The remarkable energetic versatility and adaptability of skeletal muscle provides great inspiration to develop advanced adaptive structures and materials. These notable properties may arise from the assembly of skeletal muscle's nanoscale crossbridges into microscale structures known as sarcomeres. Essential understanding of muscle energetics has been developed from models of the micro/nanoscale constituents which incorporate an intriguing, asymmetric, bistable potential energy landscape to capture trends in the experimental data on cross-bridge power stroke motions. Inspired by the capability of cross-bridges to strategically absorb and store elastic energy for achieving high energetic efficiency of sudden motions, this research studies the assembly of modular mechanical structures from asymmetrically bistable constituents to absorb and trap energy in higher-energy stable configurations. Specifically, energy features of a module with an asymmetrically bistable element are first studied; these modules are then assembled in series and parallel to generate structures with multiple stable configurations having different quantities of stored energy. Dynamic analyses are performed to illustrate the ability of these structures to trap a portion of the kinetic energy due to an impulsive excitation as recoverable and reusable strain energy, and insight is gained into how asymmetries and damping influence the energy trapping performance.