Stress and elastic constants in anisotropic solids: Molecular dynamics techniques

Lutsko, James F.

doi:10.1063/1.341877

Cited by 220 publications

(240 citation statements)

References 8 publications

Supporting

Mentioning

230

Contrasting

Order By: Relevance

“…As a result, the discrete variables such as the atomistic mass, velocity, and total energy per atom, can be mapped into the continuous fields as density, momentum and energy density, respectively. The other related works can be referred to Lutsko [66] and Cormier et al [67]. Drawing on the concept of localization function, Ulz and Moran [68] utilized the Gaussian mixture modeling to measure the similarity of atoms and decide if atoms belong to the same space-averaging volume.…”

Section: Calculation Of Local Stress In Molecular Modelsmentioning

confidence: 99%

Applicability of Continuum Fracture Mechanics in Atomistic Systems

Cheng

Sun

2011

Volume 8: Mechanics of Solids, Structures and Fluids; Vibration, Acoustics and Wave Propagation

View full text Add to dashboard Cite

Stress intensity factor is one of the most significant fracture parameters in linear elastic fracture mechanics (LEFM). Due to its simplicity, many researchers directly employed this concept to explain their results from molecular simulation. However, stress intensity factor defines the amplitude of the singular stress, which is the product of continuum elasticity. Under atomistic systems without the stress singularity, the concept of stress intensity factor must be examined. In addition, the difficulty of studying the stress intensity factor in atomistic systems may be traced back to the ambiguous definition of the local atomistic stress. In this study, the definition of the local virial stress is adopted. Subsequently, through the consideration of K-dominance, the approximated stress intensity factor based on the atomistic stress can be projected within a reasonable region. Moreover, the influence of cutting interatomic bonds to create traction free crack surfaces and the critical stress intensity factor is also discussed.

show abstract

Section: Calculation Of Local Stress In Molecular Modelsmentioning

confidence: 99%

Applicability of Continuum Fracture Mechanics in Atomistic Systems

Cheng

Sun

2011

Volume 8: Mechanics of Solids, Structures and Fluids; Vibration, Acoustics and Wave Propagation

View full text Add to dashboard Cite

show abstract

“…(5) This modulus provides a way to link the applied loading on the composite to local response, which has been widely described as the 'local' modulus in the open literatures [7,27]. However, based on traditional micromechanics [10], r C from Eq.…”

Section: Methodsmentioning

confidence: 99%

“…[7,27], since we adopt the local stress and local strain to define the local modulus. Suppose all the inhomogeneities possess the global average strain, the linear mapping between the local stress and global strain is known as the effective intermediate modulus tensor, i.e., r r s = σ C ε .…”

Section: Methodsmentioning

confidence: 99%

Fast evaluation of local elastic constants and its application to nanosized structures

2015

View full text Add to dashboard Cite

We derive a method to determine the effective local elasticity tensor by combining the local stress, local strain, and global strain in conjunction with a linear least square solver. This method reduces to the standard stress-strain fluctuation method for the estimation of global moduli if the local stress and the local strain are substituted by global counterparts. The quality of the developed method is verified by the analysis of an FCC Lennard-Jones single crystal. By using this method, surface elastic behaviors of three nano-plates are investigated. Simulation results prove that both softening and stiffening effects could be detected, depending on the surface orientations and loading directions. This novel approach could be especially valuable for complicated morphologies where the physical properties of the local material are challenging or impractical to obtain.

show abstract

“…In such approaches local stress is usually calculated at atomic sites, taking into account the contributions to the virial associated with the atom in question [37] (Basinski-Duesberry-Taylor (BDT) stress). Alternatively, local stress at a point can be expressed in terms of contributions to the virial that arise from an averaging volume encompassing the point in question [38] (Lutsko stress). The validity of the above virial-based classes of approaches has since been questioned.…”

Section: Introductionmentioning

confidence: 99%

Central-force decomposition of spline-based modified embedded atom method potential

Winczewski

Dziedzic

2016

Modelling Simul. Mater. Sci. Eng.

View full text Add to dashboard Cite

Abstract. Central-force decompositions are fundamental to the calculation of stress fields in atomic systems by means of Hardy stress. We derive expressions for a central-force decomposition of the spline-based modified embedded atom method (s-MEAM) potential. The expressions are subsequently simplified to a form that can be readily used in molecular-dynamics simulations, enabling the calculation of the spatial distribution of stress in systems treated with this novel class of empirical potentials. We briefly discuss the properties of the obtained decomposition and highlight further computational techniques that can be expected to benefit from the results of this work. To demonstrate the practicability of the derived expressions, we apply them to calculate stress fields due to an edge dislocation in bcc Mo, comparing their predictions to those of linear elasticity theory.

show abstract

Stress and elastic constants in anisotropic solids: Molecular dynamics techniques

Cited by 220 publications

References 8 publications

Applicability of Continuum Fracture Mechanics in Atomistic Systems

Applicability of Continuum Fracture Mechanics in Atomistic Systems

Fast evaluation of local elastic constants and its application to nanosized structures

Central-force decomposition of spline-based modified embedded atom method potential

Contact Info

Product

Resources

About