By Gerard A. Maugin
Exploring fresh advancements in continuum mechanics, Configurational Forces: Thermomechanics, Physics, arithmetic, and Numerics provides the final framework for configurational forces. It additionally covers a number functions in engineering and condensed subject physics. the writer provides the basics of permitted regular continuum mechanics, ahead of introducing Eshelby fabric rigidity, box concept, variational formulations, Noether’s theorem, and the ensuing conservation legislation. within the bankruptcy on complicated continua, he compares the classical viewpoint of B.D. Coleman and W. Noll with the perspective associated with summary box conception. He then describes the $64000 idea of neighborhood structural rearrangement and its courting to Eshelby pressure. After the relevance of Eshelby tension 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 talk about the exploitation of the canonical conservation legislations of momentum in nonlinear wave propagation, the appliance of canonical-momentum conservation legislation 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 booklet offers an in depth remedy of the speculation of configurational forces—one of the most recent and so much fruitful advances in macroscopic box theories. via many functions, it indicates the intensity and potency of this idea.
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Additional info for Configurational Forces: Thermomechanics, Physics, Mathematics, and Numerics
F e ) . 165) and the laws of state Srelax = ∂W , ∂E e = − ∂W , A ∂α Srelax = − ∂W . 166) Here E e is the observable mechanical variable of state. 167) where λ ≥ 0 , λ being a so-called plastic multiplier. 167 means that the plastic evolution presents no time scale (there is a time derivative on both sides), and the corresponding intrinsic dissipation is mathematically homogeneous of degree one only in the time rates. Mechanical dissipation occurs possibly, but not necessarily, when a point on the surface f has been reached.
112) is a linear (continuous) functional over the spatial gradient of v*, or rather its 33 Standard Continuum Mechanics symmetric part D*: = (∇v*)s, by virtue of the symmetry of the stress (in this case). 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 provides the so-called Kelvin–Voigt model of viscoelasticity, which is not such a good model of solid viscosity (cf. Maugin, 1992). Fortunately, there is a much better way to obtain realistic models of dissipative solids, such as viscous, elastoplastic, viscoplastic, or damaging solids, models that also completely fulfill thermodynamic requirements while keeping some contact with physical bases. This is the due application of the thermodynamics with internal variables of state (Maugin and Muschik, 1994; Maugin, 1999).
Configurational Forces: Thermomechanics, Physics, Mathematics, and Numerics by Gerard A. Maugin