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Mean-field theory is extensively used in statistical physics, solid-state physics, and biophysics to compress a large number of interacting multi-body problems into an effective single-body problem, providing some insight into the system’s behavior at a lower computing cost. Nonetheless, the mean-field approximation always suppresses the non-local effects, hence obscuring the underlying mechanisms involving unit interactions between microscopic events, such as competition, co-evolution, and self-organized criticality. This paper presents a general, non-local mean-field approximation for the medium-long-range correlation of materials based on the finite element method, which has excellent compatibility and scalability with existing theories. It ties the evolution of a deformation unit to the status of other spatial domain elements, which is analogous to the fundamental principle of cellular automata. When applied to …