Models for Dynamic Fracture Based on Griffith’s Criterion

Larsen, Christopher J.

doi:10.1007/978-90-481-9195-6_10

Cited by 33 publications

(42 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While in the quasi-static case, the ( ) limit as ε → 0 of the regularized model is well known, its derivation in our model is a very complicated and largely open mathematical problem which we do not address in this study. For a discussion of corresponding sharp-interface models, see Larsen (2010). The work presented here is quite theoretical by nature.…”

Section: Introductionmentioning

confidence: 98%

A time-discrete model for dynamic fracture based on crack regularization

2010

Self Cite

View full text Add to dashboard Cite

We propose a discrete time model for dynamic fracture based on crack regularization. The advantages of our approach are threefold: first, our regularization of the crack set has been rigorously shown to converge to the correct sharp-interface energy Ambrosio and Tortorelli (Comm.the time-step tends to zero, to solutions of the correct continuous time model Larsen (Math Models Methods Appl Sci 20:1021-1048, 2010). Furthermore, in implementing this model, we naturally recover several features, such as the elastic wave speed as an upper bound on crack speed, and crack branching for sufficiently rapid boundary displacements. We conclude by comparing our approach to so-called "phase-field" ones. In particular, we explain why phase-field approaches are good for approximating free boundaries, but not the free discontinuity sets that model fracture.

show abstract

Section: Introductionmentioning

confidence: 98%

A time-discrete model for dynamic fracture based on crack regularization

2010

Self Cite

View full text Add to dashboard Cite

show abstract

“…Second, since a stationary crack will always satisfy the above criteria, one needs to add a principle requiring that, in certain situations, the crack must grow. Such a principle, termed maximal dissipation, was formulated in [13], in a weak sense that does not require regularity of the crack.…”

Section: Introductionmentioning

confidence: 99%

“…An exception to this is given by phase-field models, which were formulated and studied in [2,14]. These papers led to the maximal dissipation approach proposed in [13].…”

Section: Introductionmentioning

confidence: 99%

Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition

Maso

Larsen

Toader

2016

Journal of the Mechanics and Physics of Solids

Self Cite

View full text Add to dashboard Cite

Abstract. There are very few existence results for fracture evolution, outside of globally minimizing quasi-static evolutions. Dynamic evolutions are particularly problematic, due to the difficulty of showing energy balance, as well as of showing that solutions obey a maximal dissipation condition, or some similar condition that prevents stationary cracks from always being solutions. Here we introduce a new weak maximal dissipation condition and show that it is compatible with cracks constrained to grow smoothly on a smooth curve. In particular, we show existence of dynamic fracture evolutions satisfying this maximal dissipation condition, subject to the above smoothness constraints, and exhibit explicit examples to show that this maximal dissipation principle can indeed rule out stationary cracks as solutions.

show abstract

“…Conditions i) and ii) follow, e.g., from [15], and a principle like iii) is necessary, since otherwise a stationary crack with elastodynamics off of it will always be a solution. In [16] this is discussed in some more detail, and a maximal dissipation condition is proposed for iii), but it is too early to claim any acceptance of this principle.…”

Section: Introductionmentioning

confidence: 99%

“…However, we are unable to prove uniqueness or energy balance. We note that a lack of energy balance, where the energy includes only the kinetic and elastic energies, is in fact desirable, as only then can the total energy, including the surface energy of the crack, be balanced, as in the models formulated in [16]. We also note that a natural idea for proving existence for those models, which in addition to balance of the total energy have a maximality property of Γ(t) , would be to find u n (t i+1 ) and Γ n (t i+1 ) by minimizing…”

Section: Introductionmentioning

confidence: 99%

Existence for wave equations on domains with arbitrary growing cracks

Maso¹,

Larsen²

2011

Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur.

View full text Add to dashboard Cite

Abstract. In this paper we formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations using Sobolev spaces. We study both damped and undamped equations, showing existence and, for the damped equation, uniqueness and energy conservation.

show abstract

Models for Dynamic Fracture Based on Griffith’s Criterion

Cited by 33 publications

References 7 publications

A time-discrete model for dynamic fracture based on crack regularization

A time-discrete model for dynamic fracture based on crack regularization

Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition

Existence for wave equations on domains with arbitrary growing cracks

Contact Info

Product

Resources

About