The deformation paths during grown of a single martensite variant in a shape memory material are treated in the present work. For get the last it is employed a non-homogenous and evolutionary displacement field which is defined in a single reference system named: transformational' basis and then it is related to a second reference system called: observation basis.

The displacement field defined before is after used for deducting a tensorial strain field and a constitutive stress-strain-temperature-orientation relationship for monocristalline shape memory materials and were simulated the next patterns:

a) Distortion of the observation surface,

b) Distortion of a mark placed on the observation surface and

c) The displacement field related to the martensite transformation on the observation surface.

 Then the model is employed for to simulate the typical uniaxil strain-temperature curves a hypothetical serial grains pilycristalline sample.

The results obtained are important to the interpretation information comes to experiments in shape memory materials during stress induced martensite transformation.

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