During growth processes many biological and physiological systems develop residual stresses. These stresses are present in the body even in the absence of external or body loadings and are known to play an important role in regulation processes. Residual stress can be observed when the body is cut and part of the stresses are relieved. A fundamental difficulty in elasticity is to describe the mechanics of a body with residual stresses.
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Simulation and modeling of fluid flow through porous media are fundamental to numerous fields of study, including chemical and petroleum engineering, hydrology, micro-fluidics, biological transport, textile science, filtration science, and solidification science. The tensor permeability provides the relationship between the pressure gradient and flow rate in these systems, and is crucial to the accurate simulation of many phenomena.