``UNIFIED MICROMECHANICS THEORY of Composites” (UMTC) by Buryachenko is proposed for analyses of composite materials (CMs) of either matrix random (statistically homogeneous or inhomogeneous probability descriptors), periodic, or deterministic (neither random nor periodic) structures, endowed with local, weakly nonlocal (higher-grade, higher-order, or micromorphic models), strongly nonlocal (strain-type or displacement-type, peridynamics), or multiphysics phase properties.
It is not only a matter of generality—which may sometimes appear to be an end in itself—but rather of the new opportunities that were previously unimaginable. UMTC introduces three conceptually transformative elements: (i) an exact Additive General Integral Equation (AGIE) valid for CMs of arbitrary structure and phase behavior under body forces with compact support (a fundamentally new training parameter); (ii) a new conception of the Representative Volume Element (RVE); and (iii) a new effective dataset (ED) eliminating edge, boundary-layer, and sample-size effects. The new ED is incorporated into existing machine-learning and neural-network (ML&NN) methodologies. UMTC establishes not merely a new theory, but a NEW PHILOSOPHY of MICROMECHANICS—one that may be viewed as the most significant conceptual advance in the field in over 200 years. The attached file provides further details and contains a list of papers published in arXiv over the holiday season.
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