History of work on growth stresses

Wood workers have known of growth stresses within trees for centuries. Usually referred to as ‘a pull towards the sap‘ when cutting boards good craftsmen would section the log in such a way as to get a straight board once it is removed from the log (and the growth stresses released) \citep{jacobs1945l}. Most work early on in the study of growth stresses surrounded investigating how/why boards changed shape when cut from an intact stem.
\citet{MARTLEY01011928} was possibly the first to study growth stresses in a scientific manner. Initially he argued that the curvature of planks sawed from logs was due to the current growth not being able to support the dead weight of the tree until lignification was complete. As a result the centre is under compression while the periphery had zero stress. However calculations showed that the self weight was not sufficient to cause the observed longitudinal dimension changes of the timber.
After Martley’s work a small number of authors investigated growth stresses through the 1930’s and 1940’s. \citet{jacobs1945l} tested 34 hardwood species, focused mainly on Eucalyptus, argued that (longitudinal) tension successively develops in the outer layers of the stem as it grows, and as a consequence of this tension, compression must form in the centre of the stem. Experimentally Jacobs made use of strip planking, measuring the deflection of the board after removal from the log, and the length change when the planks were forced back straight. He showed that wood tended to shrink in the longitudinal direction at the periphery while it extended near the pith (indicating the log is under compression in the centre and tension at the surface).
Further Jacobs put forward a number of hypotheses to explain how the growth stresses were forming. First arguing that it is very unlikely that dead cells (wood) could extend within the core in order to create the observed stress gradient. Instead suggesting the causes of; weight of the tree, surface tension and sap stream forces, cellulose and colloidal complexes, lignin intercellular substances and the primary or secondary cell wall. Without any evidence he did not claim any of these to be the major cause \citep{jacobs1945l}.
Stresses relating to reaction wood received more attention through the 30s and 40s for both soft and hardwoods. \citet{jacobs1945l} stated that the reorientation of stems is caused by a modification of the already existing stress gradient throughout the stem. One option he presented was simply that the eccentric growth causes larger numbers of cells to be added to the inner side of the curve (in hardwoods). Each cell providing the same contraction force results in an angle correction. Sap tension was also considered, but more importantly Jacobs notes the possibility of tension being formed within the cell walls of tension wood. \citet{jacobs1945l} also found that the amount of reaction wood developed and the stem angle recovery had a poor relationship. He suggested maybe it was the normal strain pattern in tension which corrected the lean, the reaction wood mealy acted as a pivot.
\citet{boyd1950a} developed a new experimental technique in order to investigate the stress profile further. By cutting a slit longitudinal in the centre of the log, attaching strain gauges onto the wood inside the slit and successively shortening the log from both ends he obtained direct extension measurements from inside the stem. He found the point of crossover from longitudinal tension to compression was approximately two thirds the radius out from the pith.
Most commonly growth stresses were investigated from the longitudinal direction, however cells also change dimension in the transverse direction, leading to a more complicated three dimensional stress field developing even within a straight stem.
\citet{koehler1933new} showed that a saw cut radially through a disk had a tendency to close near the periphery suggesting that the peripheral cells are under tangential compression with the inner cells under radial tension. He suggested this was the cause of shakes in standing timber. \citet{jacobs1945l} removed inner circles from disks of a number of species and found when an inner portion is removed the disks circumference increases. Jacobs again argued that strain in the sap stream along with cells being wider tangentially than radially led to the observed lateral stresses. He also mentioned the possibility of secondary thickening from the deposition of lignin as a contributing factor.
\citet{boyd1950a} developed an experiment whereby he removed a wedge from a disk and measured the radial expansion, showing the disks were under radial tension. Additional species were found to be in agreement with the results of \citet{jacobs1945l} when the inner circles were removed from disks. Boyd also showed that the longitudinal stresses manifesting as transverse stresses via Poisson ratios are only approximately one tenth of the measured stresses.
The Poisson effect states, the change of dimension of a material in one direction will result in a change of dimension in the perpendicular directions. This relationship is characterised by the Poisson ratio (within the elastic region of deformation). Within growth stress literature there has been some investigation of this effect as it appears the redistribution of stress through the Poisson ratio from the longitudinal to tangential direction is not sufficient to account for the observed tangential strains, which can also vary for a given longitudinal strain \citep{kubler_1987}.
 \citet{Yamamoto1992} provided an in depth rebuttal of the available theories at that time, arriving at the conclusion the cell wall development must control the shape change which results in growth stresses. Further he postulates that cellulose is primarily responsible with lignin and other carbohydrates also playing important rolls when stresses are formed in normal, compression and tension wood.
\citet{wardrop1965} commented that a tensile stress generated in the cellulose transitioning into a crystalline state could be the explanation for cells contracting during the formation of the secondary wall. Cellulose contraction aligned well with the observation of the G-layer (which has a very low MFA) being common in a number of tension wood producing species, and also give the ability for low MFA normal wood to contract. \citet{Bamber1979} further argued cellulose contraction claiming turgor pressure in normal wood cells remained high enough that the cells did not contract before the lignin was deposited, once/during lignin deposition the cellulose became crystalline and shrunk, causing the cell to become shorter, the mechanism for tension wood was sugested to be essentially the same. Compression wood on the other hand was explained by the cellulose being laid down and then the turgor pressure decreasing, causing the cell to contract before lignin was deposited. In turn the cellulose was under compression, resulting in the tendency for the compression wood cells to expand. Later \citet{bamber2001general} argues that the cellulose is laid down in a compressed or extended state to account for both compression wood and tension wood respectively.
\citet{Boyd_1972} presented (or rather popularised) the alternative (more widely accepted) hypothesis of lignin swelling (first conceived by \citet{munch1938}, in German, reviewed in \citet{Boyd_1972}). Tensile stress is gained in cells of low MFA by lignin deposition into the cell wall, pushing the cellulose fibrils apart, which in turn shrinks the longitudinal length of the cell and increases the transverse  width. When MFA is high, the opposite occurs, lengthening the cell and reducing its transverse width.
Around the same time two other lesser known hypothesis were presented, \citet{hejnowicz1967some} argued that the stresses in compression wood are related to the inhibition of water by the cell walls, which results in swelling, because the expansion of compression wood is equal to the shrinkage due to drying. \citet{brodzki1972} hypothesised strains due to 1,3-linked glucan (callose) deposition within the helical checks of the S2 cell wall layer could be the most significant factor in longitudinal growth stress generation. \citet{boyd1977basic} refuted this idea arguing (along with other issues) that the callose would expand into the cell lumen not causing any stresses in the cell wall, unless a (non-observed) constraining medium restricted the expansion.
Through the late 70’s and 80’s Archer produced a number of papers in the series, ‘On the distribution of growth stresses’ \citep{Archer_1974,archer1976,Archer_1979,Archer_1981,Archer_1985} mainly concerning the mathematical treatment of the stress fields within trees.
The ‘on the distribution of growth stresses’ series presented a comprehensive mathematical framework for the treatment of the stress field within living trees. Advancing on Küblers \citep{kubler1959a,kubler1959b} (in German, reviewed in \citet{Archer_1974}) work Archer introduced an orthotropic solution which allowed for each new growth increment to alter the stress distribution within the stem in a self equilibrating fashion. The other advancement made was the increased accuracy from the crossover point from compression to tension now being governed by the moduli in both the radial and tangential directions. Archer went on to develop a numerical approximation to the stress fields generated by asymmetric growth strains and inclined grains. He used the developed methods to present solutions for a number of hardwood species.
Archer followed up his series on growth stress distribution with ‘On the origin of growth stresses’ \citep{archer1987,archer1989} where he attempted to mathematically investigate individual cells, presenting an explicit relationship between strains and growth increment of the cell wall. The relationship relates MFA and swelling strain, he argues that these results are consistent with the lignin swelling hypothesis for compression wood. In tension wood, by amusing an MFA of zero and increasing the ratio of area of cell wall to total cell cross sectional area by adding a G layer could theoretically (with the parameters Archer used) produce a tensile stress of 36 MPa, because there are no measurements of individual cells it is hard to compare this value with experimental evidence. 
A common argument that is made for the cellulose contraction hypothesis is the correlation between cellulose content and strain. Higher proportions of cellulose compared to lignin correlate to tensile strains \citep{Sugiyama_1993,Qiu_2008,Yang_2006}, while high lignin content correlates well to compressive strains \cite{Okuyama_1998,Yamamoto1991}. It has been well reported that compression wood is partly characterised by an increase in lignin content \citep{timell1986compression}, which has been used as an argument for the lignin swelling hypothesis. Tension wood, however, is often but not necessarily correlated with an increased proportion of cellulose.Within tension wood of G-layer producing species tensile strain and whole cell cellulose content correlate well due to the G-layer having a very low lignin content \citep{gardiner2014biology}. The proportions of cellulose and lignin within the cell after the G-layer has been removed do not share this correlation. \citet{timell1969chemical} found a higher concentration of lignin within the S2 layer than in normal wood when the G-layer was present.
After \citet{Bamber1979} disputed the reliability of \citet{Boyd_1972} and \citet{boyd1977basic}, \citet{Boyd_1985} (lignin swelling) and \citet{Bamber_1987} (cellulose contraction) disputed each others analysis’s however no new information was presented, rather a number of issues around interpreting biological data were highlighted.
\citet{kubler_1987} provided an in depth review of the hypotheses, evidence and experimental methods at the time, much of which has been discussed above. He presents a table summarising the literature reporting strains for different species, highlighting the large intra and inter tree variation even within a single species.
Yamamoto et al. produced a number of papers entitled ‘Generation process of growth stresses in cell walls‘ \cite{Yamamoto1992,Yamamoto1991,Yamamoto1993,Sugiyama1993,Yamamoto1995} (and \cite{Okuyama1990,Yamamoto1988} in Japanese) where both the lignin swelling hypothesis and the cellulose contraction hypothesis are considered in detail, including new experimental evidence for each. They conclude that neither hypothesis suitably explains the experimental evedince. They find the critical MFA to be between 25 and 30 degrees for lignin swelling from both experimental evidence and an updated cell wall model including the effects of the S1 layer.
\citet[in Japanese]{Okuyama_1993} and \cite{Yamamoto1995} suggested the unified hypothesis. In an attempt to solve the critical MFA discrepancy \cite{Yamamoto1995} augmented the \citet{Barber_1964} cell wall model to include a S1 layer. The resulting model was the first to be able to account for generation of both tensile and compressive stresses over a wide range of MFAs, however this was only achievable using unnatural parameter values. The S1 layer introduced utilizes a constant MFA of 90 degrees, with the S2 layer varying from 0 to 60 degrees. Cell wall maturation occurred in two discrete steps, first the cellulose framework is constructed then the lignin deposition occurs. From the model they showed that with an increasing S1 layer thickness the critical MFA reduces. They found the model was unable to produce realistic tangential strains unless unnatural parameters were used.
\citet{Yamamoto_1998} further refined the idea by introducing a much more rigorous frame work, incorporating time dependence into the cell wall maturation model. The work presented shows the failings of each lignin swelling and cellulose contraction, even when time dependence is included. Time dependence does allow for good agreement between the modeled unified hypothesis and experimental values from Sugi. The poor agreement with tangential stresses was explained as being easy to decrease through stress relaxation in comparison to the longitudinal stress when inside the trunk.
\citet{Guitard_1999} used a S2 layer model which took the transmission of shear between fibres into account, resulting in non-zero shear moduli. Previously integral conditions had been used to govern the longitudinal stresses, presumably as they satisfy the necessary condition implicit within stress field equilibrium conditions. \citet{Guitard_1999} introduced a local condition on every elementary volume. They argue that although this approach does not satisfy the necessary equilibrium conditions it provides better agreement with experimental results when combined with dimensional changes within the microfibril bundle. In particular this model provides a much better prediction of transverse strains while being less complex than previous attempts.
\citet{Yamamoto_2002} further advanced his 1998 model to include drying stresses and moisture depend Young’s modulus, however little changes were made with regard to the growth stress model.
\citet{Alm_ras_2005} although similar made some major advancements over the \citet{Yamamoto_1998} model, producing what is currently the most advanced mechanical model for growth stress generation available. Previously fibres had been assumed to either be free \citep{Yamamoto_1998} or fully restrained \citep{archer1987,archer1989}. Various boundary conditions were investigated, with the most realistic arrangement being displacement fully restrained in the longitudinal and tangential direction while free in the radial. The virtually isolated fibre conditions were simulated and found to be in good agreement, although with some small discrepancies from \citet{Yamamoto_1998} (due to the introduction of some second order terms). Their investigation showed that differing boundary conditions had only a small effect on the longitudinal strain, however the tangential strain was significantly effected. This was explained by the cellulose being stiff at the start of maturation and therefore all of the stress within the cellulose can be released as strain. However, in the tangential direction the stiffness of the fibre progressively increases as maturation proceeds, resulting in the releasable strain being only a fraction of the total stress. In order to get good experimental agreement \citet{Alm_ras_2005} used a transverse strain release parameter allowing some strain to be released during maturation. They found that 74% of the transverse stress needs to be released during maturation to provide the best agreement with experimental data.
Many of the previous models have used a physical interpretation of the reinforced matrix hypothesis \citep{Barber_1964} which describes the cell wall as a two phase structure of cellulose fibrils and an isotropic hemicellulose and lignin matrix. \citet{Yamamoto_2007} applied Mori–Tanaka theory to small fragments of cell wall and when coupled with changes in physical state showed theoretically the two main phases could exist within the same domain.
More recently theories regarding the nature of hemicelluloses and their bonding have been used in an attempt to remove some of the issues associated with the cellulose contraction hypothesis. One major issue of cellulose contraction is that in its initial form it was argued that the crystallisation process of cellulose shortened its length but when cellulose crystallised it becomes longer as the chains straighten out. Two theories have been advanced to combat the issue of lengthening during crystallisation in order to retain an updated version of the cellulose contraction hypothesis.
\citet{walker2006primary} suggested that at the edge of the cellulose fibrils the cellulose becomes disordered and is consequently able to bond with hemicelluloses, which have a slightly shorter repeat length than the cellulose crystal. \citet{Davidson_2004} provided some evidence for the theory showing an increase in the fraction of interior chains resulted in an increase in repeat length. These hemicelluloses bonded to the outside of the fibril cause the fibril to be compressed in the crystalline centre. An interesting consequence is the contraction of the cellulose due to the hemicellulose bonding should be dependent on the area/volume to circumference/surface area ratio as would be suggested by the results from \citet{Davidson_2004}.
The second theory put forward in an attempt to correct the issues surrounding cellulose lengthening during crystallisation is that hemicelluloses are trapped between the fibrils and cause them to bend and longitudinally contract \citep{Mellerowicz_2008}. Mechanically this is very similar to the lignin swelling hypothesis. By causing the MFs to no longer run straight, instead they have to use some of their length to deviate past a cluster of hemicelluloses consequently shortening the over all distance the fibril can cover.
Both of these hypotheses would likely (although not necessarily) result in a positive correlation between strain and hemicellulose content within the G-layer, however \citet{M_ller_2006} reported low hemicellulose content in the G-layer.

Outstanding problems

There are currently a number of outstanding issues associated with all of the current hypotheses/theories. When and how do the stresses get generated is still of much debate. Over the last couple of decades it has become accepted that the generation of the stresses occurs during or immediately after the deposition of the secondary cell wall. Most commonly either the G-Layer or the S2 layer are considered responsible. What the mechanism(s) are within the cell wall has been hypothesised about at great length (as discussed above), however no theory presented so far is without contrary experimental evidence. Unfortunately most literature has investigated very few samples and reports high variability within individual trees and tree species.
Another outstanding issue, common to many biological problems is why do particular traits vary so much between individuals and species? One of the more debated topics around growth stress generation is whether or not the generation mechanisms for stress in reaction wood are extreme versions of the same mechanisms in normal wood. The G-layer is not found in normal wood, however not all tension wood producing species produce G-layers. Lignin swelling could potentially fit this criteria for normal and compression wood, however modification of Boyds theory would be needed address the dependence of a MFA as some wood with lower than 40 degree MFA still produces compressive forces. There has been reported to be little lignin within the G-layer, which is suspected to be responsible or at least partly responsible for tension generation. Boyds theory combined with excessive mild compression wood formation in corewood still allows for the same tension generation mechanisms to be used by older cambiums, as long as the MFA is suited to the task.
It is fairly well accepted (although almost by default) that growth stresses exist because they provide a mechanical advantage for survival. However, to quantify the mechanical advantage with so much variability between individuals, and no known way of controlling growth stress generation is very difficult.
Growth stress studies have been largely confined to model, or common species, however, there are a number of species which appear to form intermediates or abnormal forms of reaction wood. For example Hebe and Buxus are angiosperms which appear to form compression wood rather than tension wood \citep{Kojima_2011,Yoshizawa_1992}.

Experimentation

Macroscopic

Currently there are three commonly used experimental methods for measuring surface strains. The Nicholson method, the ‘French’ method and the strain gauge method as reviewed by \citet{Murphy_2005,Yoshida_2002} and \citet{yang2005measurement}. A detailed comparison between the systems was undertaken by \citet{kamarudin2014new}, including a new system called GSM10 (similar to  \citet{Baill_res_1995} CIRAD system).
After the developments of Boyd and Jacobs in testing for growth stresses it became apparent there was a need for a rapid testing procedure. \citet{Nicholson_1971} developed the first of these measuring the released strain between two metal pins on the surface of the sample, cut from the surface of logs. While considered a rapid method in 1971, updated versions of this test are still used for measuring surface strains but not practical (or considered rapid) for testing large numbers of stems in breeding trials. The ‘French‘ or CIRAD method (current iteration \citep{Baill_res_1995}) involves drilling a hole between two reference point on a stem, with a dial measuring the distance change between the two points.
As reviewed by \citet{kubler_1987}, \citet{Okuyama_1981} adopted the use of strain gauges to measure stem surface stresses of particular layers of wood. Other methods were also derived around the same time, \citet{gueneau1973,gueneau1973b} and \citet{kikata1977} investigated drilling holes near strain gauges to release strains. \citet{Gueneau1974} and \citet{Saurat_1976} introduced an apparatus which utilised two knife blades at a set distance, one knife blade bent as the strain was released via drilling. The strain release was measured on the curved blade.
In an attempt to introduce a rapid measurement for growth stress screening on young trees \citet{Chauhan_2010} and \citet{Entwistle_2014} introduced and tested a variant of the pairing test. \citet{naranjo2012early} and \citet{Aggarwal_2013} have used the test for investigating genetic relationships within Tectona grandis and Eucalyptus tereticornis clones. \citet{Chauhan_2011} used the test during an investigation of juvenile Eucalyptus regnans tension wood properties. The test in its current form involves taking a stem section of  300 mm long and splitting it  200 mm though the pith from the big end. The opening between the two half rounds is then measured (unpublished, updated from \citet{Chauhan_2011}).
There have been a number of studies published where the surface strains of stems have been recorded using various methods \citep{Muneri_1999,Yang_2002,Murphy_2005,Chauhan_2004,Raymond_2004}. Most recently Near Infrared spectroscopy (NIR) has been used for non-destructive testing. \citet{Watanabe_2011} was able to use NIR to predict growth strain in Sugi moderately accurately.
Measuring strains inside the stem proved to be more difficult. \citet{kikata1972} adopted Jacob’s planking method and electric strain gauges for improved accuracy (presented in \citet{kubler_1987}). \citet{wilhelmy1973probe} drilled holes of known diameters into stems and attempted to measure the change in shape of the hole as the log was successively cross cut closer to the test site, similar to \citet{boyd1950a}. \citet{ISI:A1979HU45700004} attempted to measure the effect of growth stresses on increment cores. They found that the stresses had an effect on the core itself squashing it into an oval shape. \citet{FERRAND_1982} found a correlation between 0.67 and 0.77 for the relationship between longitudinal strain and tangential core diameter. Showing they can be used for near non-destructive growth strain testing.

Microscopic

\citet{Clair_2006} provided the first direct evidence that cellulose chains are under tension at the periphery of a normal wood stem. Using X-ray diffraction they found an decrease in repeat length of 0.2% when the surface strains were released.
Individual trachieds of spruce have been investigated for swelling after soaking in a sodium iodide solution. \citet{Burgert_2007} found substantial swelling of compression wood tracheids and slight swelling of normal tracheids. They argue these results show the potential for swelling governed only by cell wall architecture to be sufficient to generate the tensile and compressive forces observed.
\citet{Chang_2013} investigated differences between normal and tension wood in poplar using FTIR. They found that cellulose is more orientated within the S2 wall of tension wood than normal wood. The orientation of lignin also increases in tension wood and that hemicelluloses and pectins in the G-layer are orientated perpendicular to that of the S2 layer.
There have been a number of attempts to investigate individual fibres and the various cell wall constituents from a micromechanical perspective, for a full review see \citet{Eder_2012}.

Cellular modeling not focusing on growth stresses

A number of mathematical models of wood have been presented from the molecular to cellular and whole organ level. Growth stress was not usually included. However these works have made significant advancements in other areas of understanding of plant cell walls which need to be incorporated into growth stress research (for a review see \citet{ISI:000261731700022}).
The first attempt at mathematically defining the mechanical behaviour of a fibre or tracheid was a single layer two phase composite model consisting of the S2 layer composed of aligned cellulose fibrils and isotropic lignin \citep{Barber_1964}. This model was quickly improved on by \citet{mark1967cell} and \citet{Cave_1968} using continuum mechanics methods. \citet{mark1967cell} provides an in depth discussion concerning both experimental and theoretical estimation of tracheids mechanical properties. \citet{Cave_1968} developed the model to include a gaussian distribution of the MFA. \citet{bergander2002cell} developed a nine layer model which emphasised the importance of the inclusion of the S1 and S3 layers when estimating transverse elastic properties. \citet{harrington2002hierarchical} developed these ideas to incorporate a three stage homogenization procedure utilizing nanostructural (supramolecular), ultrastructural (cell wall) and microstructural (whole cell) scales in order to estimate a number of material properties of softwood. Further small advancements have been made to the model over the last decade, for the most recent see \citet{Sun_2014,Saavedra_Flores_2014,wang2013gradual} and \citet{faisal2013multiscale}.
Other mathematical techniques have also been applied to plant cell walls, \citet{HEPWORTH_1998} used a discrete element approach, with limited results. Hydrogen bond dominated solids models have been used to describe paper \citep{nissan1997link,batten1987unified,nissan1987unified,batten1987unified}. \citet{Zhan_2014} used a representative volume element method to describe hardwood, however, the resolution did not alow for cell wall scale investigation. Recently molecular dynamics methods have been used to simulate small volumes of the cell wall in order to investigate their nanostructure \citep{jin2015molecular,Charlier_2012,Sangha_2011,Zhang_2009,houtman1995cellulose}.
Atomic force  microscopy, electron microscopy and other spectroscopic techneques have been used to probe the cell wall at the scale of fibril aggregates, showing that the fibrils are not straight and instead meander through the cell wall in a general direction \cite{Fahl_n_2005,Kim_2011}\citet{Salm_n_2014} argued with the help of verious imageing techneques cellulose was the most important componant when investigating cell wall properties. The fibril aggregates join and separate creating a distribution of pore sizes and shapes \cite{Yin_2015}. Fibril aggregates architecture has yet to be incorporated into cellular models.

Why growth stresses exist

Hardwoods typically have larger growth stresses than softwoods \citep{barnett1981xylem}. Some young conifers have been reported to have larger compressive stress at the periphery than at the pith \citep{jacobs1945l}, this may be due to the abundance of compression wood observed in juvenile conifers \citep{timell1986compression}. Once older they follow the same radial stress profile as hardwoods.
The commonly accepted argument for the evolutionary advantage of growth stress existence is the mechanical hypothesis. The mechanical hypothesis argues that a number of wood properties, including the development of growth stresses evolved in order to increase mechanical stability of trees to improve their survival. The mechanical hypothesis as applied to growth stresses argues, because wood is stronger in tension than in compression, by preloading the outer edge of the stem in tension the non-destructive bending radius on the inside of the curve is increased when a force is bending the stem \citep{barnett2003wood}.
Tangential stresses have been suggested to resist mechanical failure in times of frost (when water inside the cells freezes and expands) and drought (when water tension is very high) \citep{kubler1983mechanism}.
Typically when attempting to determine the reasons for why wood properties exist one of four hypotheses are used; mechanical, hydraulic, time dependent and a combination of the previous three \cite{2011}. Initial speculation for the existence of growth stresses came from \citet{MARTLEY01011928} who briefly entertained the mechanical hypothesis based on self weight. \citet{jacobs1945l} suggested they were a byproduct of sap tension (hydraulic), which he later retracted when sap pressures were recalculated at a much lower value (pressures of 200 atm was reduced to 30 atm) than the generally believed values at the time \citep{jacobs1965l}.

Growth stress as a wood defect

Growth stresses can ruin structural and veneer logs due splitting, warp, collapse and brittle-heart. Growth stresses also increase the danger for the feller by binding saws and the stem splitting longitudinally during felling (barber chairing).
End splits, heart checks, and ring shakes all reduce the value of the stem. When the stem is felled or cross cut, growth stresses are released around the saw cuts causing shortening at the periphery and extension in the centre. The dimensional change is maximal at the saw cut. Splitting occurs when the contraction/extension force exceeds the plastic limit of the stem.
Prolonged compression at the centre of the stem during growth can exceed the elastic limit of the wood, resulting in internal defects such as brittle heart. When the stem is felled these defects have already occurred. There is no way to prevent them during felling, however selection for low growth stress producing families may significantly reduce the occurrence of internal defects.  During processing technological remedies such as inline screening or lignin softening may be posible, however, have not become industry standards, probably due to cost. 
Within mills during processing growth stresses cause a number of issues leading to reductions in value recovery, an example of this can be seen in Figure \ref{950677}. Because growth stresses are released when the stem is sectioned via sawing, the resulting shape change can cause the saws to jam. The main value loss at this stage of processing comes from the need to saw boards multiple times in order to straighten deformed boards. Increasing the number of times the boards are sawed to get their end dimensions gives not only poor saw use efficiency but also major economic loss, the final yield can be reduced to 30% \citep[oral presentation]{yamamoto2007slides}.