The failure criterion is an essential part of all strength calculations of design. It was shown in the past that the tensor-polynomial equation could be regarded as a polynomial expansion of the real ...failure surface. Now it is shown that the third-degree polynomial is identical to the real failure criterion. It is also shown that the second-degree part of the polynomial is identical to the orthotropic extension of the von Mises criterion for initial yield. The third-degree polynomial hardening terms of the criterion are also shown to incorporate the earlier theoretical explained mixed-mode I-II fracture equation, showing hardening to be based on hindered microcrack extension. For uniaxial loading, the failure criterion can be resolved in factors, leading to the derivation of extended Hankinson equations. This allows the relations between the constants of the total failure criterion to be elucidated, which is necessary for data fitting of this criterion and providing a simple method to determine the constants by the simple uniaxial, obliquegrain compression and tension tests. Based on this, the numerical failure criterion is given with the simple lower bound criterion for practice and for the codes.
Rationale/Purpose: The aim is to investigate the determinants of competitive balance (CB) across countries in European men's club football. Determinants already tested previously in the literature ...include revenue sharing (proxied by countries' income inequality), differences in drawing power, prize money, talent market and sports contest format. New determinants include climate, countries' economic power, tradition, timing, number of clubs, financial regulation and international performance.
Methodology: Regressions explaining CB are tested in the European men's football first tiers over the 2006-18 period.
Findings: Results show that economic power and income inequality have a significant positive impact on CB; while climate (temperature), differences in drawing power, international performance and financial regulation have a significant negative impact.
Practical implications: Results question whether international performance is a legitimate objective given its negative impact on CB.
Research contribution: . Results enable to add new determinants explaining CB, namely countries' economic power, financial regulation and international performance.
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