Mesomechanics of energy and mass interaction for dissipative systems

Abstract

Small and large specimen data cannot be connected because the respective theories are developed independently by different physical laws. The disparities are becoming more and more transparent as nanospecimen data cannot be brought up to the macroscopic scale. The inability to address quantum and gravitational field mechanics in a unified manner adds to the diversification. One of the apparent deficiencies is not being able to treat small (atomic) and large (galaxial) bodies by a common multiscale model for addressing nonequilibrium and nonhomogeneous conditions. The time of arrow must also be reflected to invoke finiteness of the life sustaining energy. The synergis-tic thought leads to a pulsating mass manifested by matter activated by energy absorption and dissipation. The near simultaneity of energy intake and outlet of physical systems resembles the pulsation arising from contraction and expansion. The pulses, caused by the fatigue of metals, are within the range of micropulsations of geomagnetic energy fluctuations. The dualism of energy absorption and dissipation provides a common dialogue for establishing multiscale shifting laws. Mass pulsation, coupled with the equivalence of motion and energy, gives a unique mass-matter relation, bypassing the diversities of current concepts and theories in physics and mechanics. The scheme of scaling by segments such as pico, nano, micro and macro creates gaps among the scale ranges that requires cementation. Mesomechanics serves this purpose for developing scale shifting laws for connecting the gaps. Determination of energy density from velocity of physical systems was shown to be possible from the application of crack tip mechanics and ideomechanics. Four fundamental parameters l, v, M and Ware used. They stand, respectively, for the length, velocity, mass density and energy density. Their combinations can be formulated into unique mathematical groups. The three scale ranges: pico-nano, nano-micro and micro-macro are selected for demonstration. The objective is to explain real accelerated test data without making idealized assumptions for determining the life distributed over the three scale ranges. In short, a nonclassical approach will be adopted to derive scale shifting laws consisting of the transitional functions RjJ+1 which stand for the mass ratios of the absorption energies WjJ+1 and dissipation energies DjJ+1The notations J and J+1 stand for two successive scales: pico-nano, nano-micro and micro-macro. Hence, the mass ratios Rpina, Rnami and Rmima can be referred to as the transitional inhomogeneity coefficients. They make up the multiscale shifting laws WjJ+1 = RjJ+1DjJ+1 Validation of the method involves connecting the accelerated test data at the different scales, say from pico to nano to micro to macro. A key step in this development is the use of an energy density dissipation function, the definition of which is scale invariant. Referred to the contraction and expansion of a control volume, energy is said to be absorbed and dissipated, respectively. The respective mass densities M↓ and M↓ may then be regarded to pulsate by contraction and expansion. Real fatigue data for the precracked 2024-T3 aluminum panels are used to derive energy loss by dissipation. Equivalency of mass and energy also enables numerical evaluation of mass loss.