Unified Mechanics Theory: An Entropy-Based Uncertainty Quantification for Monotonic Tensile Failure of A36 Steel K. M. Asaali1, J. B. A. Agramon1, P. J. F. Chiong1, T. H. Asaali2, E. S. Cruz1, R. P. Gammag3 1 School of Civil, Environmental, and Geological Engineering, Mapúa University, City of Manila 1002, Philippines 2 Department of Mathematics, Tawi-Tawi Regional Agricultural College, Bongao, Tawi-Tawi 7500, Philippines 3 Department of Physics, Mapúa University, City of Manila 1002, Philippines Keywords: Newtonian Mechanics, Thermodynamics, Unified Mechanics Theory, 1-D analytical modelling, thermodynamic-frameworked continuum damage mechanics, monotonic tensile failure, tensile strength, A36 steel Tensile yielding and fracture failures occur as a result of plastic deformation, an irreversible degradation process, in a steel material. Historically, tensile failures in steel members have been predicted by analysing and designing structural members in accordance with the provisions of the structural building codes (e.g., National Structural Code of the Philippines or NSCP) or by extrapolating empirical curve-fitted models using phenomenological data on structural member failure. The design provisions of NSCP for structural members are also based on phenomenological data that went through laboratory trialand- error analyses. The current study contributes to the centennial effort of the scientists and physicists to unify Newtonian Mechanics and Thermodynamics and strengthen the proof for the applicability of the Unified Mechanics Theory in construction and structural engineering. The researchers employed the said theory to predict or quantify the failure uncertainty of A36 steel when subjected to monotonic tensile loading condition. Using one-dimensional analytical modelling, the unified mechanics theory was used to derive a onedimensional predictive model for failure prediction. The proposed analytical model was used to predict the A36 steel’s tensile strength. It is demonstrated in this study that using a simple predictive model based on the material’s fundamental equations derived by the researchers and thermodynamics associated with material degradation, the unified mechanics theory can be used to predict the tensile strength of an A36 steel. References [1] Basaran, C. (2021). Introduction to unified mechanics theory with applications. Switzerland: Springer Nature Switzerland AG. [2] Basaran, C., Nie, S. (2004). An irreversible thermodynamic theory for damage mechanics of solids. International Journal of Damage Mechanics, 13(3), 205-224. [3] Jamal M, N.B., Kumar, A., Lakshmana Rao, C., Basaran, C. (2020). Low cycle fatigue entropy life prediction using unified mechanics theory in ti-6al-4v alloys. Entropy, 22, 24. 18
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