The internal stability of an elastic solid

Morris, J. W.; Krenn, C. R.

doi:10.1080/01418610008223897

Cited by 151 publications

(94 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have shown that Born's results are valid only when the solid is under no load, by invoking the formulation of a Gibbs integral [6]. Further discussions were given by Zhou and Joos [7] and by Morris and Krenn [8], the latter emphasizing the thermodynamic basis of the concept of theoretical strength by showing the generalized stability criteria [6] are consistent with the internal conditions for elastic stability formulated by Gibbs in 1876. A consequence of these investigations is that theoretical strength should be considered a property which can be affected by the symmetry and magnitude of the applied load, rather than an intrinsic property of the material.…”

Section: Theoretical Strength: the Elastic Limitmentioning

confidence: 95%

Elastic criterion for dislocation nucleation

Zhu

Yip

et al. 2004

Materials Science and Engineering: A

View full text Add to dashboard Cite

The notion of theoretical strength, the critical stress at which a perfect crystal under uniform loading becomes structurally unstable, is extended to non-uniform loading. A position-dependent defect nucleation criterion has been derived and applied in molecular dynamics (MD) and finite-element simulations of dislocation emission in single-crystal nanoindentation. The resulting measure has the physical meaning of a local stiffness; it provides a rigorous basis for modeling the incipient plasticity in a thin-film material. Furthermore, a close connection has been shown to exist between the initial unstable elastic wave and the final atomistic defect.

show abstract

Section: Theoretical Strength: the Elastic Limitmentioning

confidence: 95%

Elastic criterion for dislocation nucleation

Zhu

Yip

et al. 2004

Materials Science and Engineering: A

View full text Add to dashboard Cite

show abstract

“…These rather simple criteria have been helpful in elucidating simulation results on structural phase stability [28,54]. Further discussions of the stability criteria may be found in the literature [40,54,55,59]. In the following we confine our attention to intrinsic or ideal behavior of homogeneous deformation of a defect-free the crystal, conditions achievable only in simulation.…”

Section: Theoretical Strength Of Materialsmentioning

confidence: 99%

Multiscale Materials Modelling: Case Studies at the Atomistic and Electronic Structure Levels

Silva¹,

Först²,

et al. 2007

ESAIM: M2AN

View full text Add to dashboard Cite

Abstract.Although the intellectual merits of computational modelling across various length and time scales are generally well accepted, good illustrative examples are often lacking. One way to begin appreciating the benefits of the multiscale approach is to first gain experience in probing complex physical phenomena at one scale at a time. Here we discuss materials modelling at two characteristic scales separately, the atomistic level where interactions are specified through classical potentials and the electronic level where interactions are treated quantum mechanically. The former is generally sufficient for dealing with mechanical deformation at large strain, whereas the latter is necessary for treating chemical reactions or electronic transport. We will discuss simulations of defect nucleation using molecular dynamics, the study of water-silica reactions using a tight-binding approach, the design of a semiconductor-oxide interface using density functional theory, and the analysis of conjugated polymer in molecular actuation using Hartree-Fock calculations. The diversity of the problems discussed notwithstanding, our intent is to lay the groundwork for future problems in materials research, a few will be mentioned, where modelling at the electronic and atomistic scales are needed in an integrated fashion. It is in these problems that the full potential of multiscale modelling can be realized.Mathematics Subject Classification. 74A25, 74A45, 74F25, 74M05, 81V55.

show abstract

“…There is substantial interest in understanding the ideal strength of materials, as this provides an upper bound on the achievable mechanical behavior. [74][75][76][77] Since dislocations at near theoretical strengths travel at the speed of sound or higher, nanosecond time resolution with atomic resolution is required to capture the subtle atomic-level characteristics that influence the nucleation of dislocations.…”

Section: -5 Gerberich Et Almentioning

confidence: 99%

Review Article: Case studies in future trends of computational and experimental nanomechanics

Tadmor

Kysar

Zimmerman

et al. 2017

Journal of Vacuum Science &Amp; Technology A: Vacuum, Surfaces, and Films

View full text Add to dashboard Cite

With rapidly increasing numbers of studies of new and exotic material uses for perovskites and quasicrystals, these demand newer instrumentation and simulation developments to resolve the revealed complexities. One such set of observational mechanics at the nanoscale is presented here for somewhat simpler material systems. The expectation is that these approaches will assist those materials scientists and physicists needing to verify atomistic potentials appropriate to the nanomechanical understanding of increasingly complex solids. The five following segments from nine University, National and Industrial Laboratories both review and forecast where some of the important approaches will allow a confirming of how in situ mechanics and nanometric visualization might unravel complex phenomena. These address two-dimensional structures, temporal models for the nanoscale, atomistic and multiscale friction fundamentals, nanoparticle surfaces and interfaces a) Electronic

show abstract

The internal stability of an elastic solid

Cited by 151 publications

References 13 publications

Elastic criterion for dislocation nucleation

Elastic criterion for dislocation nucleation

Multiscale Materials Modelling: Case Studies at the Atomistic and Electronic Structure Levels

Review Article: Case studies in future trends of computational and experimental nanomechanics

Contact Info

Product

Resources

About