Statistical models of brittle deformation: Part II: computer simulations

Mastilović, Sreten; Krajčinović, Dušan

doi:10.1016/s0749-6419(98)00068-0

Cited by 25 publications

(33 citation statements)

References 35 publications

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“…Next, the present MD model applied to low-velocity rigid-anvil simulations by Mastilovic and Krajcinovic (1999) reproduced the Taylor's experimental observations (1948) showing that the relative shortening of the slender projectile (L1/L0) is independent of the slenderness ratio (L0/D0). Also, these MD simulation results are in agreement with the classic analysis, originated by Taylor (and refined by Wilkins and Guinan; e.g., Meyers, 1994), which suggested the scaling relation between the relative projectile shortening and the impact energy , L1/L0 ∝ exp (K).…”

Section: Validation Of the MD Simulation Modelsupporting

confidence: 72%

Phenomenology of the Maximum Fragment Mass Dependence Upon Ballistic Impact Parameters

Mastilović

2017

Lat. Am. j. solids struct.

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Molecular dynamics simulations of the ballistic Taylor test are used to explore correlation between the largest fragment mass and the impact energy of a projectile as well as a set of selected state variables. Flat-ended, monocrystalline, nanoscale bars collide with a rigid wall with striking velocities ranging from 0.27 km/s to 60 km/s. The investigation emphasis is on two border regions of the emerging nonlinear phenomenological model identified with two transitions: the damage-fragmentation transition and the shattering transition. In between these two nonlinear regions, the maximum fragment mass is largely inversely proportional to the impact energy, and the maximum values of the pressure, temperature, and the square of the effective strain. A reverse-sigmoid phenomenological model is proposed to capture the unifying features of this nonlinear and saturable dependence. A crystallographic orientation dependence of the damage-fragmentation transition parameters is investigated.

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Section: Validation Of the MD Simulation Modelsupporting

confidence: 72%

Phenomenology of the Maximum Fragment Mass Dependence Upon Ballistic Impact Parameters

Mastilović

2017

Lat. Am. j. solids struct.

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“…The dimension of ''GN/m 2 '' reflects the interpretation of the spring constants as stiffness per unit thickness when the thickness is not assigned in computing K e . A Gaussian distribution for the stiffness has been used in the past by Mastilovic for example (Mastilovic and Krajcinovic, 1999) but this paper provides the rationale to ''calculate'' the natural distribution based on the geometry and mechanical property of the microstructure. Furthermore, the ''Central Limit Theorem'' guarantees the robustness of the results even when the sampling distribution of the material axes is not uniform.…”

Section: Test Resultsmentioning

confidence: 99%

“…In damage mechanics, for example, a finite tensile strength is randomly assigned to each spring so that a rupture occurs when the load in the spring reaches the given threshold (Mastilovic and Krajcinovic, 1999;. Unlike the spring stiffness distribution though, the strength distribution is strongly dependent on the manufacturing process and the presence of non-visible defects (<l), such as glassy pockets, voids and second phase precipitates at the grain-boundary, renders any estimate of critical strains from pure geometrical considerations unreliable.…”

Section: Considerationsmentioning

confidence: 99%

“…Hansen et al (1989), Sahimi (2000), Krajcinovic and Basista (1991), Krajcinovic and Vujosevic (1998), Mastilovic and Krajcinovic (1999), , , Delaplace et al (1996), He and Thorpe (1985) and others have shown that statistical lattice models offer a convenient framework for the study of the damage process associated to microcracks formation and growth. The usage of the statistics to account for the disorder of the microstructure is one distinctive feature of such statistical models.…”

Section: Introductionmentioning

confidence: 99%

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Lattice models of polycrystalline microstructures: A quantitative approach

Rinaldi

Krajčinović

Peralta

et al. 2008

Mechanics of Materials

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This paper addresses the issue of creating a lattice model suitable for design purposes and capable of quantitative estimates of the mechanical properties of a disordered microstructure. The lack of resemblance between idealized lattice models and real materials has limited these models to the realm of qualitative analysis. Two procedures based on the same methodology are presented in the two-dimensional case to achieve the rigorous mapping of the geometrical and the elastic properties of a disordered polycrystalline microstructure into a spring lattice. The theory is validated against finite elements models and literature data of NiAl. The statistical analysis of 900 models provided the effective Young's modulus and Poisson ratio as function of the lattice size. The lattice models that were created have in average the same Young's modulus of the real microstructure. However, the Poisson's ratio could not be matched in the two-dimensional case. The spring constants of the lattices from this technique follow a Gaussian distribution, which intrinsically reflects the mechanical and geometrical disorder of the microscale. The detailed knowledge of the microstructure and the Voronoi tessellation necessary to implement this technique are supplied by modern laboratory equipments and software. As an illustrative example of lattice application, damage simulations of several biaxial loading schemes are briefly reported to show the effectiveness of discrete models towards elastic anisotropy induced by damage and damage localization.

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“…A lot of attention is paid to the plasticity models in composites in terms of probabilistic mechanics-in macro-scale [3], smaller scales [20] or even in the area of nano-composites [7]. The generalized stochastic perturbation theory [8] is an interesting alternative to the other existing theoretical and computational approaches in stochastic mechanics [14,15,22,23]. The main reason of an introduction of the generalized method is full Taylor expansion including as many probabilistic moments as it is necessary for an accurate solution.…”

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confidence: 99%

A generalized stochastic perturbation technique for plasticity problems

Kamiński

2009

Comput Mech

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The main aim of this paper is to present an algorithm and the solution to the nonlinear plasticity problems with random parameters. This methodology is based on the finite element method covering physical and geometrical nonlinearities and, on the other hand, on the generalized nth order stochastic perturbation method. The perturbation approach resulting from the Taylor series expansion with uncertain parameters is provided in two different ways: (i) via the straightforward differentiation of the initial incremental equation and (ii) using the modified response surface method. This methodology is illustrated with the analysis of the elasto-plastic plane truss with random Young's modulus leading to the determination of the probabilistic moments by the hybrid stochastic symbolic-finite element method computations.

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Statistical models of brittle deformation: Part II: computer simulations

Cited by 25 publications

References 35 publications

Phenomenology of the Maximum Fragment Mass Dependence Upon Ballistic Impact Parameters

Phenomenology of the Maximum Fragment Mass Dependence Upon Ballistic Impact Parameters

Lattice models of polycrystalline microstructures: A quantitative approach

A generalized stochastic perturbation technique for plasticity problems

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