Exoskeletons by microelectromechanical textures attached to an elastic structure: higher-order gradients metamaterials and soft robotics

We present a theoretical framework for designing an "exoskeleton" composed of distributed micromechanisms attached to a continuous elastic structure. Rigid and deformable microcomponents impose local kinematic constraints on the host continuum, effectively altering its elastic response. Enabled by advances in additive manufacturing, such micromechanism textures can impart special higher-order gradient elasticity to a soft substrate while bridging classical and soft robotics. Using Hamilton's principle, we derive the governing equations and show that the elastic energy stores contributions depending on first-and second-order spatial derivatives of displacement. A simple three-point linkage mechanism is illustrated: it yields first-and second-order strain-gradient potentials via internal springs. The kinetic energy similarly exhibits novel mixed spatiotemporal inertia terms. Numerical examples confirm that the discrete microstructure homogenizes to a continuum with the targeted higher-gradient stiffness. This approach offers a new design paradigm for metamaterials and soft robots, allowing precise control of elasticity and deformation through integrated micromechanical actuation.