The remarkable versatility and adaptability of skeletal muscle that arises from the assembly of its nanoscale cross-bridges into micro-scale assemblies known as sarcomeres provides great inspiration for the development of advanced adaptive structures and material systems. Motivated by the capability of cross-bridges to capture elastic strain energy to improve the energetic efficiency of sudden movements and repeated motions, and by models of cross-bridge power stroke motions and sarcomere contractile behaviors that incorporate asymmetric, bistable potential energy landscapes, this research develops and studies modular mechanical structures that trap and store energy in higher-energy configurations. Modules exhibiting tailorable asymmetric bistability are first designed and fabricated, revealing how geometric parameters influence the asymmetry of the resulting double-well energy landscapes. These experimentally-observed characteristics are then investigated with numerical and analytical methods to characterize the dynamics of asymmetrically bistable modules. The assembly of such modules into greater structures generates complex, multi-well energy landscapes with stable system configurations exhibiting different quantities of stored elastic potential energy. Dynamic analyses illustrate the ability of these structures to capture a portion of the initial kinetic energy due to impulsive excitations as recoverable strain potential energy, and reveal how stiffness parameters, damping, and the presence of thermal noise in micro-and nano-scale applications influence energy capture behaviors. The insights gained could foster the development of advanced structural/material systems inspired by skeletal muscle, including actuators that effectively capture, store, and release energy, as well as adaptive, robust, and reusable armors and protective devices.