Soft robots have drawn great interest due to their ability to take on a rich range of shapes and motions, compared to traditional rigid robots. However, the motions, and underlying statics and dynamics, pose significant challenges to forming well-generalized and robust models necessary for robot design and control. In this work, we demonstrate a five-actuator soft robot capable of complex motions and develop a scalable simulation framework that reliably predicts robot motions. The simulation framework is validated by comparing its predictions to experimental results, based on a robot constructed from piezoelectric layers bonded to a steel-foil substrate. The simulation framework exploits the physics engine PyBullet, and employs discrete rigid-link elements connected by motors to model the actuators. We perform static and AC analyses to validate a single-unit actuator cantilever setup and observe close agreement between simulation and experiments for both the cases. The analyses are extended to the five-actuator robot, where simulations accurately predict the static and AC robot motions, including shapes for applied DC voltage inputs, nearly-static 'inchworm' motion, and jumping (in vertical as well as vertical and horizontal directions). These motions exhibit complex non-linear behavior, with forward robot motion reaching 1 cm/s. Our open-source code can be found at: https://github.com/zhiwuz/sfers.