Continuum physics by Peter Hertel

By Peter Hertel

Stability Equations -- fabric Equations -- Linear reaction conception -- Examples

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If, however, the solid medium suffers strain, there will be stress. We shall formulate the idea that, to a first approximation, stress and strain are proportional which is known as Hooke’s law. Before we must explain the notion of strain. 8 By the way, one speaks of the ideal gas because B1 D 1 holds true for all kinds of molecules. 1 Strain Think of a material point at a certain location x. These are the coordinates with respect to a Cartesian coordinate system if the medium is relaxed. “Relaxed” means that no forces are present, neither volume forces nor forces upon the boundary of the medium.

Water and air may serve as prototypes of fluid media. , a liquid. Air under normal conditions behaves, to a very good approximation, as an ideal gas. “Normal” in this context means “as encountered in nature”. In the following we will discuss these idealizations in some length, while we just touch how to describe non-ideal gases and not-Newtonian fluids. , mass times acceleration per unit volume, as felt by a co-moving observer. On the right hand side we find three terms which describe the cause of acceleration: pressure gradient, external forces, and friction.

Y / separates into a left hand side which is a proper scalar and a right hand side which consists of two contribution each of which transforms properly as a scalar. Y / properly transforms as a vector. Y / rewrites the left hand side of the former formulation as one term which is easily interpreted from a physics point of view. , the amount of Y per unit mass. 5 Linear and Angular Momentum Linear momentum is an additive and transportable physical quantity. It is transported not only by convection, but also by conduction.

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Continuum physics by Peter Hertel
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