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


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),
$$\tilde T(t) = g(E) + \mathop {{\text{ }}B}\limits_{s \geqq 0} [E_d^t(s);E],$$
or by the representations (7.80) and (7.70),
$$T(t) = f(B) + \mathop \Im \limits_{s \geqq 0} \left[ {{G^t}(s);B(t)} \right],$$
$$T(t) = - p(\rho )1 + \mathop {{\text{ }}O}\limits_{s \geqq 0} \left[ {{G^t}\left( s \right);\rho } \right],$$
which describe the behaviour of isotropic solids and fluids. The mechanical process history is represented here in terms of the relative strain history,
$$s \mapsto E_d^t(s) = E(t - s) - E(t) = \frac{1}{2}(C(t - s) - C(t)),$$
$$s \mapsto {G^t}(s) = 2{F^{T - 1}}(t)[E(t - s) - E(t)]{F^{ - 1}}(t).$$


Evolution Equation Internal Variable Influence Function Equilibrium Stress Material Function 
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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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