A relation between a dynamic fracture model and quasi-static evolution

Versieux, Henrique

doi:10.1051/m2an/2015032

Cited by 4 publications

(13 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to [28], our dynamic gradient damage model (1) converges to the quasi-static model of [2] with the directional stability condition replaced by its first-order static equilibrium and damage criterion condition, supposing temporel regularity of the crack (as in the classical Griffith theory). We verify this result by imposing a small loading speed k/c ≈ 0.2% in the above antiplane tearing case.…”

Section: Quasi-static Limits Of the Dynamic Modelmentioning

confidence: 99%

Variational Approach to Dynamic Brittle Fracture via Gradient Damage Models

Li¹,

Marigo

Guilbaud³

et al. 2015

AMM

View full text Add to dashboard Cite

In this paper we present a family of gradient-enhanced continuum damage models which can be viewed as a regularization of the variational approach to fracture capable of predicting in a unified framework the onset and space-time dynamic propagation (growth, kinking, branching, arrest) of complex cracks in quasi-brittle materials under severe dynamic loading. The dynamic evolution problem for a general class of such damage models is formulated as a variational inequality involving the action integral of a generalized Lagrangian and its physical interpretation is given. Finite-element based implementation is then detailed and mathematical optimization methods are directly used at the structural scale exploiting fully the variational nature of the formulation. Finally, the link with the classical dynamic Griffith theory and with the original quasi-static model as well as various dynamic fracture phenomena are illustrated by representative numerical examples in quantitative accordance with theoretical or experimental results.

show abstract

Section: Quasi-static Limits Of the Dynamic Modelmentioning

confidence: 99%

Variational Approach to Dynamic Brittle Fracture via Gradient Damage Models

Li¹,

Marigo

Guilbaud³

et al. 2015

AMM

View full text Add to dashboard Cite

show abstract

“…In this work we study through formal asymptotic expansions the homogenization of a regularized fracture model. This regularized quasi static model was obtained in [14] in the limit of vanishing viscosity and inertia terms of a dynamic fracture model proposed by Bourdin, Larsen and Richardson [1]. This model is similar to the regularized version of the Francfort and Marigo model proposed in [3].…”

Section: Introductionmentioning

confidence: 84%

“…The difference between these two models concern the minimality condition imposed on the problem, while the regularized Francfort and Marigo model uses a global minimality condition ( see condition (c) in section 2 below) the regularized model from [14] has a separate minimality condition ( see condition (c) in section 2 below). We observe that in general the numerical approximations of the regularized Francfort and Marigo model correspond to approximations of the model satisfying the separate minimality condition; see [14] for more details.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A porous media fracture model based on homogenization theory

Galvis,

Versieux

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…According to [37], when the loading speed k is decreased the dynamic gradient damage model converges to the following first-order quasi-static gradient damage evolution model:…”

Section: Discontinuous Fracture Toughness Casesmentioning

confidence: 99%

Numerical investigation of dynamic brittle fracture via gradient damage models

Marigo

Guilbaud

et al. 2016

Adv. Model. and Simul. in Eng. Sci.

View full text Add to dashboard Cite

Background: Gradient damage models can be acknowledged as a unified framework of dynamic brittle fracture. As a phase-field approach to fracture, they are gaining popularity over the last few years in the computational mechanics community. This paper concentrates on a better understanding of these models. We will highlight their properties during the initiation and propagation phases of defect evolution. Methods: The variational ingredients of the dynamic gradient damage model are recalled. Temporal discretization based on the Newmark-β scheme is performed. Several energy release rates in gradient damage models are introduced to bridge the link from damage to fracture. Results and discussion: An antiplane tearing numerical experiment is considered. It is found that the phase-field crack tip is governed by the asymptotic Griffith's law. In the absence of unstable crack propagation, the dynamic gradient damage model converges to the quasi-static one. The defect evolution is in quantitative accordance with the linear elastic fracture mechanics predictions. Conclusion: These numerical experiments provide a justification of the dynamic gradient damage model along with its current implementation, when it is used as a phase-field model for complex real-world dynamic fracture problems.

show abstract

A relation between a dynamic fracture model and quasi-static evolution

Cited by 4 publications

References 10 publications

Variational Approach to Dynamic Brittle Fracture via Gradient Damage Models

Variational Approach to Dynamic Brittle Fracture via Gradient Damage Models

A porous media fracture model based on homogenization theory

Numerical investigation of dynamic brittle fracture via gradient damage models

Contact Info

Product

Resources

About