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A new generalized hypothesis of elastic energy equivalence is proposed. The proposed generalized hypothesis is inclusive of all the existing different hypotheses of equivalence in continuum damage mechanics and all are obtained as special cases. Specifically, the hypothesis of elastic strain equivalence and the hypothesis of elastic energy equivalence are obtained as special cases of the generalized hypothesis proposed here. In addition, the generalized hypothesis has some unusual properties when the integer exponent n approaches infinity. In particular, it turns out that the strain energy density function is a vector for even values of the integer exponent. This conclusion is totally unexpected but an attempt is made to explain this result based on geometry.
Although the gravitational energy within the distance of the radius of a singularity for a current estimated mass of the universe is equal to ~1069 Joules, congruent solutions for different ages of the universe reflect changes by a factor of π or 8π for identities. The total energy value is equal to the product of primary constants G·μ·ε·ħ·σ·c2 (which results in power, W) when divided by the area of smallest unit of space (area of a circle with a radius of Planck’s Length) and then multiplied by the universe’s current surface area and age. The conspicuous discrepancies of ~2∙103 between the predicted average magnetic intensity within the universe from that total energy and contemporary measurements can be accommodated by the quantitative product of 21.3π4 derived from the classic four-dimensional metric. The equivalent electric field potential divided by the predicted magnetic intensity results in a velocity that has been suggested to reflect the latency for excess correlations to occur across the universe. The most parsimonious explanation for these results is that a large component of the magnetic manifestation of energy in the universe is recondite or occluded within its submatter spatial structure and that the required cohesion or “diffusivity” throughout the volume involves the electric field component. These quantifications may facilitate understanding of Mach’s principle that any part of the universe is influenced by all of its parts.
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