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Multiscale approaches for hierarchical biological materials

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USMW02 - Mathematical mechanical biology: old school and new school, methods and applications


We present new approaches for a direct deduction of the macroscopic properties of biological and rubberlike materials, starting from a detailed discussion of the behavior at the molecular and cellular scale. By adapting classical methods of equilibrium and non equilibrium statistical mechanics, we describe different types of instabilities observed in polypeptide chains. From one side conformational transitions corresponding to the unfolding of crystal hard domains, such as beta-sheets and alpha helices secondary structures are modeled by considering multiwells energy functions. From the other side bonds breaking as in the case of RNA /DNA denaturation or molecules and cell decohesion are modeled by considering a ‘degenerate’ second energy well, corresponding to constant (debonding) energy and zero force. In this way the purely mechanical approaches for phase transition and hysteresis that we previously proposed  in discrete models based on the introduction of internal (spin type) variables, are extended to the cases when thermal, rate, and entropic effects cannot be neglected. Different phenomena will be described such as protein unfolding taking care of intermolecular or external devices interaction, non-local interactions and interfaces energy effects, intermediate ‘damaged’ configurations anticipating decohesion. Based then on classical multiscale modelling and continuum mechanics we deduce effective macroscale constitutive models with damage, residual strains, hysteresis, healing, growth and rate effects.

This talk is part of the Isaac Newton Institute Seminar Series series.

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