Download Mechanics of porous and fractured media by V N Nikolaevskiĭ PDF

By V N Nikolaevskiĭ

The most objective of this e-book is to supply a self-contained, entire and geometrically transparent presentation of the hot effects on international controllability and stabilization. It includes many photos and workouts on the way to strengthen a geometric regulate instinct and encourage the reader to imagine independently. the fabric offered is equipped in order that for the interpreting of half I, it is just assumed that the reader has mastered the very uncomplicated notions of standard differential equations idea, normal topology and analytic geometry. For half II, the reader is believed to be acquainted with the weather of differential geometry

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Extra resources for Mechanics of porous and fractured media

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The equation of entropy growth has the following form TdS = (TU + Q)dt . The exclusion of the heat source Q gives an opportunity to express the entropy production Flas 1 / du d<§ n = — (P T dS\ + T— \ dt dr At / If one introduces the free energy $ = & - TS then „ P du 1 d dT dr II = S— . 79) n = T dt T dt s— dt . T dt T dt dt Another definition of the entropy production n is connected with the total dissipation ¥ of mechanical energy in the body. 80) the variations of rates u = = uee + + uP , e ue , and the crack length / being assumed nonequal to zero.

The classical Griffith criterion for brittle fracture of an elastic body uses only the condition for the energy discharge at the point of fracturing. The conditions for the discharge (or income) of material mass may be necessary if the fracture is connected with chemical reaction, and independent impulse balance is for some types of dynamical fracture. 1. = Pdu + Qdt Basic Concepts of Continuum Mechanics 29 where P is the generalized external action, u is the corresponding displacement. The equation of entropy growth has the following form TdS = (TU + Q)dt .

In the mathematical models of multiphase mechanics the porosity m has to be used as the essential variable. The porosity m is the volume of pores per the unit volume of the whole medium. Therefore m = = 1\ - mS1' = mS2' For the media with a chaotic internal microstructure it is possible to claim that m = = TT7 AV J\ AV fat* f v ™i = ft*• f; {f) i = TT" AAj \ J AA. ; w >dF ") AA Basic Concepts of Continuum Mechanics 21 where f(xit r; to) = 1, if the micropoint x{, t belongs to a pore space and /(*,•, t; to) = 0 if the point x{, t belongs to the matrix.

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