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Continuum Mechanics, physical science par excellence inasmuch it studies the world commonly perceived by human senses, lacks its most important result consisting of a thermomechanical model of general applicability, free of approximations of laws valid for all matter and mathematically solvable. In previous works we expounded a theory that, by introducing completely new principles including the new law in question (that links density, velocity and thermodynamic pressure), arrived to a system of partial differential equations (PDEs) conceivable to constitute said result. This monograph, in front of need for further theoretical, numerical and experimental checks of this new general model, has preparatory purpose of theoretically validating said law in coherence with Continuum Mechanics normally consolidated and shared. To this aim, necessary tools of logic, tensor calculus and mathematical analysis are premised, also circumstantiating laws and principles of state of art. It is lastly considered the compatibility of new law with current general model and with its best known specifications, and a significant advantage of new model over current one is identified in being absent the stress constitutive equation.
Giacomo Lorenzoni (https://orcid.org/0000-0002-2329-2881) graduated in Mechanical Engineering in 1979 at Sapienza – University of Rome, where has then collaborated until 1984 in research and educational activities related to mechanical components. He continued until 2014 at an Italian public research body, by studying the erosion by drops and stress corrosion cracking in steam turbines, energy efficiency, cogeneration, gas/steam turbine combined cycles, mathematical optimization, by carrying out frontier research on combinatorics, cryptography, heat engines, thermodynamics, continuum mechanics, mathematical analysis, numerical analysis, probability and statistics. Currently works to better circumstantiate and validate numerically the said PDEs system.
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