling of fracture in multi-physics problems. Part I. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids
TL;DR: In this paper, a generalization of recently developed continuum phase field models for brittle fracture towards fully coupled thermo-mechanical and multi-physics problems at large strains is presented.
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Phase Field Modeling of Fracture in Multi-Physics Problems. Part II. Coupled Brittle-to-Ductile Failure Criteria and Crack Propagation in Thermo-Elastic-Plastic Solids
TL;DR: In this article, a generalization of recently developed continuum phase field models from brittle to ductile fracture coupled with thermo-plasticity at finite strains is presented, which uses a geometric approach to the diffusive crack modeling based on the introduction of a balance equation for a regularized crack surface.
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A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects
TL;DR: In this paper, a cubic degradation function was proposed to provide a stress-strain response prior to crack initiation, which more closely approximates linear elastic behavior, and a derivation of the governing equations in terms of a general energy potential from balance laws that describe the kinematics of both the body and phase-field.
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Particle reinforced aluminium and magnesium matrix composites
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