论文标题
一维应变限制粘弹性的热力学一致应力速率类型模型
A thermodynamically consistent stress-rate type model of one-dimensional strain-limiting viscoelasticity
论文作者
论文摘要
我们引入了遵守应变理论假设的固体的一维应力率类型非线性粘弹性模型。与经典的粘弹性理论不同，当前应变限制理论中的关键假设是线性菌株非线性地取决于应力和应力率。我们使用互补的自由能（等效地）显示模型的热力学一致性。这使我们能够将压力和应力速率作为原始变量而不是运动量（例如变形或应变）。我们还表明，所考虑的材料的非隔离部分具有存储的能量。我们将新的应力速率类型模型与应变率类型的粘弹性模型进行比较，这是由于能量衰减的观点，非线性运动方程以及相应线性模型的傅立叶分析。
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.
