Finite deformation viscoelasticity laws

It is proved that two different decompositions of strain may be assigned to every linear viscoelastic solid. In particular, this is true for the so-ca lled three-parameter solids. For this case, the two decompositions of defor mation are in a natural way associated with the two well known spring-dashp ot models, the first one being a spring in parallel with a Maxwell element and the second model consisting of a spring in series with a Kelvin element . Furthermore, it is shown how the two decompositions of deformation may be generalized to finite deformations in the framework of a multiplicative de composition of the deformation gradient tensor. This enables, to assign to each version of the three-parameter solids a corresponding class of finite deformation counterparts, Note that the finite deformation models are deriv ed so, that the second law of thermodynamics is satisfied for every admissi ble process. To this end, use is made of the so-called Mandel stress tensor . As one may expect, unlike the linear case, the finite deformation models obtained do not predict identical mechanical responses generally. This is i llustrated for the:loading case of uniaxial tension-compression. Also, an a nalysis of the model responses for simple shear is given. (C) 2000 Elsevier Science Ltd. All rights reserved.