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.

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.

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.

The elastic—full plastic loading curve is for all materials sufficient to explain the strength of beams and beam columns loaded by bending and compression. This theory is extended for the influence of shear stress, and it is shown to be the only way to explain the combined bending-shear strength from test results. Also, the in the past derived bearing strength theory is extended here for bracing action. It will be shown for continuous beams as example, that besides moment redistribution by plastic flow in bending, a plastic shear flow mechanism exists that is also able to cause full moment redistribution. The derivations lead to requirements for the design rules and show how the shear stress may reduce the ultimate bending capacity.

The classical nucleation and growth model is modified and it is shown that the concept of fluctuations, instability and surface energy is not needed and that (as applies for glass transition) nucleation is a common example of the kinetic theory of structural change processes, with a special driving force and a special property of the activation volume parameter. This last follows from explanation of diffusion tests. This new nucleation equation leads to a new vision on heterogeneous nucleation, applicable to solids. The equation also provides, as necessary, the theoretical equation of the thus far empirical C-curves of the time-temperature-transformation diagrams (TTT-diagrams).

Based on the elasticplastic strength calculation, necessary for precise data explanation, a derivation is given of the failure criterion for combined bending, compression and shear. This exact limit state criterion should replace the unacceptable unsafe criteria of Eurocode 5 (EN 1995-1-1:2004). It is shown that the principle used thus far, of limited ‘‘flow’’ in axial compression as a determining failure criterion, for example, predicting no influence of a size effect, does not hold. Instead, it is derived and confirmed by the data that bending tension failure is always determining, showing the existence of a size effect, and correction of the existing calculation method is therefore necessary. Because of the primary importance of the size effect for the strengths, also for combined bendingcompression, a simple derivation of the size effect design equations is given and discussed in an appendix.

Based on the deformation kinetics approach, the theoretical derivation is given of the empirical WLF-equation of the time–temperature equivalence. The same is done for annealing at glass transition. The derivation provides a general theory for any loading history and replaces the inconsistent free volume model.

By the earlier derived theory of the embedding strength, based on the equilibrium method of plasticity, it is possible to fully explain the empirical relations and test results of an investigation of the embedding strength of particle boards leading to a new insight for the right design rules.

Based on a polynomial expansion of the failure surface, a general failure criterion, satisfying equilibrium in all directions. was developed for wood long ago (IUFRO Borns 1982) and shown to apply for clear wood. For wood with (small) defects and (local) grain deviations, equivalent strengths can be defined in the main directions and a comparable equivalent failure criterion applies as was shown by K. Hemmer (PhD thesis 1985). It was shown at the last COST-508 meeting that the second order terms of the polynomial failure criterion represent the critical distorsional energy of initial yield (or failure at initial yield when the test becomes unstable at this point). It will be shown that the third order terms represent special hardening effects (clue to micro-crack arrest by strong layers), occurring after initial yield, determining ultimate failure in longitudinal direction in a stable test. As known. the singularity approach of fracture mechanics predicts for the critical energy release rate: G_C = G_IC + G_IIC for collinear crack propagation in grain direc­tion. As p.e. mentioned in the RILEM State of the Art report on fracture mechanics of wood, this is against experimental evidence and in stead, the empirical Wu-­equation is used for layered composites. It was shown at the COST SOS-meeting at Bordeaux that this wrong prediction is due to this singularity method that, by the critical stress intensities, does not satisfy in all cases the failure criterion and, although this method is generally applied in fracture mechanics of materials, it therefore has to be rejected. It further was shown that the Wu-criterion can be derived from oriented (in grain direction) crack propagation of elliptic micro-cracks and is a necessary condition for the (right form of the) energy principle. It now wilI be shown that this Wu- (or Mohr-) criterion is also determining the failure criterion of wood, showing the same oriented micro-cracking to be responsible for failure in general. Based on this criterion, the existing criteria can be explained as the Hankinson, Norris, and Coulomb criterion. A derivation is given of an exact modified Hankinson criterion and of the general form of the higher order constants and how they can (safely) be determined from uni-axial tests in the main plane. The exact criterion is as easy to apply as the invalid approximations, now used for the Codes.

One of the conclusions of the stability group of CIB-Wl8A was that the Code must allow for analytical solutions for stability design based on quasi linear behaviour and must rever to these methods (p.e. to the Larsen-Theilgaard method for columns). Although a new parabolic failure criterion for bending with compression is proposed for the Eurocode, based on glulam simulation, the interaction equation for in plane buckling of the code, being applicable for short columns as well, suggests a much less curved failure criterion. It therefore could be seen as a task of the stability group to reconsider the failure criterion.
For that purpose a derivation is given of a consistent simple improved failure crite­rion for bending with compression, that may account for the influence of quality and moisture content, leads to simple interaction equations for beam-columns and may meet the requirements of the Eurocode.
Together with the proposal of CIB-paper 23-15-2 a possible consistent design method for braced and free beam-columns is proposed for the Eurocode and is used in the new Dutch Code.
In the appendix an explanation is given of the bearing- and shear strength.

It is possible to explain the so called mechano-sorptive effect that occurs in wood by moisture cycling by an earlier derived general deformation kinetics model, as a bond breaking process of secondary bonds, causing internal shifts of adjacent layers with respect to each other, due to sorption.