A MULTI-SCALE MODEL FOR STRESS DISTRIBUTION IN CELLULAR MEMBRANE (first part) Introduction and theoretical approach

A new approach modeling the fails in biological tissue is here proposed. Under the assumption that the cell membrane may be modeled, similarly as neo-Hookean materials, I develop the problem in the framework of nonlinear elasticity. I try to model the ice nucleation phenomenon when freezing and thawing occurs in cellular cryo-preservation. The generated surface of the ice seed can be either soft or wrinkled and, in the latter case a punch contact against the cell membrane take place. Restricting the attention on rescaled mono-dimensional sub-set, we extend the structured deformations theory by Del Piero & Owen, in the proposed model. I find a particular solution in agree to the classical fracture models besides a response function in according to the stress and strain fields distribution in biological materials. Developing the paper in two parts, in this one take care of nonlinear elasticity and biomechanics fundamentals.
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