Ordering effect of kinetic energy on dynamic deformation of brittle solids

Mastilović, Sreten; Rinaldi, Antonio; Krajčinović, Dušan

doi:10.1016/j.mechmat.2007.10.003

Cited by 14 publications

(45 citation statements)

References 21 publications

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“…The time histories of the normal stress (in the loading direction) divided by the corresponding strain rate and the Poisson's ratio are presented in Figure 1. It is evident from Figure 1(a) that the two characteristic slopes are the short-time and long-time moduli (E ð"Þ st ,E ð"Þ lt , respectively 1 ) observed by Mastilovic et al (2008), presented herein in a more convenient graph.…”

Section: Lattice Simulationsmentioning

confidence: 79%

“…The particular model used herein is described in a number of papers published over the last decade [see for instance, Mastilovic et al (2008) and references therein]; the only, but noteworthy, difference from those previous studies is that the present simulation setup does not include the application of the initial velocity field that cancels out the inertial effects. Thus, to put it as succinctly as possible, the lattice is formed by 'continuum particles' located at lattice nodes (1000 Â 1201) and connected by nonlinear springs characterized by a critical elongation defining rupture.…”

Section: Lattice Simulationsmentioning

confidence: 99%

“…The solid curve in Figure 1(a) is common for all loading rates that remain elastic for the given graph limits; departures from that curve mark onsets of the inelastic deformation that is characterized by damage nucleation and, depending on the loading rate, different levels of cooperative phenomena (Mastilovic et al, 2008). Thus, the only difference between the moderate and the high loading rates is that in the later case specimens fail before the E ð"Þ st !…”

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confidence: 99%

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A Note on Short-time Response of Two-dimensional Lattices during Dynamic Loading

Mastilović

2008

International Journal of Damage Mechanics

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The disordered 2D lattices are used extensively to study damage evolution and fracture of inhomogeneous or multi-phase systems. The present note addresses their initial elastic response during dynamic loading. Namely, a transition from short-time values of modulus of elasticity and Poisson's ratio to respective long-time values, which is not accompanied by the corresponding change of stiffness tensor components. The study is performed on three 2D truss-type lattices. It is demonstrated that the difference between the two sets of elastic properties is a result of combining effects of the initial lateral inertia and the disorder of the system.

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Section: Lattice Simulationsmentioning

confidence: 79%

Section: Lattice Simulationsmentioning

confidence: 99%

mentioning

confidence: 99%

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A Note on Short-time Response of Two-dimensional Lattices during Dynamic Loading

Mastilović

2008

International Journal of Damage Mechanics

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“…The effects of this loading procedure are demonstrated in literature (as reported by Mastilovic et al, 2008).…”

Section: Computer Simulations Of Uniaxial Tensionmentioning

confidence: 79%

“…The natural randomness of the mesoscale material texture is an example of the aleatory variability. The intrinsic (pre-existing) disorder is, in the course of deformation, further enhanced by the extrinsic disorder due to the damage evolution that is governed (to an extent depending on deformation rate; Mastilovic et al, 2008) by the local fluctuations of energy barriers quenched within the material and the local fluctuations of stress. The nonlocal and nonlinear character of these far-from-equilibrium processes is such that concepts of strain and damage (and temperature, in general) based on spatial and temporal averaging are, at best, conditionally acceptable (Mastilovic and Krajcinovic, 1999).…”

Section: Introductionmentioning

confidence: 99%

Further Remarks on Stochastic Damage Evolution of Brittle Solids Under Dynamic Tensile Loading

Mastilović

2010

International Journal of Damage Mechanics

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This article illuminates some general features and provides elementary interpretations of the deformation, damage, and failure of brittle solids characterized by very low fracture energy. The dynamic response of these materials is determined to a large extent by stochastic and random factors. The investigation emphasis is on the moderate-to-extremely high rate range (10 s À1 , 1 Â 10 9 s À1 ), explored under practically identical in-plane stress conditions. The statistical approach is based on repeated particle dynamics simulations for different physical realizations of micromechanical disorder of a 2D brittle discrete system. The proposed strategy is computationally intensive, which necessitates simplicity of the laws governing the interparticular interaction. Based on the simulation results, an expression is proposed to model the mean tensile strength dependence on the strain rate. The linearity of the rate dependence of the stress-peak macroscopic response parameters is observed and discussed.KEY WORDS: brittle systems, dynamic strength, damage energy rate, time to failure, disorder.

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A microscale second gradient approximation of the damage parameter of quasi‐brittle heterogeneous lattices

Rinaldi

Placidi

2013

Z Angew Math Mech

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Lattice models are powerful tools to investigate damage processes in quasi‐brittle material by a microscale perspective. Starting from prior work on a novel rational damage theory for a 2D heterogenous lattice, this paper explores the connection between the series of critical strains at which the microcracks form (i.e. lattice links fail) and the second gradient of the microscale displacement field. Taking a simple tensile test as a representative case study for this endeavour, the analysis of accurate numerical results provides evidence that the second gradient of the microscale displacement field (notably the quantity | ∇ (∂ ux/∂ x)| for the specific example elaborated here) conveys indeed crucial information about the microcracks formation process and can be conveniently used to introduce simplifications of the rational theory that are of relevance by practical purposes as full field strain measurements become routinely possible with digital imaging correlation techniques. Note worthy, the results support the new view that the damage evolution is a three regimes process (I dilute damage, II homogeneous interaction, III localization.) The featured connection with the second gradient of the microscale displacement field is applicable in regions II–III, where microcracks interactions grow stronger and the lattice transitions to the softening regime. The potential impact of these findings towards the formulation of new and physically based CDM models, which are consistent with the reference discrete microscale theory, cannot be overlooked and is pointed out.

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Ordering effect of kinetic energy on dynamic deformation of brittle solids

Cited by 14 publications

References 21 publications

A Note on Short-time Response of Two-dimensional Lattices during Dynamic Loading

A Note on Short-time Response of Two-dimensional Lattices during Dynamic Loading

Further Remarks on Stochastic Damage Evolution of Brittle Solids Under Dynamic Tensile Loading

A microscale second gradient approximation of the damage parameter of quasi‐brittle heterogeneous lattices

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