Three-dimensional third medium contact model for hyperelastic contact and pneumatically actuated systems

TL;DR

This paper introduces a novel 3D third-medium contact model for hyperelastic solids and pneumatically actuated systems, enabling unified, robust contact modeling without interface discretization, suitable for soft robotics and flexible structures.

Contribution

It extends a 2D regularization approach to 3D, incorporating pneumatic effects and ensuring element quality, with detailed linearization within the finite element framework.

Findings

Demonstrates high accuracy and robustness in complex contact scenarios.

Applicable to soft robotics and flexible mechanisms.

Shows versatility across different simulation benchmarks.

Abstract

This work presents a comprehensive three-dimensional third-medium contact framework for modeling complex contact interactions in hyperelastic solids and pneumatically actuated systems. The proposed third-medium formulation embeds a fictitious medium (or third medium) between potentially interacting bodies, enabling a unified and robust treatment of hyperelastic contact and self-contact without the need for discretization of the contact interface. Unlike the widely studied two-dimensional problem, this paper extends the new regularization term given in Reference \cite{TMCWriggers2} to three-dimensional problems and ensures element quality in a third medium. Due to the need for higher-order elements for the regularization term, this paper details the linearization process of this problem within the finite element framework. In addition, pneumatically actuated systems are considered by introducing a pneumatic term to represent pneumatic loading (pressure or suction) and inducing contact caused by internal inflation. This approach is suitable for complex hyperelastic contact and self-contact, and has potential applications in the fields of soft robotics and flexible mechanisms. The framework is developed in a fully three-dimensional setting, making it also suitable for isogeometric methods and meshless methods. Several benchmark and application-level simulations demonstrate the accuracy, robustness, and versatility of the proposed approach. The results highlight the capability of the three-dimensional third-medium model to handle challenging nonlinear contact scenarios relevant to soft materials, soft actuators, and emerging multifunctional structures.