Abstract
In this chapter, we present the basic equations of continuum physics both in global and local formulations. The local balance laws together with the global Clausius–Duhem inequality define the class of admissible thermodynamic processes. Boundary conditions and discontinuities appear as prominent issues. We give a few examples of constitutive equations for the stress tensor and for the transport fluxes. A set of worked-out practical modeling scenarios is emphasized.
An equation means nothing to me unless it expresses a thought of God.
— Srinivasa Ramanujan, Quotations by 60 Greatest Indians
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Notes
- 1.
Essentially, for composite materials made of simple microstructures the tortuosity tensor \(\tau \) can be approximated.
- 2.
In particular, the order of the involved partial differential equations matters here.
- 3.
A detailed modeling of the flow (and particularly of the pressure) is then avoided by deciding for simple fluid motions.
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Muntean, A. (2015). Balance Equations in Continuum Physics. In: Continuum Modeling. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-319-22132-8_2
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DOI: https://doi.org/10.1007/978-3-319-22132-8_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22131-1
Online ISBN: 978-3-319-22132-8
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