We continue our investigation of viscoelasticity by extending the Holzapfel-Simo approach discussed in Part I to the fully nonlinear regime. By scrutinizing the relaxation property for the non-equilibrium stresses, it is revealed that a kinematic assumption akin to the Green-Naghdi type is necessary in the design of the potential. This insight underscores a link between the so-called additive plasticity and the viscoelasticity model under consideration, further inspiring our development of a nonlinear viscoelasticity theory. Our strategy is based on Hill's hyperelasticity framework and leverages the concept of generalized strains. Notably, the adopted kinematic assumption makes the proposed theory fundamentally different from the existing models rooted in the notion of the intermediate configuration. The computation aspects, including the consistent linearization, constitutive integration, and modular implementation, are addressed in detail. A suite of numerical examples is provided to demonstrate the capability of the proposed model in characterizing viscoelastic material behaviors at large strains.

翻译：我们通过将第一部分中讨论的Holzapfel-Simo方法拓展至完全非线性区域，继续对粘弹性问题的研究。通过审视非平衡应力的松弛特性，发现需要在势函数设计中引入类似Green-Naghdi类型的运动学假设。这一认识揭示了所谓可加塑性模型与本研究所考虑的粘弹性模型之间的联系，进而启发我们发展出非线性粘弹性理论。该理论基于Hill超弹性框架并利用广义应变概念。值得注意的是，所采用的运动学假设使得本理论从根本上区别于基于中间构型概念的现有模型。本文详细阐述了包括一致线性化、本构积分及模块化实现在内的计算方面的问题。通过一系列数值算例展示了所提模型在表征大应变条件下粘弹性材料行为方面的能力。