It is shown, that the applied fracture mechanics textbook boundary value problem solution is identical to the sum of the transformed exact solutions of pure normal stress loading alone, and of pure shear stress loading alone, although these two solutions exclude each other and cannot apply at the same time. This delivers, already since the fifties, a wrong, incompatible, equilibrium system with incorrect transformed field stresses, which does not represent linear elastic fracture mechanics. As correction, the right exact limit analysis solution is given, which also provides the derivation of “mixed I-II-mode” fracture criterion, which is shown to be precisely verified by empirical research. It further is shown that the postulated stress function is based on a stress transformation from elliptical coordinates to confocal polar coordinates. However that transformation applies for lower order distances to the singularity and therefore don’t give the right result on the applied macro scale. The discussion of a necessary limit analysis approach for failure, provides the proof of a necessary linear elastic analysis up to initial yield. Linear elastic stress and displacement terms represent the none vanishing, first order terms of virtual work behavior, of any non-linear stress division. This has consequences for non-linear fracture mechanics, which is shown, to be necessarily replaced by the linear approach of limit analysis. As example, the critical stress intensity is given of a test series with different initial crack lengths, which, in terms of nonlinear fracture mechanics, was subject to undeterminable failure behavior by large scale yielding.@en

Limit Analysis is an prescribed exact approach of Wood Science, what is shown to also apply for wood Fracture Mechanics. Knowledge of the gradual elastic to plastic behavior and of the imitation by non-linear elasticity (and J-integral) is shown to be not needed. The linear – full plastic limit approach delivers an elastic lower bound, up to this full plastic boundary, the fracture- or yield criterion, where ultimate load behavior is described, by virtual work approach and “flow” by the normality rule. This delivers the possibility to look at any equilibrium system, which satisfies compatibility and boundary conditions and nowhere exceeds this “flow” criterion and is verified by test data. Because the accepted singularity approach does not deliver a right mixed mode fracture criterion, it is necessary to make comparisons with other possible Airy stress functions. Therefore, the derivation of the accepted, general applied, elementary singularity solution with its 3 failure modes, is discussed and compared with new theory. This new limit analysis theory is based on an older, forgotten, Airy stress function, and shows e.g., by the new approach and application to wood, that there is no real difference between strength theory and fracture mechanics and between linear and non-linear theory. It delivers the, empirical verified, exact mixed mode failure criterion for wood; shows that stresses in the isotropic wood matrix also have to be regarded separately, to explain the, only by isotropy, possible, extremely high triaxial hydrostatic stress, and stress increase by the stress spreading effect. @en

The developed exact theory is given in the appended publications denoted by D, thus: D(1991), D(2008a), D(2008b), D(2010), D(2011), D(2012a) D(2012b) and primary, by the partly expired D(2006a), D(2006b). Other relevant derivations and applications are mentioned in these publications. The theory in all appended publications was derived by T.A.C.M. van der Put as theory of perfect plasticity. Because a complete loading history analysis, with gradual increasing plasticity, until collapse is too extended and not necessary for ultimate state estimation, the relatively simple limit analysis method can always be applied instead. Then, no matter how complex the geometry of a problem, or loading condition, is, it is always possible to obtain a realistic value of the collapse load. This basic theory is discussed in the next section: D-1. @en

The results of the here discussed article of Yoshihara (2012), are unsatisfactory and need to be reconsidered. The existence of two critical stress intensities is postulated, which may differ a factor 3 to 4 from each other. A questionable push up of the lower data-curve, as given by Fig. 3 of Yoshihara (2012), may diminish this difference, but what to do with the conclusion that the critical stress intensity is effectively obtained. It is not mentioned when the high, and when the low values apply and why. Any conclusion should be based on theory and the theoretical explanation of the in Yoshihara (2012) and (2008) mentioned data, is given in van der Put (2012), because these data provide a confirmation for mode II softening like behavior. Based on this theory, correction is necessary of the interpretation and conclusion of Yoshihara (2008). This discussion is given here in the light of the achievements of wood mechanics. @en

To correct the empirical design rules for locally loaded beams and blocks of Eurocode 5, the theoretical explanation of these rules and of the applied test data is given. It appears that the design rule may be far too conservative, or too unsafe in other cases, and only approximately applies for thin long bearing blocks and not for the short test specimens and support stresses of beams. The theory of the determining influence of load spreading possibility on the strength is verified by all other sufficient extended investigations leading to simple and reliable design rules.@en