In this paper, a viscoelastic model able to capture important mechanical features of a wide class of glassy polymers is presented. Among them, the ability of reproducing the highly nonlinear rate-dependent stress response and the post-yield strain softening phenomenon. The simplicity of the proposition allows to recover the same mathematical structure of classical constitutive approaches, well suited for the use of implicit finite element codes. To this aim, the flow resistance concept, elsewhere known as shear strength, is reframed as a state variable of an accumulated strain measure. Three alternative expressions for this function are presented. The model is cast within a variational framework in which consistent constitutive updates are obtained by a minimization procedure. Convenient choices for the conservative and dissipative potentials reduce the local constitutive problem to the solution of a single nonlinear scalar equation, emulating the simplest case of viscoelastic models. Numerical tests on the constitutive model show excellent agreement with experimental data. Finally, a 3D simulation of a standard specimen with heterogeneous material properties illustrates the ability of the present proposition to be implemented in implicit finite element codes.

中文翻译：

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有限应变下玻璃态聚合物建模的变体框架

在本文中，提出了一种能够捕获多种玻璃态聚合物重要机械特征的粘弹性模型。其中，具有重现高度非线性速率相关应力响应的能力和屈服后应变软化现象。命题的简单性允许恢复经典本构方法的相同数学结构，非常适合使用隐式有限元代码。为了这个目的，流动阻力概念，也称为剪切强度被重新构造为累积应变测量的状态变量。给出了此函数的三个替代表达式。该模型在变式框架中进行转换，在该框架中，通过最小化过程获得了一致的本构更新。保守势散和耗散势的便捷选择将局部本构问题简化为单个非线性标量方程的解，从而模拟了粘弹性模型的最简单情况。本构模型的数值测试表明与实验数据具有很好的一致性。最后，具有异质材料特性的标准样品的3D模拟说明了本命题以隐式有限元代码实现的能力。