Atomistic viewpoint of the applicability of microcontinuum theories

Chen, Youping; Lee, James; Eskandarian, Azim

doi:10.1016/j.ijsolstr.2003.11.030

Cited by 228 publications

(94 citation statements)

References 12 publications

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“…A discussion of the relation between nonlocal theories and atomistic models can be found in, e.g., Chen et al (2004). In Silling (2000), various properties of peridynamic models and the relationship to the classical continuum mechanics theories are presented in detail (isotropy, elasticity, wave dispersion, etc.).…”

Section: Nonlocal Modelsmentioning

confidence: 99%

Impact Mechanics and High-Energy Absorbing Materials: Review

2008

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Section: Nonlocal Modelsmentioning

confidence: 99%

Impact Mechanics and High-Energy Absorbing Materials: Review

2008

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“…The intrinsic incompatibility of coupling mechanical models with local/nonlocal force interaction suggests that we consider generalizations of classical continuum mechanics as described in [7,13,19,35,36,37], or continuum realizations of molecular dynamics [1,42,12,43,30]. We refer to these classes of methods as generalized continua.…”

Section: Generalized Continuamentioning

confidence: 99%

Blending Methods for Coupling Atomistic and Continuum Models

Bochev¹,

Lehoucq²,

Parks³

et al. 2009

Multiscale Methods

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In this paper we review recent developments in blending methods for atomisticto-continuum (AtC) coupling in material statics problems. Such methods tie together atomistic and continuum models by using a bridge domain that connects the two models. There are several reasons why AtC coupling methods (of which blending methods are a subset) are important and have been subject to an increased interest in the recent years. Despite tremendous increases in computational power, fully atomistic simulations on an entire model domain remain computationally infeasible for many applications of interest. As a result, attention has focused on hybrid schemes where in all regions with well-behaved solutions, the atomistic (microscopic) model is replaced by a (macroscopic) continuum model enabling a more efficient computational scheme (see [14,29,9] for general information). The main challenge is the synthesis of the two distinct models in a manner that minimizes, or altogether eliminates, undesirable artifacts such as ghost forces, unphysical solutions let alone supporting mathematical analysis. Notable AtC coupling methods include the quasicontinuum method [39], the bridging scale decomposition [41], and [24] where atomistic and continuum models are overlapped (see the latter two references, and those mentioned above for numerous citations to the literature). The numerical analysis of AtC methods has lagged in comparison to the number of methods proposed; see the recent papers [2,3,17,31,26,27] for analyses of the quasicontinuum method.Blending methods couple atomistic/continuum modes via a dedicated blending, or bridge, region inserted between the atomistic and continuum subdomains. The atomistic and continuum models are tied together by using a suitable "continuity" condition (or balance law) for the atomistic and continuum positions or displacements in this region. A complicating factor is that the atomistic and (classical) continuum elastic models rely on nonlocal and local models of force interaction, respectively. In the (classical) elastic context, the "local force" is that exerted on a body by contact forces occurring on the surface (of the body). In contrast, in the atomistic model, forces are summed from atoms separated by a finite distance. The incompatibility arising from coupling local and nonlocal force models is intrinsic. The goal of our paper is threefold. First, we review how blending approaches attempt to ameliorate the various negative effects by relying on an interface between the two models. Second, we discuss the beginnings of a JFISH: "CHAP06" -2009/6/4 -17:33 -PAGE 166 -#2 166Blending methods for coupling atomistic and continuum models numerical analysis by discussing consistency of the resulting numerical schemes. Third, we suggest how the intrinsic limitation associated with coupling nonlocal and local mechanical theories may be avoided by replacing the classical elastic theory with a nonlocal elastic theory.The use of a bridge domain in blending methods bears a resemblance to conventional overlapping...

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“…In the case of Cosserat continua the degree of freedom for each material point are six: three translations and three microrotations. The domain of applicability of the theory of continua with inner structure has investigated by Fischer-Hjalmars (1982), Kunin (1983), Eringen (1999), Dyszlewicz (2004) and Chen et al (2004). The classical theory of Cosserat elastic solids is characterized by constitutive functions which depend on the deformation gradient, microrotation vector and gradient of microrotation.…”

Section: Introductionmentioning

confidence: 99%

Strain gradient theory of chiral Cosserat thermoelasticity without energy dissipation

Ieşan

Quintanilla

2016

Journal of Mathematical Analysis and Applications

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In this paper, we use the Green-Naghdi theory of thermomechanics of continua to derive a linear strain gradient theory of Cosserat thermoelastic bodies. The theory is capable of predicting a finite speed of heat propagation and leads to a symmetric conductivity tensor. The constitutive equations for isotropic chiral thermoelastic materials are presented. In this case, in contrast with the classical Cosserat thermoelasticity, a thermal field produces a microrotation of the particles. The thermal field is influenced by the displacement and microrotation fields even in the equilibrium theory. Existence and uniqueness results are established. The theory is used to study the effects of a concentrated heat source in an unbounded homogenenous and isotropic chiral solid.

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Atomistic viewpoint of the applicability of microcontinuum theories

Cited by 228 publications

References 12 publications

Impact Mechanics and High-Energy Absorbing Materials: Review

Impact Mechanics and High-Energy Absorbing Materials: Review

Blending Methods for Coupling Atomistic and Continuum Models

Strain gradient theory of chiral Cosserat thermoelasticity without energy dissipation

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