  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.
