Adaptive Modelling and Optimization of Hyperelastic Cellular Structures

Cellular solids are strong, flexible structures, built from seemingly fragile materials. Among the best known mechanical qualities of these structures are their high strength-to-weight ratio and energy absorption capacity, which arise from the inextricable relation between the geometric architecture and the nonlinear elastic responses of their constituents. In living structures, such as biological tissue, apposition and resorption of cellular matter are determined by the magnitude of the stresses, with structures under loading becoming denser at the point of stress. In cellular structures in general, several main factors determine the magnitude of the enhancement of stress level in the cellular material, including the cell geometry, the cell wall thickness, and the presence of cell inclusions. While new physical criteria associated with different stages of development or healing in natural structures are still to be identified, there is also a need for appropriate theoretical approaches to be developed that take into account the large stress and strain fields during physiological or pathological changes.
The main objectives of this project are as follows:
(i) To identify mechanical properties amenable to mathematical treatment and produce physically realistic mathematical models for natural cellular structures capable of recovering completely after large deformations;
(ii) To carry out the mathematical mechanical analysis of these models within the theoretical framework of large strain elasticity, which provides a complete description of the elastic responses of a solid material under loading;
(iii) To design and test computational models based on the finite element method for the numerical analysis of these structures.