A non‐local continuum damage approach to model dynamic crack branching

Wolff, Cyprien; Richart, Nicolas; Molinari, Jean‐François

doi:10.1002/nme.4837

Cited by 49 publications

(24 citation statements)

References 35 publications

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“…This problem has been previously investigated experimentally in [72] (it is also quite close to the experiments of [60]) and from a numerical point of view using cohesive elements [73] and a non-local integral damage model [67]. Contrary to more traditional numerical benchmark problems in dynamic branching such as those investigated in [7,8,29] where a constant stress echelon loading is applied, in this particular geometry, no stress waves are produced by the loading but only by crack propagation.…”

Section: Position Of the Problemmentioning

confidence: 82%

“…The geometry and boundary conditions are represented in Figure 3 and are identical to those used in [73,67]: the plate is 32 mm wide and 16 mm high with a 4 mm pre-notch and modeled as a 2D plane-stress medium. It is pre-strained by applying uniform displacements ±∆U in the vertical direction on the bottom and top surfaces.…”

Section: Position Of the Problemmentioning

confidence: 99%

“…One can mention the non-local integral approach [53,31,67], gradient-enhanced models [51], eigenerosion [49], peridynamics [7], thick-level sets [47] and phase-field approaches, which will be described later in more details. Generally, such non-local approaches do not require additional criteria to obtain branched patterns [34,27,29,30].…”

Section: Finite Element Models Of Dynamic Crack Propagationmentioning

confidence: 99%

“…Fig. 3 Pre-strained PMMA plate problem (left) and crack patterns (right) sketched from experimental observations [72] for different imposed displacements (taken from [67]). For low loading levels, single crack propagation is observed.…”

Section: Numerical Aspectsmentioning

confidence: 99%

See 3 more Smart Citations

Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms

2016

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Section: Position Of the Problemmentioning

confidence: 82%

Section: Position Of the Problemmentioning

confidence: 99%

Section: Finite Element Models Of Dynamic Crack Propagationmentioning

confidence: 99%

Section: Numerical Aspectsmentioning

confidence: 99%

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Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms

2016

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“…New sound approaches based on physical behavior are needed. Different damage models have been successfully used to represent crack branching in brittle materials (see for example the work of Ha and Babaru [12] and Wolff et al [13]). In this contribution a rate enhanced version of the latest Mazars damage model [14] is used to numerically study dynamic crack branching in concrete.…”

Section: Introductionmentioning

confidence: 99%

Simulation of dynamic behavior of quasi-brittle materials with new rate dependent damage model

Pereira

Weerheijm²,

Sluijs³

2016

Proceedings of the 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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Abstract. In concrete often complex fracture and fragmentation patterns develop when subjected to high straining loads. The proper simulation of the dynamic cracking process in concrete is crucial for good predictions of the residual bearing capacity of structures in the risk of being exposed to extraordinary events like explosions, high velocity impacts or earthquakes.As it is well known, concrete is a highly rate dependent material. Experimental and numerical studies indicate that the evolution of damage is governed by complex phenomena taking place simultaneously at different material scales, i.e. micro, meso and macro-scales. Therefore, the constitutive law, and its rate dependency, must be adjusted to the level of representation. For a proper phenomenological (macroscopic) representation of the reality, the constitutive law has to explicitly describe all phenomena taking place at the lower material scales. Macro-scale inertia effects are implicitly simulated by the equation of motion.In the current paper, dynamic crack propagation and branching is studied with a new rate-dependent stress-based nonlocal damage model. The definition of rate in the constitutive law is changed to account for the inherent meso-scale structural inertia effects. This is accomplished by a new concept of effective rate which governs the dynamic delayed response of the material to variations of the deformation (strain) rate, usually described as micro-inertia effects. The proposed model realistically simulates dynamic crack propagation and crack branching phenomena in concrete.

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Dynamic soil consolidation model using a nonlocal continuum poroelastic damage approach

Chen

Mobasher

Waisman

2021

Num Anal Meth Geomechanics

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We present a novel dynamic poroelastic model for soil consolidation in an isotropic homogeneous fluid saturated porous media. A nonlocal integral‐type continuum damage formulation is applied to describe the damage evolution under dynamic excitations, in which a bilinear damage law is assumed. The governing equations are obtained by considering the conservation of momentum and mass balance for the solid–fluid mixtures, in which the fluid flow obeys Darcy's seepage law in the entire domain. The numerical solution of the fully coupled problem is achieved via a mixed FEM displacement–pressure false(u−pfalse)$(u-p)$ element formulation. The mechanical equilibrium equations are evolved in time using a Newmark method and the resulting nonlinear system is solved via a Newton–Raphson method. Consistent linearization is then used to obtain the block Jacobian matrix analytically and the linear system is solved monolithically at each time step. Several numerical results are presented to study soil consolidation problems under harmonic excitations. We investigate the time‐dependence response of the skeleton displacement, pressure, and damage evolution. In addition, the examples demonstrate that the nonlocal integral‐type damage model can effectively overcome mesh dependence and yield smooth behavior.

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A non‐local continuum damage approach to model dynamic crack branching

Cited by 49 publications

References 35 publications

Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms

Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms

Simulation of dynamic behavior of quasi-brittle materials with new rate dependent damage model

Dynamic soil consolidation model using a nonlocal continuum poroelastic damage approach

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