Cosserat Theories: Shells, Rods and Points by M.B. Rubin

By M.B. Rubin

Continuum Continuum mechanics mechanics presents offers a a theoretical theoretical constitution constitution for for examining studying the the reaction reaction of of fabrics fabrics to to mechanical mechanical and and thermal thermal a lot. so much. One certainly one of of the the beauties beauties of of continuum continuum mechanics mechanics is is that that the the elemental basic stability stability legislation legislation (conservation (conservation of of mass mass and and balances balances of of linear linear momentum, momentum, angular angular momentum, momentum, strength strength and and entropy) entropy) are are legitimate legitimate for for all all easy easy fabrics. fabrics. so much such a lot of of the the trendy sleek examine learn in in continuum continuum mechanics mechanics focuses makes a speciality of at the the improvement improvement of of constitutive constitutive equations equations which that are are used used to to signify represent the the reaction reaction of of a a specific specific classification type of of fabrics fabrics (e.g. (e.g. invisicid invisicid fluids, fluids, viscous viscous fluids, fluids, elastic elastic solids, solids, viscoelastic viscoelastic solids, solids, elastic­ elastic­ plastic solids, elastic-viscoplastic solids, etc.). plastic solids, elastic-viscoplastic solids, etc.).

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Additional resources for Cosserat Theories: Shells, Rods and Points

Example text

And T . of the stress T "'". 32) of the balance momentum. 8) is properly invariant under SRBM. (v) The tensors f* and y* are both independent of the rate L*. 5), can be rewritten in the form (f* - g-112 y* y*). y*) 0 n* = 0 . 11) vanishes. 5) for arbitrary values of the other components of n*. 13) where y* remains an arbitrary function of (x *,t) that is determined by the equations of motion and the boundary conditions. 14) In general, the constraint response f* influences the equation of linear momentum but not the conservation of mass or angular momentum equations (since it is a symmetric tensor).

4). 3) of mechanical power to remain form invariant under SRBM. 6 An averaged form of the balance of linear momentum In the purely mechanical three-dimensional theory the balance of angular momentum places restrictions on the constitutive equations which require the Cauchy stress tensor to be symmetric. Also, the conservation of mass and the balance of linear momentum are used to determine the mass density and the position of each material point in the continuum. For the Cosserat theories that will be developed in the next chapters, alternative equations representing the conservation of mass and the balances of linear and angular momentum will be used in a similar manner to determine the mass density and the position of each material point.

On the other hand, if the detailed stress distribution is needed in the body, then it is not appropriate to use the simple model of a rigid body. 1) that the mechanical power due to this part of the stress is equal to the rate of change of the strain energy function. 15). 9 Initial and boundary conditions In this section attention is confined to the discussion of initial and boundary conditions for the purely mechanical theory. In general, the number of initial conditions required and the type of boundary conditions required will depend on the specific type of material under consideration.

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