Summary
Asymptotic constitutive approximations for the rapid finite deformation of general viscoelastic materials are developed. The zero-order approximation is an elastic-type constitutive equation, although different from the elastic equation for the slow-deformation approximation. The higher-order terms are multiple integrals of the departure of the deformation history from the step-function history. The approximations are shown to be form-invariant to change of deformation measure. The approximations are specialized to isotropic solids and to fluids. As observed byMetzner, White andDenn [3] andPipkin [4], fluids undergoing rapid deformations exhibit a solid-like behavior.
Zusammenfassung
Es werden asymptotische Materialgleichungen für die rasche endliche Deformation eines allgemeinen viskoelastischen Materials entwickelt. Die nullte Näherung ist eine Materialgleichung vom elastischen Typ, wenn auch verschieden von der elastischen Näherungsgleichung für langsame Deformationen. Die Glieder höherer Ordnung sind Vielfachintegrale der Abweichung der Deformationsgeschichte von der Stufenfunktionsgeschichte. Es wird gezeigt, daß die Näherungen invariant sind gegen eine Änderung des Deformationsmaßes. Sie werden für isotrope Festkörper und für Flüssigkeiten spezialisiert. WieMetzner, White undDenn [3] sowiePipkin [4] beobachtet haben, zeigen Flüssigkeiten, die raschen Deformationen unterworfen werden, ein festkörperähnliches Verhalten.
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Leigh, D.C. Asymptotic constitutive approximations for rapid deformations of viscoelastic materials. Acta Mechanica 5, 274–288 (1968). https://doi.org/10.1007/BF01178664
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DOI: https://doi.org/10.1007/BF01178664