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Inspired by natural earthworms' locomotion mechanism, this paper investigates how the earthworm's muscle works and presents the approach to mimic segmental muscle by employing rigid elements-based morphing structures. Specifically, the proposed earthworm-like robot employs a class of 2D rigid elements and their array to achieve programmable bidirectional 3D deformation, making the formed mechanism precisely controllable and work effectively, thus facilitating the robot's peristaltic locomotion more efficient. To comprehensively investigate the morphing structure and it formed earthworm-like robot, the kinematics, mechanics, deformation-dependent locomotion framework with its adapted model, as well as the factors that affect the optimal velocity are developed and presented. Extensive simulations and experiments on the proposed robot are performed. The results verify the effectiveness of the morphing mechanism and it enabled earthworm-like robot, and the consistency between the proposed locomotion model and the practical tests. The results also prove that regardless of the condition of the contact surface, the optimal phase shift angle can be achieved when each segment approximately contract and relax once in one wavelength period. Our developed prototype achieves a speed of 4.57~9.23 body lengths per minute, which is very competitive compared with most developed earthworm-like robots.