Modeling shape evolution in a system composed of interacting elastic bodies based on individually assigned and temporally evolving energy landscapes

Abstract

In both engineered and living systems composed of mechanically interacting elastic bodies, variational modeling, which assigns an energy function to a system, has effectively captured the shape evolution in the elastic body system in response to the mechanical interactions. However, to make an energy function represent component-level shape evolution, the energy function should account for the evolution of mechanical interactions along with the shape evolution of the individual elastic bodies. In this study, we develop an energy function-based model that assigns an energy function with landscape evolution to each elastic body in a system. This model formulates the shape evolution of individual elastic bodies and the evolution of their contact forces, based on the shape gradients of the assigned energy functions and the landscape evolution, respectively. To clarify a characteristic of the system dynamics, we implement this formulation on finite element simulations for a simple two-dimensional system with concave-convex joint-like geometry under axial and oblique loading conditions. Under axial loading, the contact force distribution remains substantially constant, and the energy values decrease as expected from the shape gradients. Under oblique loading, localized increases in the contact force at specific corners generate landscape evolution that increases the energy. Consequently, our formulation has clarified that the energy increase of the components emerges as a characteristic of system dynamics associated with the landscape evolution of the energy functions.

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