This paper proposes a new way of describing effective stress in granular materials, in which stress is represented by a continuous function of direction in physical space. The proposal provides a rigorous approach to the task of upscaling from particle mechanics to continuum mechanics, but is simplified compared to a full discrete element analysis. It leads to an alternative framework of stress–strain constitutive modelling of granular materials that in particular considers directional dependency. The continuous function also contains more information that the corresponding tensor, and thereby provides space for storing information about history and memory. A work-conjugate set of geometric rates representing strain-rates is calculated, and the fundamental principles of local action, determinism, frame indifference, and rigid transformation indifference are shown to apply. A new principle of freedom from tensor constraint is proposed. Existing thermo-mechanics of granular media is extended to apply for the proposed functions, and a new method is described by which strain-rate equations can be used in large-deformations modelling. The new features are illustrated and explored using simple linear elastic models, producing new results for Poisson’s ratio and elastic modulus. Ways of using the new framework to model elastoplasticity including critical states are also discussed.

本文提出了一种描述粒状材料中有效应力的新方法，其中应力由物理空间中方向的连续函数表示。该提议为从粒子力学到连续谱力学的升级任务提供了严格的方法，但是与完整的离散元素分析相比，该提议得到了简化。这导致了颗粒材料的应力-应变本构模型的替代框架，该框架特别考虑了方向依赖性。连续函数还包含对应张量的更多信息，从而为存储有关历史记录和内存的信息提供了空间。计算代表应变率的几何共轭功共轭集，并进行局部作用，确定性，框架无差异，和僵化的变换冷漠都适用。提出了不受张量约束的新原理。扩展了现有的颗粒介质热力学方法，以适用于所提出的功能，并描述了一种新的方法，通过该方法，应变率方程可用于大变形建模。使用简单的线性弹性模型说明和探索了这些新功能，从而产生了泊松比和弹性模量的新结果。还讨论了使用新框架对包括临界状态的弹塑性进行建模的方法。使用简单的线性弹性模型说明和探索了这些新功能，从而产生了泊松比和弹性模量的新结果。还讨论了使用新框架对包括临界状态的弹塑性进行建模的方法。使用简单的线性弹性模型说明和探索了这些新功能，从而产生了泊松比和弹性模量的新结果。还讨论了使用新框架对包括临界状态的弹塑性进行建模的方法。