一维应变限制粘弹性的应力-速率相容模型
A thermodynamically consistent stress-rate type model of one-dimensional strain-limiting viscoelasticity
摘要：
我们介绍了一个一维应力率型非线性粘弹性模型的固体，服从应变极限理论的假设。与经典的粘弹性理论不同，目前的应变极限理论的关键假设是，线性化应变与应力和应力率非线性相关。我们使用的补充自由能，或等价地，吉布斯自由能模型的热力学一致性。这使得我们可以把应力和应力率作为原始变量，而不是像变形或应变这样的运动学量。我们还表明，在考虑材料的非耗散部分有一个存储的能量。从能量衰减、运动的非线性微分方程和相应的线性模型的傅里叶分析的观点，比较了新的应力-速率型模型和Rajagopal的应变-速率型粘弹性模型。
英文摘要：
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, or equivalently, 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 have 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.
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