Non-Linear Homogenization of Porous Anisotropic Materials: Applications to Plastic and Magnetic Shape-Memory Alloys

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The research objective of this award is to investigate the effect of porosity and to develop constitutive models accounting for this effect in two different types of kinematically constrained material systems. Examples of the first type include low-symmetry metals, such as magnesium and zirconium alloys, which are nominally incompressible polycrystalline aggregates, but which can undergo significant volumetric strains when porosity is present. Examples of the second type include magnetic shape-memory alloys, such as nickel-manganese-gallium systems, which have been found to exhibit "giant" field-induced strains in costly single crystals, but only minimal magnetostriction in cheaper polycrystals. In this case, the presence of porosity can help relax the internal kinematic constraints in the polycrystal due to the strong orientational character of the magnetostriction in the grains that tend to block each other?s strains. The main challenge is to properly account for the dilatational and relaxational effects of the porosity in constitutive models for the response of these materials under general loading conditions. This will be accomplished by means of a recently developed "iterated" nonlinear homogenization technique, which makes use of suitably chosen "linear comparison" media to generate highly accurate and efficient estimates for the coupled, nonlinear response of porous single-crystal and polycrystalline samples of these materials.If successful, the benefits of this research will include improved understanding and advanced modeling of the mechanical properties of high-performance metal alloys for energy-efficient applications in the automotive, aerospace and nuclear industries, as well as of the magneto-elastic response of magnetic shape-memory alloys for applications such as actuators, sensors and energy-harvesting devices. The research is also expected to lead to improved characterization of net-shape metal-forming operations, as well as of ductile failure in polycrystalline materials via void growth and coalescence. In addition, the results will be of interest for modeling of geomaterials, such as ice, halite and olivine. The work may also be relevant for the development of other active material systems, such as certain types of polycrystalline ferroelectrics.