Explicit dynamics with a non‐local damage model using the thick level set approach

Moreau, K.; Moës, Nicolas; Picart, Didier; Stainier, Laurent

doi:10.1002/nme.4824

Cited by 30 publications

(29 citation statements)

References 45 publications

(119 reference statements)

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“…In subsequent publications, the authors will build upon the current work in order to explore three new aspects: first, the consideration of an alternative residual-based dissipative mechanism widely known as Petrov-Galerkin stabilisation [40]; second, the consideration of non-isothermal materials [43] and third, an adaptation of the current computational framework to highstrain ductile fracture application [72] incorporating an alternative Updated Lagrangian formalism in the style of [17].…”

Section: Discussionmentioning

confidence: 99%

A new Jameson–Schmidt–Turkel Smooth Particle Hydrodynamics algorithm for large strain explicit fast dynamics

Lee

Gil

Greto

et al. 2016

Computer Methods in Applied Mechanics and Engineering

128

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This paper presents a new Smooth Particle Hydrodynamics (SPH) computational framework for large strain explicit solid dynamics. A mixed-based set of Total Lagrangian conservation laws [1,2] is presented in terms of the linear momentum and an extended set of geometric strain measures, comprised of the deformation gradient, its co-factor and the Jacobian. Taking advantage of this representation, the main aim of this paper is the adaptation of the very efficient Jameson-Schmidt-Turkel (JST) algorithm [3], extensively used in computational fluid dynamics, to a SPH based discretisation of the mixed-based set of conservation laws, with three key distinct novelties. First, a conservative JST-based SPH computational framework is presented with emphasis in nearly incompressible materials. Second, the suppression of numerical instabilities associated with the non-physical zero-energy modes is addressed through a well-established stabilisation procedure. Third, the use of a discrete angular momentum projection algorithm is presented in conjunction with a monolithic Total Variation Diminishing Runge-Kutta time integrator in order to guarantee the global conservation of angular momentum. For completeness, exact enforcement of essential boundary conditions is incorporated through the use of a Lagrange multiplier projection technique. A series of challenging numerical examples (e.g. in the near incompressibility regime) are examined in order to assess the robustness and accuracy of the proposed algorithm. The obtained results are benchmarked against a wide spectrum of alternative numerical strategies.

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Section: Discussionmentioning

confidence: 99%

A new Jameson–Schmidt–Turkel Smooth Particle Hydrodynamics algorithm for large strain explicit fast dynamics

Lee

Gil

Greto

et al. 2016

Computer Methods in Applied Mechanics and Engineering

128

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“…In contrast, we reinitialize by projecting the level-set field from all local minima, an approach that preserves the individual damage zones that represent cracks regardless of their proximity, until the damage gradient forces their coalescence. Another contribution is the time-independent softening constitutive model which allows for an exact level-set update in the explicit approach, whereas in a previous dynamic implementation, a delay-damage evolution model had been employed for the update [35]. We find that our specific choice of post-yield function achieves the expected fragmentation results while other constitutive models may not.…”

Section: Introductionmentioning

confidence: 91%

“…as a function of the residual function R and its derivative T , where [j] indicates the iteration number: (47) The iterative level-set update to bring the residual function to zero (44) can be seen as an implicit time integration of the level-set equation within each time-step:φ + φ ,xuφ = 0 whereφ = ∆φ/∆t is the extension velocity [36,35]. This Newton-Raphson solve represents a trade-off between high accuracy and computational expediency; one may limit the solve to one iteration per damage zone to minimize the computational cost of the non-local update or use additional iterations to further minimize the residual.…”

Section: Damage Evolutionmentioning

confidence: 99%

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The Thick Level-Set model for dynamic fragmentation

Stershic

Dolbow

Moës

2017

Engineering Fracture Mechanics

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The Thick Level-Set (TLS) model is implemented to simulate brittle media undergoing dynamic fragmentation. This non-local model is discretized by the finite element method with damage represented as a continuous field over the domain. A level-set function defines the extent and severity of damage, and a length scale is introduced to limit the damage gradient. Numerical studies of one-dimensional problems demonstrate that the proposed method reproduces the rate-dependent energy dissipation and fragment length observations from analytical, numerical, and experimental approaches. Additional studies emphasize the importance of appropriate bulk constitutive models and sufficient spatial resolution of the length scale.

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“…As can be seen from Figure 12, the crack speed is well bounded by the Rayleigh wave speed (here 0:7c R ), the theoretical limiting speed for an in-plane crack. It should be noted that this upper bound is rooted in the stability condition (7) and the energy balance (8), contrary to the thick level set approach [43] where this limiting speed is considered as an additional modeling parameter. The crack length is approximately 90 mm at t D 8 10 5 s when the crack is about to reach the boundary (cf.…”

Section: Edge-cracked Plate Under Shearing Impactmentioning

confidence: 99%

Gradient damage modeling of brittle fracture in an explicit dynamics context

Marigo

Guilbaud

et al. 2016

Numerical Meth Engineering

123

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International audienceIn this contribution we propose a dynamic gradient damage model as a phase-field approach for studying brutal fracture phenomena in quasi-brittle materials under impact-type loading conditions. Several existing approaches to account for the tension-compression asymmetry of fracture behavior of materials are reviewed. A better understanding of these models is provided through a uniaxial traction experiment. We then give an efficient numerical implementation of the model in an explicit dynamics context. Simulations results obtained with parallel computing are discussed both from a computational and physical point of view. Different damage constitutive laws and tension-compression asymmetry formulations are compared with respect to their aptitude to approximate brittle fracture

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Explicit dynamics with a non‐local damage model using the thick level set approach

Abstract: International audienc

Cited by 30 publications

References 45 publications

A new Jameson–Schmidt–Turkel Smooth Particle Hydrodynamics algorithm for large strain explicit fast dynamics

A new Jameson–Schmidt–Turkel Smooth Particle Hydrodynamics algorithm for large strain explicit fast dynamics

The Thick Level-Set model for dynamic fragmentation

Gradient damage modeling of brittle fracture in an explicit dynamics context

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