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

该奖项的研究目标是调查孔隙率的影响，并开发在两种不同类型的运动学约束材料系统中考虑这种影响的本构模型。第一种类型的例子包括低对称性的金属，如镁和锆合金，它们名义上是不可压缩的多晶聚集体，但当存在孔洞时，它们可能会经历显著的体积应变。第二种类型的例子包括磁性形状记忆合金，如镍-锰-镓系统，已发现这种合金在昂贵的单晶中表现出“巨大”的场致应变，但在廉价的多晶体中只表现出极小的磁致伸缩。在这种情况下，孔隙率的存在有助于松弛多晶中的内部运动约束，这是因为晶体中的磁致伸缩具有很强的取向特性，容易相互阻碍--S应变。主要的挑战是在用于这些材料在一般加载条件下的响应的本构模型中适当地考虑孔隙率的膨胀和松弛效应。这将通过最近开发的“迭代”非线性均匀化技术实现，该技术利用适当选择的“线性比较”介质，对这些材料的多孔单晶和多晶样品的耦合非线性响应产生高精度和高效率的估计。如果成功，这项研究的好处将包括更好地理解汽车、航空航天和核工业中高性能金属合金的机械性能，以及用于执行器、传感器和能量收集设备等应用的磁性形状记忆合金的磁弹性响应。这项研究还有望改善对净形金属成形操作的表征，以及通过空洞生长和结合来研究多晶材料的延性失效。此外，研究结果将对冰、岩盐和橄榄石等岩土材料的建模具有重要意义。这项工作也可能与其他活性材料系统的开发有关，例如某些类型的多晶铁电体。

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.