Download Configurational Forces: Thermomechanics, Physics, by Gerard A. Maugin PDF
By Gerard A. Maugin
Exploring contemporary advancements in continuum mechanics, Configurational Forces: Thermomechanics, Physics, arithmetic, and Numerics offers the final framework for configurational forces. It additionally covers more than a few functions in engineering and condensed topic physics. the writer offers the basics of approved average continuum mechanics, earlier than introducing Eshelby fabric pressure, box idea, variational formulations, Noether’s theorem, and the ensuing conservation legislation. within the bankruptcy on advanced continua, he compares the classical standpoint of B.D. Coleman and W. Noll with the point of view associated with summary box idea. He then describes the $64000 thought of neighborhood structural rearrangement and its dating to Eshelby rigidity. After the relevance of Eshelby rigidity within the thermodynamic description of singular interfaces, the textual content makes a speciality of fracture difficulties, microstructured media, structures with mass exchanges, and electromagnetic deformable media. The concluding chapters speak about the exploitation of the canonical conservation legislation of momentum in nonlinear wave propagation, the appliance of canonical-momentum conservation legislations and fabric strength in numerical schemes, and similarities of fluid mechanics and aerodynamics. Written by means of a long-time researcher in mechanical engineering, this publication presents a close therapy of the speculation of configurational forces—one of the newest and such a lot fruitful advances in macroscopic box theories. via many purposes, it indicates the intensity and potency of this idea.
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Additional info for Configurational Forces: Thermomechanics, Physics, Mathematics, and Numerics
Example text
62). 121). This reasoning applies only to elasticity. Now define the true symmetric material tensor, called the second Piola– Kirchhoff stress or energy stress in the case of elasticity, S—not to be mistaken for the material entropy flux—by { S = TF = J F F −1σ F − T = SKL = J F ( F −1 ) σ ij ( F −1 ) Ki Lj }, σ = J F−1FSFT . 128) θ where the first of these justifies the name of energy stress. Then a classical writing of the balance of linear momentum clearly is in components R emar k 2 . 8 : ∂2 ui ∂ KL δ + u S f + ρ = ρ .
V and ∂(dV )/∂ t X = 0 . 8 Rigid-Body Motions This special class of motions is defined in geometry by Killing’s equations for isometries (conservation of a metric in time), here, for instance, ∂ E(X, t) = 0. 51) at all times t. The integral in space of this partial differential equation is shown to read (cf. Maugin, 1988, pp. 54) where P(t) ∈ O(3) is a spatially uniform finite rotation, x* is the position of a particular point in the material body in the reference frame, a(t) is a spatially uniform time-dependent vector, and x is the position of points of the solid in R.
109) yields the global form of the kinetic energy theorem (cf. 97)): d dt ∫ Bt ( K t ) dv = Pext ( Bt , ∂Bt ) + Pint ( Bt ). 67), we shall obtain a global statement of the internal energy theorem. We can proceed along this line. 109 as an a priori statement in which the virtual power of internal forces (stresses) accounts for the objectivity of the stress tensor, hence the writing as a linear continuous functional over D*, an objective tensor, as is easily shown. This basic formulation of continuum thermomechanics is in the tradition of d’Alembert (notice the affiliation of the author) and presents the advantage of easy generalization to the case of generalized continuum mechanics by enlarging a priori the field of virtual velocities in agreement with the degree of fineness selected for the generalized velocity fields (see Maugin, 1980).