Stimuli–responsive programmable mechanics of bi-level architected nonlinear mechanical metamaterials

Mechanical metamaterials which are often conceptualized as a periodic network of beams have been receiving significant attention over the last decade, wherein the major focus remains confined to the design of micro-structural configurations to achieve application-specific multi-functional characteristics in a passive framework. It is often not possible to actively modulate the metamaterial properties post-manufacturing, critically limiting the applications for a range of advanced intelligent structural systems. To achieve physical properties beyond conventional saturation limits attainable only through unit cell architectures, we propose to shift the design paradigm towards more innovative bi-level modulation concepts involving the coupled design space of unit cell geometries, architected beam-like members and their stimuli–responsive deformation physics. On the premise of revolutionary advancements in additive manufacturing technologies, we introduce hard magnetic soft (HMS) material architectures in the beam networks following physics-informed insights of the stress resultants. Through this framework, it is possible to achieve real-time on-demand control and modulation of fundamental mechanical properties like elastic moduli and Poisson’s ratios based on a contactless far-field stimuli source. A generic semi-analytical computational framework involving the large-deformation geometric non-linearity and material non-linearity under magneto-mechanical coupling is developed for the effective elastic properties of HMS material based bi-level architected lattices under normal or shear modes of mechanical far-field stresses, wherein we demonstrate that the constitutive behaviour can be programmed actively in an extreme-wide band based on applied magnetic field. Under certain combinations of the externally applied mechanical stress and magnetic field depending on the residual magnetic flux density, it is possible to achieve negative stiffness and negative Poisson’s ratio with different degrees of auxecity, even for the non-auxetic unit cell configurations. The results further reveal that a single metamaterial could behave like extremely stiff metals to very soft polymers through contactless on-demand modulation, leading to a wide range of applicability in statics, stability, dynamics and control of advanced mechanical, aerospace, robotics and biomedical systems at different length scales.