Implicit Constitutive Relations
نویسنده
چکیده
Classical Constitutive equations like the Navier-Stokes model for fluids and the linearized elastic model for solids are explicit models in that they provide explicit expressions for the stress in terms of kinematical quantities. Similarly, the constitutive equation for a Simple Material is also an explicit equation for the stress in terms of the histories of the deformation gradient and the density. However, many rate type models that have been developed to describe viscoelastic and inelastic materials are implicit in that a equation is provided for the stress, and its time rates, as well as appropriate kinematical quantities and their time rates. Even when time rates are not involved, such implicit models are very useful in describing a large class of materials, especially those wherein the material moduli depend on the Lagrange multiplier that is associated with a constraint. Thus, for example, such implicit equations can describe incompressible materials in which the material moduli depend on the pressure (mean normal stress). In this chapter we discuss very briefly the role of implicit constitutive relations in mechanics.
منابع مشابه
Implicit constitutive relations for nonlinear magnetoelastic bodies.
Implicit constitutive relations that characterize the response of elastic bodies have greatly enhanced the arsenal available at the disposal of the analyst working in the field of elasticity. This class of models were recently extended to describe electroelastic bodies by the present authors. In this paper, we extend the development of implicit constitutive relations to describe the behaviour o...
متن کاملOn the Flows of Fluids Defined through Implicit Constitutive Relations between the Stress and the Symmetric Part of the Velocity Gradient
Though implicit constitutive relations have been in place for a long time, wherein the stress, the strain (or the symmetric part of the velocity gradient), and their time derivatives have been used to describe the response of viscoelastic and inelastic bodies, it is only recently purely algebraic relationships between the stress and the displacement gradient (or the velocity gradient) have been...
متن کاملOn the treatment of non-solvable implicit constitutive relations in solid mechanics
We report results concerning the treatment of elastic bodies described by implicit constitutive relations which are not solvable, in the sense of expressing the stresses as functions of the strains or vice versa. Motivated by the theory of generalized hyperelastic materials, which applies also to polyatomic crystals, the field equations to be solved for a body described by a non-solvable implic...
متن کاملOn a New Class of Models in Elasticity
Recently, Rajagopal and co-workers have shown (see Rajagopal [1], Rajagopal and Srinivasa [2],[3], Bustamante and Rajagopal[4], Rajagopal and Saccomandi [5]) that if by an elastic body one means a body that is incapable of dissipation, then the class of such bodies is far larger than either Green elastic or for that matter Cauchy elastic bodies as one could model elastic bodies using implicit c...
متن کاملUse of Some Theorems Related with the Tensor Equation Ax + Xa = H for Some Classes of Implicit Constitutive Relations
The implicit function theorem is used to obtain some necessary and sufficient conditions, for which an implicit constitutive relation can be solved in terms of the stresses and strains, in the sense of expressing, for example, the strains in terms of the stresses or vice versa. For an isotropic body some exact solutions for the strains in term of the stresses are presented, using the theory of ...
متن کامل