Utilising a single time step across a domain may be computationally inefficient, when modelling the dynamical response of heterogeneous media. The use of multi time stepping (subcycling) algorithms have shown to be an accurate method to speed up the simulation of stress wave propagation problems in such structures. However, current algorithms utilise time steps that assume a constant ratio between coarse and fine temporal discretisations, over a single coarse time step. This is even though compressive waves, fracture, and element distortion all lead to non-constant ratios. This work proposes a stable algorithm, in an updated Lagrangian formulation, that does not. We ensure that the time steps do not extend over the critical time step of a finite element within an explicit formulation. It omits the need for element and nodal clocks, with the same algorithm applicable to integer and non-integer subcycling. Continuity of acceleration is enforced across subdomain interfaces, without the need for the interpolation of other kinematic quantities. Transfer of nodal masses lead to an increased numerical stability, therefore allowing the use of larger time steps. The algorithm does not introduce spurious energy on the interface between subdomains. Unlike the concurrent coupling of many two subdomain algorithms, we implement an algorithm that also extends across several subdomains, each with their own respective time step. The algorithm is demonstrated in three dimensions, for a variety of time step ratios, regardless of chosen element formulation. Metamaterials are studied numerically, to demonstrate the effectiveness of the algorithm. Compared to monolithic simulations, our multi time stepping algorithm significantly accelerates the solution of the propagation of waves in Metaconcrete.