Finite Element Modeling in Absolute Nodal Coordinate Formulation of the Mechanical Behavior of Pneumatic Actuators

Abstract

The application of the finite element method in terms of absolute nodal coordinate formulation (ANCF) for solving elasticity problems in the field of soft robots is considered. These problems are related to modeling the mechanical behavior of pneumatic actuators under internal pressure. In contrast to the traditional ANCF approach, only absolute node coordinates are used as sets of nodal degrees of freedom of the finite element. This allows calculations to be performed on unstructured hexahedral meshes and allows the complex geometric shape of pneumatic actuators to be described. The hyperelastic material models used in the article are specified through the strain energy density function. To construct the stiffness matrix, a second-order automatic differentiation algorithm is used. This algorithm guarantees the symmetrical form of the matrix and provides analytical accuracy in calculating the derivative. Within the presented modeling examples, the reliability of the Ogden model in terms of ensuring the stability of the problem’s numerical solution is shown. It is demonstrated that the features of the change in the actuator’s shape (swelling, bending, twisting, presence of self-contact of surfaces) depend on the characteristics of the actuator’s design. The obtained results are compared with the numerical and experimental data from other studies.