Multi-scale analysis of multiple damage mechanisms coupled with inelastic behavior of composite materials

Voyiadjis, George Z.; Deliktaş, Babür

doi:10.1016/s0093-6413(00)00095-1

Cited by 27 publications

(14 citation statements)

References 23 publications

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“…The latter form has been used by de Borst and his co-workers and by many others in solving the localization problem (see for example de Borst and Mü hlhaus, 1992;de Borst et al, 1993;de Borst and Pamin, 1996;Claudia and Perego, 1996;Chen et al, 2000;Zervos et al, 2001;Voyiadjis et al, 2001Voyiadjis et al, , 2003Engelen et al, 2003; and references quoted therein).…”

Section: Gradient Plasticity Theoriesmentioning

confidence: 99%

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Gradient plasticity theory with a variable length scale parameter

Voyiadjis

Al‐Rub

2005

International Journal of Solids and Structures

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240

118

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Section: Gradient Plasticity Theoriesmentioning

confidence: 99%

“…de Borst and Mü hlhaus, 1992;de Borst et al, 1993;Pamin, 1994;de Borst and Pamin, 1996). Gradient thermodynamic damage models were also introduced by Fremond and Nedjar (1996) and Voyiadjis et al (2001Voyiadjis et al ( , 2003.…”

Section: Introductionmentioning

confidence: 99%

Gradient plasticity theory with a variable length scale parameter

Voyiadjis

Al‐Rub

2005

International Journal of Solids and Structures

Self Cite

240

118

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“…A number of continuum mechanics models have also attempted to incorporate a multiscale analysis [9,10]. These approaches, however, are unable to describe certain atomistically induced stresses at the interface of two different materials (especially if one or both are amorphous), where microscopic details of chemical bonding are important.…”

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confidence: 99%

Coupling Length Scales for Multiscale Atomistics-Continuum Simulations: Atomistically Induced Stress Distributions inSi/Si3N4Nanopixels

et al. 2001

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A hybrid molecular-dynamics (MD) and finite-element simulation approach is used to study stress distributions in silicon/silicon-nitride nanopixels. The hybrid approach provides atomistic description near the interface and continuum description deep into the substrate, increasing the accessible length scales and greatly reducing the computational cost. The results of the hybrid simulation are in good agreement with full multimillion-atom MD simulations: atomic structures at the lattice-mismatched interface between amorphous silicon nitride and silicon induce inhomogeneous stress patterns in the substrate that cannot be reproduced by a continuum approach alone.

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“…Aifantis (1981, 1982) and Aifantis (1984a, b) suggested a gradient approach to deformation to describe plastic instabilities including dislocation patterning and spatial characteristics of shear bands. This initial work and subsequent articles by Aifantis and coworkers (e.g., Aifantis and Hirth, 1985;Aifantis, 1987;Zbib and Aifantis, 1988;Walgraef and Aifantis, 1988;Vardoulakis and Aifantis, 1989;Mu¨hlhaus and Aifantis, 1991;Walgraef and Aifantis, 1995;Voyiadjis et al, 2001a) have contributed to appreciating the potential and applicability of the gradient approach to a variety of material instability problems ranging from metal fatigue and polycrystal/soil shear banding to the failure of concrete and liquefaction. Computational issues of the gradient theory for plasticity (e.g., Mu¨hlhaus and Aifantis, 1991;de Borst et al, 1995;Ramaswamy and Aravas, 1998;Bammann et al, 1999;Dorgan, 2004a, 2005), damage (e.g., Pijaudier-Cabot and Bazˇant, 1987;Bammann et al, 1999;Peerlings et al, 1996;Kuhl et al, 2000), and coupled damage-plasticity (e.g., Pamin and de Borst, 1999;Dorgan, 2001, 2005;Voyiadjis et al, 2001aVoyiadjis et al, , b, 2004 have been discussed extensively in the literature.…”

Section: Gradient-enhanced Coupled Damage-plasticity Modelmentioning

confidence: 99%

A Mixed Finite Element Implementation of a Gradient-enhanced Coupled Damage—Plasticity Model

Dorgan

Voyiadjis

2006

International Journal of Damage Mechanics

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ABSTRACT:The numerical implementation of a gradient-enhanced continuum coupled damage-plasticity model as a constitutive framework to model the nonlocal response of materials is presented. By the introduction of 'nonlocal,' gradientenhanced measures in the plasticity potential function and yield criterion and in the damage potential function and damage criterion, the proposed model introduces microstructural characteristic material length scales, which allow us to predict the size of localized zones based on material constants, as opposed to local models where the loss of ellipticity causes localized zones to be mesh dependent.As numerical methods are used to compute the gradients of the hardening terms, no additional gradient internal state variables are introduced into the Helmholtz free energy. As opposed to previous theories that only incorporate linear hardening, the gradient model proposed here uses coupled nonassociative plasticity -nonassociative damage and can account for a wide range of material models because of the consistently expanded Laplacian evolution equations. However, due to the nonassociative material model, anisotropic hardening, and the corresponding gradients in plasticity, the model becomes highly complex as additional equations have to be introduced for the evolution of the gradients of plastic normal, plastic strains, damage normal, and damage tensor.The numerical implementation uses a small deformation finite element formulation and includes the displacements, plastic multiplier, and damage multiplier as nodal degrees of freedom, thus allowing the three fields to have different interpolation functions. Higher-order elements are used for the plastic multiplier and damage multiplier to enforce continuity of the second gradients, which requires the introduction of additional boundary conditions.

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Multi-scale analysis of multiple damage mechanisms coupled with inelastic behavior of composite materials

Cited by 27 publications

References 23 publications

Gradient plasticity theory with a variable length scale parameter

Gradient plasticity theory with a variable length scale parameter

Coupling Length Scales for Multiscale Atomistics-Continuum Simulations: Atomistically Induced Stress Distributions inSi/Si3N4Nanopixels

A Mixed Finite Element Implementation of a Gradient-enhanced Coupled Damage—Plasticity Model

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