Soft actuators with auxetic, or negative Poisson's ratio (NPR), behavior offer a way to create soft robots with novel kinematic behavior. This paper presents an original framework for reinforcement of a soft actuator using a generalized NPR element, called a Representative Auxetic Element (RAE), and an experimental validation of the kinematic behavior that it enables. We build a generalized kinematic model that enables the design of RAE-patterned actuators and reveal the distinct auxetic behavior of RAE actuators with comparable model accuracy to the legacy McKibben actuators. A simple, reproducible way of designing and fabricating RAE actuators is described and varied prototypes are shown. This RAE-based design scheme can be used to create actuators with specified kinematics like bending, extension, and radial expansion, which can also vary across the actuator's surface both circumferentially and axially in a tractable, scalable manner.