By Reinhold Kienzler, Gerard A. Maugin
These lecture notes hide quite a few parts of configurational mechanics, together with mathematical foundations, linear and nonlinear elasticity and continuum mechanics, coupled fields, fracture mechanics, in addition to power of materials.
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Extra resources for Configurational Mechanics of Materials (CISM International Centre for Mechanical Sciences)
6 t) ' =p. 6 g) Here N = EAu' is the axial force and p =mu• is called the canonical momentum density (Morse and Feshbach, 1953) and corresponds to the momentum of a bar of unit length moving with velocity u• . 9) a being the phase velocity. We wish now to calculate the components of the material momentum tensor, here truly the elastic energy momentum tensor, because one of the independent variables is the time. 38), J oL J (LJlJ.. oL P:1 =tnp--+~. 'f' Ov Ov fl,i p,i we know that -oLI Ovp,i must supply the components of physical momentum and LJij - vp,j oLI 8v p,i the negative components of material momentum.
38), J oL J (LJlJ.. oL P:1 =tnp--+~. 'f' Ov Ov fl,i p,i we know that -oLI Ovp,i must supply the components of physical momentum and LJij - vp,j oLI 8v p,i the negative components of material momentum. We already identified the components of physical momentum. Here it is a vector with components N and - p . 43) 47 Conservation Laws and their Application b·· = u · oL - L() .. IJ ,j ou . rx is the material force per unit of length, also called wave stress (cf. Morse and Feshbach, 1953), whereas bxt is the stress rate of work or rate of energy flow along the bar, b1x is called the wave momentum and finally, bu is the total energy per unit of length H = T + W or the Hamiltonian per unit of length.
A somewhat different viewpoint is expressed in the book of Gurtin ( 1999). A progressive approach in complexity has been adopted in the present lecture notes. First (Section 2) we remind the reader of some elements of field theory (notion of energymomentum, Noether's theorem, Noether's identity). Then (Section 3), as a simple application we consider the paradigmatic case offinite-strain elasticity- in the absence of any thermal and intrinsic dissipations at all material points - which helps one define the notions of material uniformity and inhomogeneity.