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Viscoelasticity

  • Peter Haupt
Part of the Advanced Texts in Physics book series (ADTP)

Abstract

The theory of viscoelasticity models rate-dependent material behaviour without equilibrium hysteresis. A systematic development of special material models of viscoelasticity can be based on the general constitutive equations for simple materials, in which the total stress response is split into an elastic part and a memory part. This is expressed by the reduced form (7.28),
$$\tilde T(t) = g(E) + \mathop {{\text{ }}B}\limits_{s \geqq 0} [E_d^t(s);E],$$
(10.1)
or by the representations (7.80) and (7.70),
$$T(t) = f(B) + \mathop \Im \limits_{s \geqq 0} \left[ {{G^t}(s);B(t)} \right],$$
(10.2)
$$T(t) = - p(\rho )1 + \mathop {{\text{ }}O}\limits_{s \geqq 0} \left[ {{G^t}\left( s \right);\rho } \right],$$
(10.3)
which describe the behaviour of isotropic solids and fluids. The mechanical process history is represented here in terms of the relative strain history,
$$s \mapsto E_d^t(s) = E(t - s) - E(t) = \frac{1}{2}(C(t - s) - C(t)),$$
(10.4)
$$s \mapsto {G^t}(s) = 2{F^{T - 1}}(t)[E(t - s) - E(t)]{F^{ - 1}}(t).$$
(10.5)

Keywords

Evolution Equation Internal Variable Influence Function Equilibrium Stress Material Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Peter Haupt
    • 1
  1. 1.Institute of MechanicsUniversity of KasselKasselGermany

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