Thermal stresses in frozen organs

An analysis was performed to determine the thermal stresses in the solid region of an organ frozen so that a constant cooling rate is imposed on its outer surface. The analysis shows that at the instant the water freezes at a certain location in the organ, compressive azimuthal stresses develop in the region close to the change of phase front. The compressive asimuthal stresses decrease and become tensile at that location as the change of phase front propagates further. The radial stresses are always compressive. It is hypothesized that those stresses might induce mechanical damage to the cellular components of the organ. The analysis shows that the magnitude of these stresses is a function of the material properties and the product of the outer surface cooling rate and the square of the outer surface radius.