We introduce a one-dimensional stress-rate type nonlinear viscoelastic model for solids that obey the assumptions of the strain-limiting theory. Unlike the classical viscoelasticity theory, the critical hypothesis in the present strain-limiting theory is that the linearized strain depends nonlinearly on the stress and the stress rate. We show the thermodynamic consistency of the model using the complementary free energy and then using the Gibbs free energy. This allows us to take the stress and the stress rate as primitive variables instead of kinematical quantities such as deformation or strain. We also show that the non-dissipative part of the materials in consideration has a stored energy. We compare the new stress-rate type model with the strain-rate type viscoelastic model due to Rajagopal from the points of view of energy decay, the nonlinear differential equations of motion and Fourier analysis of the corresponding linear models.

我们针对固体引入一维应力-速率类型非线性粘弹性模型，该模型遵循应变限制理论的假设。与经典的粘弹性理论不同，当前的应变限制理论的关键假设是线性化应变非线性地取决于应力和应力率。我们使用互补自由能然后使用吉布斯自由能来显示模型的热力学一致性。这使我们可以将应力和应力率作为原始变量，而不是诸如变形或应变之类的运动学量。我们还表明，考虑中的材料的非耗散部分具有存储的能量。从能量衰减的角度，我们将新的应力率类型模型与拉贾戈帕尔引起的应变率类型粘弹性模型进行了比较，