Continuum Mechanics and Theory of Materials

Generalized parameter identification for finite viscoelasticity

“…In 1998 Reese and Govindjee [65] proposed a continuum formulation which is, in contrast to many other theories, not restricted to viscoelastic response for states near the thermodynamic equilibrium (for further elaborations see, e.g. Reese and Govindjee [64], Govindjee and Reese [18], Lion [34], [35], Haupt [21], Holzapfel [23] and Huber and Tsakmakis [25]). In recent years the identification of the material parameters for viscoelastic constitutive laws has additionally been investigated.…”

“…Darüber hinaus müssen für die Simulation des viskoelastischen Materialverhaltens typischer gummiähnlicher Materialien große Deformationen und große Abweichungen vom thermodynamischen Gleichgewicht berücksichtigt werden. Von Reese and Govindjee [65] wurde 1998 eine neue Kontinuumsformulierung vorgeschlagen, die im Gegensatz zu vielen anderen Theorien nicht auf kleine Abweichungen vom thermodynamischen Gleichgewicht beschränkt ist, siehe auch Reese und Govindjee [64], Govindjee und Reese [18], Lion [34], [35], Haupt [21], Holzapfel [23] sowie Huber und Tsakmakis [25]. In den letzten Jahren wurde ebenfalls die Identifikation von Materialparametern für visko-elastische konstitutive Gesetze untersucht.…”

Toward a Field Theory for Elastic Bodies Undergoing Disarrangements

“…Consequently, the pairs (M(X, t), G(X, t)) available through dynamical processes in E d lie in a submanifold of Lin V × Lin V. In particular, for each (X, t), the pairs (Ṁ(X, t),Ġ(X, t)) of time-derivatives available through dynamical processes in E d lie in the tangent space of the submanifold at (M(X, t), G(X, t)) and, hence, cannot be arbitrary elements of Lin V × Lin V. Similarly, the mixed power inequality (7.14) imposes a restriction on the quantities M, G,Ṁ andĠ, or, equivalently, on F , G,Ḟ andĠ, that can arise for dynamical processes in the constitutive class E d , and we shall discuss some of these restrictions in Section 8. Finally, for every classical dynamical process χ, ∇χ, S, ψ in E d , the consistency relation (7.15), and the fact that K = I when M = F − G = 0, yield for all X, t: 16) and, equivalently, by (7.3),…”

“…Suppose that the response function (M, G) →˜ (M, G) is chosen to satisfy the condition 16) for all tensors G with det G > 0. If we consider a smooth deformation χ and put G := ∇χ, then the tensor field M = ∇χ − G is identically zero and (1.2)-(1.4) are satisfied identically, the last with " " replaced by "=".…”

“…The stress tensor (det K)S is an analogue of the "weighted Cauchy tensor" (det F )T discussed in [16], and equations (3.1) and (3.5) show that it is this weighted measure of stress that readily decomposes into a part without disarrangements plus a part due to disarrangements.…”