Controlling multistimuli elastic response by bistable micromodules

Controlling the elastic response of materials to multiple stimuli is a key prerequisite for the design of adaptive soft matter, e.g., for applications in medicine or soft robotics. Here, we discuss a statistical mechanics model in which the nonlinear elastic response is governed by mechanically coupled bistable micromodules which can be switched by external stimuli. Exact analytical solutions show complex stimuli-mediated, nonlinear stiffening/softening responses tuneable by the microscopic switching parameters. Importantly, we report up to two maxima in the softness (compliance) originating from cooperative transitions and show how to control their existence and properties. We demonstrate the usefulness of the model by fitting it to experimental extension-force data on various scales. We further illustrate how to explore the entire nonlinear response map as a function of multiple stimuli, utilizing distinct pathways to either cancel/reset or amplify the elastic responses through a combination of these stimuli. Our analysis should be useful for the design of nonlinear elasticity, e.g., in bistable microgel networks or mechanical metamaterials.