  We perform the linear stability analysis for a new model for poromechanical
processes with inertia (formulated in mixed form using the solid deformation,
fluid pressure, and total pressure) interacting with diffusing and reacting
solutes convected in the medium. We find parameter regions that lead to
spatio-temporal instabilities of the coupled system. The mutual dependences
between deformation and diffusive patterns are of substantial relevance in the
study of morphoelastic changes in biomaterials. We provide a set of
computational examples in 2D and 3D (related to brain mechanobiology) that can
be used to form a better understanding on how, and up to which extent, the
deformations of the porous structure dictate the generation and suppression of
spatial patterning dynamics, also related to the onset of mechano-chemical
waves.
