If a porous media is being damaged by excessive stress, the elastic matrix at every infinitesimal volume separates into a ‘solid’ and a ‘broken’ component. The ‘solid’ part is the one that is capable of transferring stress, whereas the ‘broken’ part is advecting passively and is not able to transfer the stress. In previous works, damage mechanics was addressed by introducing the damage parameter affecting the elastic properties of the material. In this work, we take a more microscopic point of view, by considering the transition from the ‘solid’ part, which can transfer mechanical stress, to the ‘broken’ part, which consists of microscopic solid particles and does not transfer mechanical stress. Based on this approach, we develop a thermodynamically consistent dynamical theory for porous media including the transfer between the ‘broken’ and ‘solid’ components, by using a variational principle recently proposed in thermodynamics. This setting allows us to derive an explicit formula for the breaking rate, i.e., the transition from the ‘solid’ to the ‘broken’ phase, dependent on the Gibbs’ free energy of each phase. Using that expression, we derive a reduced variational model for material breaking under one-dimensional deformations. We show that the material is destroyed in finite time, and that the number of ‘solid’ strands vanishing at the singularity follows a power law. We also discuss connections with existing experiments on material breaking and extensions to multi-phase porous media.

如果多孔介质因过大的应力而损坏，则每个无穷小体积处的弹性基体都会分离成“固体”和“破碎”成分。“实心”部分是能够传递应力的部分，而“破碎”部分是被动平流的，不能传递应力。在之前的工作中，通过引入影响材料弹性性能的损伤参数来解决损伤力学问题。在这项工作中，我们采取更微观的角度，考虑从可以传递机械应力的“固体”部分到由微观固体颗粒组成且不传递机械应力的“破碎”部分的过渡。基于这种方法，我们通过使用热力学中最近提出的变分原理，开发了一种多孔介质热力学一致的动力学理论，包括“破碎”和“固体”成分之间的传递。这种设置使我们能够导出断裂率的明确公式，即从“固体”相到“破碎”相的转变，取决于每个相的吉布斯自由能。使用该表达式，我们推导出一维变形下材料断裂的简化变分模型。我们证明了材料在有限的时间内被破坏，并且在奇点处消失的“固体”股线的数量遵循幂律。我们还讨论了与现有材料破碎和多相多孔介质扩展实验的联系。