deletions | additions       diff --git a/method.tex b/method.tex  index 4f01e1f..00cab39 100644  --- a/method.tex  +++ b/method.tex 
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Where S is the stocking rate, assumed to be either open grown, one stem per hectare or 741 stems per hectare.  As trees grow, the newest cells are superimposed on the existing structure, creating a time evolving stress state. In order to acomidate these time dependent changes, the mesh needs to be 'grown', here time is treated in descrete steps. Wind effects are not acounted for during growth, however, self weight and growth stress are.Gravity is the only external force considered during the growth phase, as the tree grows it compresses under self weight, resulting in the lower parts of the stem becoming successively compressed by the new growth.  Growth stresses develop as cells divide in the cambium, resulting in the new cells being in a non-stressed state on the surface of a pre-stressed structure. During secondary wall formation there is a tendency for cells to contract longatudinly, for more details see ---refs---. As the pre-existing strucute restrains further contraction a stress profile of longitudinal compression at the centre of the stem and tension at the outer edge. The pre-stressed state of the cambium from gravity and growth stresses produces the need to successively ’grow’ the mesh which is to be used so that each mesh addition is added in a non stressed state on top of a stressed surface. Mesh growth is achieved by first defining an initial state, this state can be thought of as a seedling. The seedling is subjected to gravitational forces, deformation occurs and a new deformed mesh is created. The positions of the nodes and vertices of the deformed mesh are used to calculate the positions of new vertices and nodes to be added in order to represent cambial growth in a non stressed state onto the stressed surface along with apical growth to a predefined height.