Viscoelastic liquid or solid

Deformation of a viscoelastic liquid or solid through which a mass point of the viscoelastic liquid or solid with co-ordinates x[,x[,x[ at time t moves to a point with co-ordinates x, X2, X3 at time t such that there are functions / = 1, 2, 3, where... 

Tensor whose components are deformation gradients in a viscoelastic liquid or solid. 

Time derivative of a strain tensor for a viscoelastic liquid or solid in homogeneous deformation at reference time, t. 

Rivlin-Ericksen tensor of order n, for a viscoelastic liquid or solid in homogeneous deformation, is the nth time derivative of the Cauchy strain tensor at reference time, t. Note 1 For an inhomogeneous deformation the material derivatives have to be used. 

Note 3 The Finger strain tensor for a homogeneous orthogonal deformation or flow of incompressible, viscoelastic liquid or solid is... 

Equation relating stress and deformation in an incompressible viscoelastic liquid or solid. Note 1 A possible general form of constitutive equation when there is no dependence of stress on amount of strain is... 

Time characterizing the response of a viscoelastic liquid or solid to the instantaneous application of a constant strain. 

Given a sufficiently long time of creep, the velocity of creep will decelerate to zero and y t) attains an equilibrium limit if a viscoelastic solid is being measured. On the other hand, if the material is a viscoelastic liquid, the velocity of creep will decelerate to a finite constant value. Viscoelastic steady state is achieved, and y t) increases indefinitely. The creep experiment has a second part when the stress is set to zero after a period of creeping. A portion or all of the strain accumulated during creeping is then recovered as a function of time for a viscoelastic liquid or solid, respectively.For a viscoelastic liquid, the portion that is permanent deformation and irrecoverable reflects the contribution of viscous flow to the total deformation accumulated during creep. Since a viscoelastic solid does not flow, all of its creep deformation is recoverable. 

Stress response t versus time for a step input in strain y. The Hookean solid (b) shows no stress relaxation the Newtonian fluid (c) relaxes as soon as the strain is constant, while the viscoelastic liquid or solid shows stress relaxation over a significant time. In a viscoelastic liquid the stress relaxes to zero, while for the viscoelastic solid it asymptotically approaches an equilibrium stress r,. A small overshoot is shown in the strain versus time plot (a). This is typical of actual control systems, which may require 0.01 second or more to stabilize (see Chapter 8). 

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