The purpose of this paper is to present a general upscaling strategy for deriving macroscopic constitutive laws for rubber-like materials from the knowledge of the network distribution and a mechanical description of the individual chains and of their free energy. The microscopic configuration is described by the position of the cross-links and is not obtained by an affine assumption but by minimizing the corresponding free energy on stochastic large representative volume elements with adequate boundary conditions. This general framework is then approximated by using a microsphere (directional) description of the network. It is presented in a global setting and is extended in order to handle situations with tube-like constraints and stress-induced crystallization.

本文的目的是提出一种通用的升级策略，用于从网络分布的知识以及单个链及其自由能的机械描述中得出类橡胶材料的宏观本构定律。微观结构是由交联的位置描述的，不是通过仿射假设获得的，而是通过在具有适当边界条件的情况下，将随机大型代表体积元素上的相应自由能最小化来获得的。然后，通过使用网络的微球（定向）描述来近似此通用框架。它以全局设置显示，并进行扩展以处理具有管状约束和应力引起的结晶的情况。