We propose a modeling framework for finite viscoelasticity, inspired by the kinematic assumption made by Green and Naghdi in plasticity. This approach fundamentally differs from the widely used multiplicative decomposition of the deformation gradient, as the intermediate configuration, a concept that remains debated, becomes unnecessary. The advent of the concept of generalized strains allows the Green-Naghdi assumption to be employed with different strains, offering a flexible mechanism to separate inelastic deformation from total deformation. This leads to a constitutive theory in which the kinematic separation is adjustable and can be calibrated. For quadratic configurational free energy, the framework yields a suite of finite linear viscoelasticity models governed by linear evolution equations. Notably, these models recover established models, including those by Green and Tobolsky (1946) and Simo (1987), when the Seth-Hill strain is chosen with the strain parameter being -2 and 2, respectively. It is also related to the model of Miehe and Keck (2000) when the strain is of the Hencky type. We further extend the approach by adopting coercive strains, which allows us to define an elastic deformation tensor locally. This facilitates modeling the viscous branch using general forms of the configurational free energy, and we construct a micromechanical viscoelastic model as a representative instantiation. The constitutive integration algorithms of the proposed models are detailed. We employ the experimental data of VHB 4910 to examine the proposed models, which demonstrate their effectiveness and potential advantages in the quality of fitting and prediction. Three-dimensional finite element analysis is also conducted to assess the influence of different strains on the viscoelastic behavior.

翻译：我们提出了一种有限粘弹性建模框架，其灵感来源于Green和Naghdi在塑性理论中提出的运动学假设。该方法与广泛使用的变形梯度乘法分解有根本区别，因为它无需引入中间构型这一仍存争议的概念。广义应变概念的出现使得Green-Naghdi假设可与不同应变度量结合使用，为从总变形中分离非弹性变形提供了一种灵活机制。这导出了一套运动学分离可调且可标定的本构理论。对于二次构型自由能，该框架生成了一系列由线性演化方程控制的有限线性粘弹性模型。值得注意的是，当选择Seth-Hill应变且应变参数分别为-2和2时，这些模型可退化为经典模型，包括Green和Tobolsky（1946）以及Simo（1987）的模型。当采用Hencky型应变时，该框架也与Miehe和Keck（2000）的模型相关联。我们进一步通过采用强制应变扩展了该方法，这使得我们能够在局部定义弹性变形张量。这便于使用一般形式的构型自由能对粘性分支进行建模，并构建了一个微力学粘弹性模型作为代表性实例。文中详细阐述了所提模型的本构积分算法。我们采用VHB 4910的实验数据检验了所提模型，结果表明其在拟合与预测质量方面具有显著效果和潜在优势。此外，还进行了三维有限元分析以评估不同应变对粘弹性行为的影响。