Continuum modeling for layer jamming structures

• This study presents a continuum constitutive model for Layer Jamming Structures (LJS) that captures both solid-like and liquid-like states under various loading conditions. • The model incorporates average-field technique, enabling analytical expressions for stress-strain relationships, energy dissipation, and yield surface tracking. • The proposed model is validated against finite element simulations, demonstrating strong agreement with numerical results in uniaxial, multi-directional, and coupled shear-normal loading scenarios. • The model's accuracy and versatility offer significant insights for the design and optimization of jamming-based adaptive structures in soft robotics and related applications. Layer jamming structures (LJS) are a class of variable stiffness structures that are valuable for adaptive and soft robotic systems. However, existing models for LJS often rely on discrete approximations or are tailored to specific configurations, limiting their generalizability and computational efficiency. In this study, we propose a continuum elastoplastic constitutive model for LJS based on the average-field technique. The model captures both the jamming (no interlayer slipping) and slipping states of LJS, enabling analytical expressions for yield criteria, and dissipated energy density. Finite element simulations in Abaqus incorporating periodic boundary conditions were conducted to validate the theoretical model under various deformation scenarios, including uniaxial shear, multi-directional shear, and coupled shear-normal loading. The results demonstrate strong agreement between numerical and theoretical predictions, effectively capturing the nonlinear transitions in stiffness and energy evolution. This continuum framework offers a unified, scalable tool for modeling the mechanical behavior of LJS and supports the design and optimization of stiffness-tunable systems in soft robotics and beyond.