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On the mechanical modeling of matter, molecular and continuum. (English) Zbl 1412.74006

Summary: Any mechanical modeling of matter depends primarily on the chosen spatial and temporal observation scales. Roughly speaking, there are three such scales, microscopic for quantum, mesoscopic for statistical, and macroscopic for continuum mechanics. This by itself demands for adequate scale-bridging procedures. This paper focuses on the passage from molecular to continuum formulations of the basic balance laws of linear momentum and energy, kinetic, internal, and total. The procedure used is a modification of that introduced by J. H. Irving and G. Kirkwood [J. Chem. Phys. 18, No. 6, 817–829 (1950; doi:10.1063/1.1747782)], as improved by W. Noll [J. Ration. Mech. Anal. 4, 627–646 (1955; Zbl 0065.19405); English transltion J. Elasticity 100, No. 1–2, 5–24 (2010; Zbl 1200.80002)] alternative procedures are mentioned. The proposed modification consists primarily in equipping provisionally the target continuum balances with internal-source terms accounting at the macroscopic scale for microscopic motion randomness, when, e.g., a loosely aggregated material system evolves at relatively high temperature. Attention is also devoted to those continuum notions that either are hardly given a universally accepted molecular counterpart or even cannot and ultimately need not be given one, such as the notion of material point.

MSC:

74A25 Molecular, statistical, and kinetic theories in solid mechanics
70A05 Axiomatics, foundations
74A05 Kinematics of deformation
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