This paper presents the testing and constitutive modeling of a Thermoplastic Polyurethane (TPU) compound used in commercial applications. The tested specimens were extracted directly from a TPU sphere used in check valves through water-jet cutting. The tests included tensile and compression tests under complex uniaxial loading protocols to capture different nonlinear phenomena, such as stress softening, hysteresis, relaxation, creep, and rate dependence. The material is modeled assuming a nonlinear elastic equilibrium path that may exhibit stress softening (i.e., Mullins effect), and a hysteretic viscoplastic response that presents rate dependence at three different time scales. To achieve this constitutive behavior, a Parallel Rheological Framework model is used. The nonlinear elastic equilibrium path is modeled using the generalized Yeoh hyperelastic model. The stress softening of the equilibrium path is modeled using the Ogden-Roxburgh damage model on the deviatoric response. The hysteretic viscous response is further split into three viscoplastic chains to represent time dependence at three different time scales in a decoupled way. Each viscoplastic chain is modeled using the Bergstrom-Boyce model with its standard evolution law of the creep strain. The model parameters were found using a stochastic optimization scheme to simultaneously fit all the considered tests. The outstanding agreement between the model and the experimental data across a wide range of loading scenarios provides additional insight into the time-dependent behavior and deformation mechanism of TPUs. Moreover, it shows that the mechanical behavior of these materials can be represented by decoupling the nonlinear viscoplastic behavior in different time scales.

中文翻译：

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复杂单轴载荷下热塑性聚氨酯的实验表征和本构建模

本文介绍了商业应用中使用的热塑性聚氨酯 (TPU) 化合物的测试和本构建模。测试样本通过水射流切割直接从止回阀中使用的 TPU 球体中提取。测试包括复杂单轴加载协议下的拉伸和压缩测试，以捕获不同的非线性现象，例如应力软化、滞后、松弛、蠕变和速率依赖性。该材料的建模假设可能表现出应力软化（即马林斯效应）的非线性弹性平衡路径，以及在三个不同时间尺度上呈现速率依赖性的滞后粘塑性响应。为了实现这种本构行为，使用了并行流变框架模型。使用广义 Yeoh 超弹性模型对非线性弹性平衡路径进行建模。使用偏响应的 Ogden-Roxburgh 损伤模型对平衡路径的应力软化进行建模。迟滞粘性响应进一步分为三个粘塑性链，以解耦的方式表示三个不同时间尺度上的时间依赖性。每个粘塑性链均使用 Bergstrom-Boyce 模型及其蠕变应变的标准演化定律进行建模。使用随机优化方案找到模型参数，以同时拟合所有考虑的测试。该模型与各种负载场景下的实验数据之间的出色一致性为 TPU 的时间依赖性行为和变形机制提供了额外的见解。此外，它表明这些材料的力学行为可以通过解耦不同时间尺度的非线性粘塑性行为来表示。