Numerical implementations of bond based peridynamics are computationally intensive. We propose a new class of fast interaction functions for constitutive modelling that reduce calculation time when compared to other formulations in the literature [1, 2]. This is achieved by substituting the stretch definition from the original interaction functions [1] with a new stretch measure that we call modified stretch. The resultant interaction functions are proven to approximate the existing formulations, and proven to require equivalent stability and convergence conditions under explicit time integration. Gains of speed greater than 11% were obtained in numerical tests that compared the new functions with those in the literature [1]. The new approach was verified against classical elastic theory using simple examples and shows good agreement. Examples describing three-dimensional quasi-brittle structures are also presented. The proposed fast interaction functions lead to improvements in the ability to calculate the load response of realistic structures, since they usually require fine discretisation and large computation time.