Payne effect is the complex nonlinear response of filled elastomers to oscillatory loading. Although usually characterized by the decrease in the storage modulus with strain amplitude, and by the bell-shaped curve of loss modulus with strain amplitude, the response has many other peculiar features. The manner of decrease in storage modulus with strain amplitude does not change when the frequency of the test is changed. Static strain offsets do not change the relationship between storage modulus and strain amplitude. In addition, when tested at relatively large strain amplitude levels, the material behavior changes and requires a certain period of time before it returns to what was initially observed. In this study, a model is developed to describe Payne effect using a framework of multiple natural configurations. Assuming appropriate functional forms for the Helmholtz potential and the rate of dissipation, and maximizing the rate of dissipation over all allowable mechanical processes, the constitutive equations were obtained. In a simple one-dimensional setup, the model was able to describe many aspects of Payne effect reasonably well, including the independence of the nature of modulus decrease on the frequency of loading and static strain offsets.

Payne效应是填充的弹性体对振荡载荷的复杂非线性响应。尽管通常的特征是储能模量随应变幅度的降低而下降，而损耗模量的钟形曲线随应变幅度的升高而变化，但响应具有许多其他独特的特征。当测试频率改变时，储能模量随应变幅度降低的方式不会改变。静态应变偏移不会改变储能模量和应变幅度之间的关系。此外，在相对较大的应变幅度水平下进行测试时，材料的性能会发生变化，并且需要一定的时间才能恢复到最初观察到的状态。在这项研究中，开发了一个模型来描述使用多种自然结构构架的Payne效应。假定亥姆霍兹势和耗散率具有适当的函数形式，并在所有允许的机械过程中使耗散率最大化，则获得了本构方程。在简单的一维设置中，该模型能够很好地描述Payne效应的许多方面，包括模量下降性质与载荷频率和静态应变偏移的独立性。