Mechanical integrated circuit materials.

Recent developments in autonomous engineered matter have introduced the ability for intelligent materials to process environmental stimuli and functionally adapt1-4. To formulate a foundation for such an engineered living material paradigm, researchers have introduced sensing5-11 and actuating12-16 functionalities in soft matter. Yet, information processing is the key functional element of autonomous engineered matter that has been recently explored through unconventional techniques with limited computing scalability17-20. Here we uncover a relation between Boolean mathematics and kinematically reconfigurable electrical circuits to realize all combinational logic operations in soft, conductive mechanical materials. We establish an analytical framework that minimizes the canonical functions of combinational logic by the Quine-McCluskey method, and governs the mechanical design of reconfigurable integrated circuit switching networks in soft matter. The resulting mechanical integrated circuit materials perform higher-level arithmetic, number comparison, and decode binary data to visual representations. We exemplify two methods to automate the design on the basis of canonical Boolean functions and individual gate-switching assemblies. We also increase the computational density of the materials by a monolithic layer-by-layer design approach. As the framework established here leverages mathematics and kinematics for system design, the proposed approach of mechanical integrated circuit materials can be realized on any length scale and in a wide variety of physics.