A method for modelling microstructural material discontinuities in a finite element analysis

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Abstract
A new method is proposed for studying the effects of various microstructural material discontinuities, within a body, in a finite element analysis. The material discontinuities are accounted for by introducing a transformation strain in those regions. This formulation leads to two matrix equations; the first corresponds to the finite element analysis of the body without material discontinuities, and the second accounts for the microstructure. An important feature of the new method is that the first equation is solved only once, then the second equation can be solved repetitively for different microstructures. Thus, it is possible to study the effect of different microstructures within the body without reanalysing the entire body. It is expected that this method will be particularly useful in materials research to study the mechanisms that occur in materials at the microstructural level.The transformation strain formulation is reviewed, and the matrix equations for the new method are derived. Several numerical examples are presented to illustrate the versatility of the new method.

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