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This involved using a compatible volume and taper function (Katz et al. 1984) along with data on the diameter and heights of each disc sampled from the tree.
To overcome the problem of missing heights, total height was predicted for each tree using a compatible volume and taper function along with data on the diameter and heights of each disc sampled from the tree.
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Total stand volume was calculated from a compatible tree volume equation (Tewariet al., 2013).
The compatible volume and taper equation for the direct sawlog regime developed by Katz et al. ([1984]) generally performed better than the local taper and volume functions, and hence was used to estimate the heights of trees in all forests.
A compatible polynomial volume-taper equation for radiata pine in New Zealand was used for this purpose, which has the following form: d 2 = V kH β 1 X + β 2 X 2 + β 3 X 3 + β 4 X 4 + β 5 X 5 + β 6 X β 7 + β 8 X β 9 (A1).
The strain-compatible volume-averaging method, a recently developed micromechanical method for the analysis of multi-phase composites, is extended here to deal with viscoplastic behavior.
The influence of the loading orientation on the viscoplastic response of the composite is investigated using the strain-compatible volume-averaging method and the widely utilized generalized method of cells.
As far as the effective response of the composite is concerned, it is found that the results of the strain-compatible volume-averaging method are in good agreement with those of the other two methods.
It is shown that the response predictions of the strain-compatible volume-averaging method are invariant with respect to coordinate transformations while those of the generalized method of cells are not.
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