Reviewing the roots of continuum formulations in molecular systems. Part I: Particle dynamics, statistical physics, mass and linear momentum balance equations

DOI10.1177/1081286512467790zbMath1356.74008OpenAlexW2319802645MaRDI QIDQ2875343

Paul Steinmann, D. Davydov

Publication date: 14 August 2014

Published in: Mathematics and Mechanics of Solids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1177/1081286512467790

zbMATH Keywords

balance equationsaveragingcentral force decompositionextended third Newton axiommulti-body potentials

Mathematics Subject Classification ID

Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21) Molecular, statistical, and kinetic theories in solid mechanics (74A25)

Related Items (4)

On the modeling of transport phenomena in continuum and statistical mechanics ⋮ Comparison of several staggered atomistic-to-continuum concurrent coupling strategies ⋮ Asymmetry of the atomic-level stress tensor in homogeneous and inhomogeneous materials ⋮ Reviewing the roots of continuum formulations in molecular systems. Part III: Stresses, couple stresses, heat fluxes

Cites Work

• On the identification of continuum concepts and fields with molecular variables
• A corpuscular approach to continuum mechanics: Basic considerations
• Continuum equations of balance in classical statistical mechanics
• On the microscopic interpretation of stress and couple stress
• Connecting molecular dynamics to micromorphic theory. I: Instantaneous and averaged mechanical variables
• Connecting molecular dynamics to micromorphic theory. II: Balance laws
• A material frame approach for evaluating continuum variables in atomistic simulations
• A critique of atomistic definitions of the stress tensor
• On a statistical-kinetic model for generalized continua
• A new look at the atomic level virial stress: on continuum-molecular system equivalence
• Revisiting quantum notions of stress
• Translation of Walter Noll's ``Derivation of the fundamental equations of continuum thermodynamics from statistical mechanics
• A unified interpretation of stress in molecular systems

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