Quasi-brittle materials are characterized by progressive damage and crack propagation, leading to softening and irreversible strain after the peak load is reached. Examples include concrete as well as many types of rocks, shale and sandstone, The approach taken here is formulated using a nonlocal constitutive law together with a phase field that is nonlocal in space and time. The displacement field inside the material is shown to be uniquely determined by an initial boundary value problem. The fracture set is characterized by the evolving phase field taking the value one inside intact material and zero in the fully damaged material. The theory satisfies energy balance, with positive energy dissipation rate in accordance with the laws of thermodynamics. Notably, these properties are not imposed but follow directly from the evolution equation by multiplying the equation of motion by the velocity and integrating by parts. The field theory uses a peridynamic interpretation of Newton’s 2nd law to evolve the displacement inside the material and there is no separate equation for phase field evolution. Instead, the phase field is part of a history dependent constitutive law dynamically coupled to the displacement field. Elasticity, fracture energy, and strength are independent of each other in this model. Here, a characteristic length scale L is derived using geometric measure theory and is proportional to the ratio of fracture toughness to material strength. The formulation delivers a mesh-free method for predicting crack patterns. The computational method successfully captures the cyclic load–deflection response of crack mouth opening displacement, the structural size-effect related to ultimate load, and fracture nucleating from boundary defects. It provides dynamic results identical to dynamic phase field methods introduced in M.J. Borden, C.V. Verhoosel, M.A. Scott, T.J. Hughes, and C.M. Landis, CMAME (2012). These results are reported in Coskun, Damircheli, and Lipton, JMPS (2025) and Lipton and Bhattacharya J. Elasticity (2025).