Non-Newtonian mechanics for small bodies

摘要

Interaction of mass and energy for small bodies acquires non-Newtonian behavior. Postulated is the existence of space/time to depend on the activation and deactivation of mass in relation to the absorption and dissipation of energy. Borne from the manifestation of the creation of matter is the concept that the intrinsic inhomogeneity gives rise to interfaces. Objects and events appear to exist as opposing poles with a transitional character across the interface. Simultaneity of direct-absorption and self-dissipation energy density, denoted, respectively, by W and D , is further hypothesized to depend on the square of the velocity a_↑~2 that increases monotonically with time as indicated by the arrow head notation. The demise is that W = M_↓ a_↑~2 and D = M~↓ a_↑~2 where M_↓ is the activated mass associated with the direct-absorption energy density and JW is the deactivated mass associated with the self-dissipation energy density. The scheme also applies to large bodies. Scale segmentation justifies localizing attention to the energy source and/or sink as the region of damage. By specifying the life distribution for the different size/time scales, say t_(pi)/t_(na)/t_(mi)/t_(ma)/t_(st), the rate at which damage is being done for each scale segment can be determined. The subscripts pi, na, mi, ma, and st designate, respectively, pico, nano, micro, macro, and structure. The actual time distribution in years may be 1.5/2.5/3.5/5.5/7.0 for a total of 20 years. The time of arrow in years will depend on the problem definition. The direction of pico→ nano→micro→macro →struc. corresponds to progressive damage while other choices can also be considered. The energy density function can be found without a knowledge of the entire field quantities such as stress and strain. Demonstrated will be a picoano/micro/macro fatigue cracking model of a 2024-T3 aluminum panel. Only the undamaged material properties are employed. Time degradation of the picoano/micro/macro material structure is derived by using nine scale transitional physical parameters: three for the picoano range ( μ_(pia)~* , σ_(pia)~*, d_(pia)~*), three for the nano/micro range (μ_(na/mi)~* , σ_(na/mi)~* ,d_(na/mi)~*) and three for the micro/macro range (μ_(mi/ma)~*, σ_(mi/ma)~*,d_(mi/ma)~*). Only the ratios of two successive scale sensitive parameters need to be specified. The time dependent physical parameters at the lower scale are implicit and needed only for analytical continuation. More precisely, the transitional character of picocracks, nanocracks, microcracks and macrocracks are determined from the specified life expectancy of time arrow according to pico→nano→micro→macro with the respective singularity strength of λ given by 1.25/1.00/0.75/0.50. Note that λ=0.5 corresponds to the inverse square root r~(-0.5) in fracture mechanics with r being the distance from the macro-crack tip. The micro-crack, nanocrack and pico-crack tips are assigned with the singularities r~(-0.75), r~(-1.00), and r~(-1.25), respectively. The time dependent material degradation process over the total life span is enforced such that the energy dissipated in damaging the internal material structure at each scale range can be matched with that caused by loading. Material inhomogeneities at the different scales are thus compensated by the inhomogeneous reinforcements at the same different scales. In this way, the energy release rate at each scale would be relatively homogeneous and controlled.