Large deforming hyperelastic curved cantilever beams with intermediate kinematic constraints: Analysis and design within a physics-informed semi-analytical framework

Abstract

Beam-like flexible structures made of soft materials have been drawing significant attention for their broad application prospects. For rigorously designing such soft continuum structures, several unaddressed large deformation problems need to be analysed as the foundation. We consider one such unaddressed fundamental large deformation problem of hyperelastic curved cantilever beams, which maintain prescribed kinematic constraints at the desired intermediate location. For maintaining the prescribed kinematic constraints, we propose three different kinetic designs. In the first design, a concentrated design force with unknown magnitude and direction is applied at the prescribed intermediate location in addition to the applied load. Whereas in the second and third designs, uniformly distributed and linearly varying unknown design forces are applied. For analysing the large deformation problem under the known applied and unknown design forces, a variational energy principle-based semi-analytical framework is developed, considering the geometric and material nonlinearities. An iterative computational algorithm is integrated with the framework for determining the magnitude and direction of the unknown design forces by satisfying the prescribed kinematic constraints. A parametric study is performed on the effects of the initial curved geometry, location of the kinematic constraints, and the external loading configuration on the design variables. The considered nonlinear problem, along with the developed physically insightful framework including the proposed designs and parametric investigations, may facilitate analyzing the complicated kinematic interaction between the large deforming stimuli-active portion of soft continuum structures and their stimuli-inactive portion providing support for steering, which in turn may facilitate more rigorous designs.