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The evolution of Hooke’s law under finite plastic deformations for fiber-reinforced materials

Stahn, Oliver; Bertram, Albrecht; Müller , Wolfgang H.

FG Kontinuumsmechanik und Materialtheorie

When an elastoplastic material undergoes large plastic deformations, the elastic law and particularly the stiffness tetrad will evolve. This evolution is strongly dependent on the particular material. In the present paper, we consider a fiber-reinforced composite with fibers in different distinct directions. These directions introduce the anisotropy into the material behavior, particularly into the elastic law. Under plastic deformations, these directions are deformed together with the material (in contrast to crystal plasticity). This effect is called material plasticity and gives the basis for our new method. It consists of superimposing transversely isotropic stiffnesses for each fiber direction at any stage of the deformation process. A comparison for different composites and deformation paths shows the range of applicability of this method.