Abstract This study presents a variationally consistent formulation of the thermo-mechanically coupled problem with non-associative viscoplasticity for glassy amorphous polymers. First, the decomposition of the equivalent plastic strain is carried out to derive the variational consistent evolution law of the shear yield strength with reference to the analogous approach taken for formulating the Armstrong-Frederick model. Second, an alternative form of the dual viscoplastic dissipation potential is proposed to recast the principle of maximum plastic dissipation for viscoplasticity to be of the same form of rate-independent plasticity with the introduction of the extended yield function. Third, we address the optimization problem relevant to the thermo-mechanically coupled behavior of glassy amorphous polymers within the incremental variational framework with the help of the parameterization of flow rules. Thanks to the achieved variational consistency, the mathematical model derived by the proposed formulation can enjoy several benefits for ensuring the stability of the strongly coupled discretized equations in the monolithic method under the condition that the material behavior is stable. In addition, since the present formulation does not require the time derivative of the shear yield strength, the resulting evolution equation accommodates the time variations of temperature in terms of its material properties, implying that it is amenable to various thermal processes other than isothermal ones. Numerical examples are presented to demonstrate the capability of the proposed formulation in simulating actual compression tests conducted on a PMMA specimen that exhibits complex thermo-mechanically coupled phenomena.

中文翻译：

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玻璃态无定形聚合物具有非缔合粘塑性的热机械耦合问题的变相一致公式

摘要 本研究提出了玻璃态无定形聚合物具有非缔合粘塑性的热机械耦合问题的变分一致公式。首先，参考建立Armstrong-Frederick模型的类似方法，对等效塑性应变进行分解，推导出剪切屈服强度的变分一致演化规律。其次，提出了双粘塑性耗散势的另一种形式，通过引入扩展屈服函数，将粘塑性的最大塑性耗散原理改写为与速率无关的塑性相同的形式。第三，我们在流动规则参数化的帮助下，解决了在增量变分框架内与玻璃态无定形聚合物的热机械耦合行为相关的优化问题。由于实现了变分一致性，由所提出的公式导出的数学模型可以在材料行为稳定的条件下确保整体方法中强耦合离散方程的稳定性。此外，由于本公式不需要剪切屈服强度的时间导数，因此所得的演化方程根据其材料特性适应了温度的时间变化，这意味着它适用于除等温过程之外的各种热过程。