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Strain Increments

Both total and incremental forms of the strain vector are required for substitution in Internal Virtual Work Statement (Eq.10). The linear strains are expressed in the usual way in terms of the nodal variables by:

       (2)

where is the standard “beta” matrix relating strains to displacements. The incremental form is simply:

       (3)

Similarly for the nonlinear strain, the total strain is given by Internal Virtual Work Statement (Eq.6), and the incremental value is derived as:

       (4)

which gives:

       (5)

where . Additionally, the total nonlinear term can be written in the form:

       (6)