Fundamental Defects of Classical Material Strength Sciences

by

© Ph. D. & Dr. Sc. Lev Gelimson

Academic Institute for Creating Fundamental Sciences (Munich, Germany)

Physical Journal

of the "Collegium" All World Academy of Sciences

Munich (Germany)

12 (2012), 2

Keywords: Material strength science, megascience, revolution, megastrength, megamathematics, overmathematics, unimathematical test fundamental metasciences system, knowledge, philosophy, strategy, tactic, analysis, synthesis, object, operation, relation, criterion, conclusion, evaluation, measurement, estimation, expression, modeling, processing, symmetry, invariance, bound, level, worst case, defect, mistake, error, reserve, reliability, risk, supplement, improvement, modernization, variation, modification, correction, transformation, generalization, replacement.

Introduction

There are many separate scientific achievements of mankind but they often bring rather unsolvable problems than really improving himan life quality. One of the reasons is that the general level of earth science is clearly insufficient to adequately solve and even consider many urgent himan problems. To provide creating and developing applicable and, moreover, adequate methods, theories, and sciences, we need their testing via universal if possible, at least applicable and, moreover, adequate test metamethods, metatheories, and metasciences whose general level has to be high enough. Mathematics as universal quantitative scientific language naturally has to play here a key role.

But classical mathematics [1] with hardened systems of axioms, intentional search for contradictions and even their purposeful creation cannot (and does not want to) regard very many problems in science, engineering, and life. This generally holds when solving valuation, estimation, discrimination, control, and optimization problems as well as in particular by measuring very inhomogeneous objects and rapidly changeable processes. It is discovered [2] that classical fundamental mathematical theories, methods, and concepts [1] are insufficient for adequately solving and even considering many typical urgent problems.

Megamathematics including overmathematics [2] based on its uninumbers, quantielements, quantisets, and uniquantities with quantioperations and quantirelations provides universally and adequately modeling, expressing, measuring, evaluating, and estimating general objects. This all creates the basis for many further megamathematics fundamental sciences systems developing, extending, and applying overmathematics. Among them are, in particular, science unimathematical test fundamental metasciences systems [3] which are universal.

Material Strength Science Unimathematical Test Fundamental Metasciences System

Material strength science unimathematical test fundamental metasciences system in megastrength [2] is one of such systems and can efficiently, universally and adequately strategically unimathematically test any material strength science. This system includes:

fundamental metascience of material strength science test philosophy, strategy, and tactic including material strength science test philosophy metatheory, material strength science test strategy metatheory, and material strength science test tactic metatheory;

fundamental metascience of material strength science consideration including material strength science fundamentals determination metatheory, material strength science approaches determination metatheory, material strength science methods determination metatheory, and material strength science conclusions determination metatheory;

fundamental metascience of material strength science analysis including material strength subscience analysis metatheory, material strength science fundamentals analysis metatheory, material strength science approaches analysis metatheory, material strength science methods analysis metatheory, and material strength science conclusions analysis metatheory;

fundamental metascience of material strength science synthesis including material strength science fundamentals synthesis metatheory, material strength science approaches synthesis metatheory, material strength science methods synthesis metatheory, and material strength science conclusions synthesis metatheory;

fundamental metascience of material strength science objects, operations, relations, and criteria including material strength science object metatheory, material strength science operation metatheory, material strength science relation metatheory, and material strength science criterion metatheory;

fundamental metascience of material strength science evaluation, measurement, and estimation including material strength science evaluation metatheory, material strength science measurement metatheory, and material strength science estimation metatheory;

fundamental metascience of material strength science expression, modeling, and processing including material strength science expression metatheory, material strength science modeling metatheory, and material strength science processing metatheory;

fundamental metascience of material strength science symmetry and invariance including material strength science symmetry metatheory and material strength science invariance metatheory;

fundamental metascience of material strength science bounds and levels including material strength science bound metatheory and material strength science level metatheory;

fundamental metascience of material strength science directed test systems including material strength science test direction metatheory and material strength science test step metatheory;

fundamental metascience of material strength science tolerably simplest limiting, critical, and worst cases analysis and synthesis including material strength science tolerably simplest limiting cases analysis and synthesis metatheories, material strength science tolerably simplest critical cases analysis and synthesis metatheories, material strength science tolerably simplest worst cases analysis and synthesis metatheories, and material strength science tolerably simplest limiting, critical, and worst cases counterexamples building metatheories;

fundamental metascience of material strength science defects, mistakes, errors, reserves, reliability, and risk including material strength science defect metatheory, material strength science mistake metatheory, material strength science error metatheory, material strength science reserve metatheory, material strength science reliability metatheory, and material strength science risk metatheory;

fundamental metascience of material strength science test result evaluation, measurement, estimation, and conclusion including material strength science test result evaluation metatheory, material strength science test result measurement metatheory, material strength science test result estimation metatheory, and material strength science test result conclusion metatheory;

fundamental metascience of material strength science supplement, improvement, modernization, variation, modification, correction, transformation, generalization, and replacement including material strength science supplement metatheory, material strength science improvement metatheory, material strength science modernization metatheory, material strength science variation metatheory, material strength science modification metatheory, material strength science correction metatheory, material strength science transformation metatheory, material strength science generalization metatheory, and material strength science replacement metatheory.

The material strength science unimathematical test fundamental metasciences system in megastrength [2] is universal and very efficient.

In particular, apply the material strength science unimathematical test fundamental metasciences system to classical material strength sciences.

Fundamental Defects of Classical Material Strength Sciences

Even the very fundamentals of classical material strength sciences have evident cardinal defects of principle.

Modern engineering (astronautics, aircraft-building, ship-building, deep-sea industry, power engineering, electronics, chemical industry, building, etc.) requires optimal design of structural elements. It is based on a rational control of the necessary and sufficient strength of such elements and corresponding materials. Their types are diverse: ductile materials like metals; brittle alloys and nonmetals (glass, crystalline glass, concrete, and stone); anisotropic materials (fiber-reinforced ones and other composites). They are intended for extreme exploiting conditions (variable loading, high pressure, high or low temperature, radiation, etc.).

It is universally recognized that the most effective approach to solving strength problems in modern engineering is phenomenological. It provides considering more or less adequate mathematical, mechanical, physical, etc. models of materials and structural elements instead of real ones and uses mathematical (analytic and numeric) methods in theories of differential equations, elasticity, plasticity, creep, fracture, etc. to determine the usually triaxial stress state (in the stationary case) or process (in nonstationary loading) at each point of a structural element. It remains to compare the diverse triaxial stress states at all points of a solid (structural element) with one another by the degree of danger to reach the closest critical state (initiation of yielding, fracture etc.). Therefore, it is necessary to use so-called critical (limiting, ultimate) state (process) criteria (elasticity criteria, yield criteria, failure criteria, etc.) that reduce the problems to the simplest ones dealing with uniaxial stress states only investigated enough. To measure the proximity of a real stress state (process) to the closest critical one, safety factors might be used.

The well-known critical state and process criteria are separate for diverse materials types, have nothing in common with simple and universal fundamental laws of nature, and possess evident defects. Even if a ductile material is isotropic and has equal strength in tension and compression, the criteria ignore increasing strength in uniform triaxial compression. If a material has unequal strength in tension and compression, the criteria possess obviously restricted ranges of applicability and do not allow to compare arbitrary stress states with one another. No critical process criterion for anisotropic materials under variable loading, when the directions of the principal stresses at a solid's point under consideration can arbitrarily turn, is known at all.

Notata bene:

1. Modern engineering requires optimal design and rational control of resistant structural elements of ductile and brittle, isotropic and anisotropic materials under extreme stationary and variable loading. This needs adequately determining the danger of the real spatial stress process at any point of a solid with respect to the closest critical (limiting, ultimate) stress process. Critical (limiting, ultimate) spatial stress processes should be obtained from critical process criteria by using strength data available in simple experiments. The dangers of real spatial stress processes should be given by measures of the proximity of a real stress process to the closest critical one.

2. A usual stress is not a pure number, depends on the choice of physical dimensions (units) for a force and a length, is not numerically invariant by unit transformations, and alone represents no degree of the danger of itself even in stationary loading. If a solid’s material is not isotropic with equal strength in tension and compression, it is not reasonable even in stationary loading to compose functions of different stresses without their adequate weighing because of mixing their values having distinct limits and hence diverse degrees of danger. If loading is variable, the same holds even for different values of the process of a stress alone.

3. The known critical state criteria separate for diverse materials types, unlike simple and universal fundamental laws of nature, have contradictions, restricted and vague ranges of adequacy, sometimes lose physical sense, not always bring a suitable equivalent stress, and are applicable in the stationary case only. For an isotropic ductile material with equal strength in tension and compression even under stationary loading, the criteria ignore considerable strength increase in uniform triaxial compression. The only known attempts to propose a critical process criterion are reduced to very special cases of uniaxial stress cycles and of combined cyclic bending and twisting a bar. For anisotropic materials under variable loading, when the directions of the principal stresses at a solid's point under consideration can arbitrarily turn, there has been no attempt to propose a critical process criterion at all.

4. The only known measure of the proximity of a real stress process to the closest critical one is a safety factor as the ratio of a limiting stress to an equivalent stress. This could suffice only if all the principal stresses are directly proportional to a common variable parameter. Otherwise, a usual safety factor does not determine the permissible combinations of the initial data in a strength problem, can overestimate actual reserves by an order of magnitude, and is manifestly insufficient.

5. There were no fundamental mechanical and strength sciences satisfying the complex of modern requirements for inherent unity, consistency, sufficient completeness, universality, naturalness, simplicity, and convenience for practical application.

Therefore, the very fundamentals of classical material strength sciences have a lot of obviously deep and even cardinal defects of principle.

References

[1] Encyclopaedia of Mathematics / Managing editor M. Hazewinkel. Volumes 1 to 10. Kluwer Academic Publ., Dordrecht, 1988-1994.

[2] Lev Gelimson. Elastic Mathematics. General Strength Theory. The "Collegium" All World Academy of Sciences Publishers, Munich (Germany), 2004, 496 pp.

[3] Lev Gelimson. Science Unimathematical Test Fundamental Metasciences Systems. Mathematical Journal of the “Collegium” All World Academy of Sciences, Munich (Germany), 12 (2012), 1.