The research objective of this grant is to create fundamental solutions for defects in solids under dynamic loading that concern dynamically expanding inclusions, which are regions within the material that possess general transformation strain (such as due to thermal expansion that is constrained by the matrix), and also solutions concerning expanding inhomogeneities (regions where the material properties change as the region of transformation strain expands). The solutions will allow the calculation of the "driving force," i.e. the mechanical rate of work needed to be supplied to create dynamically an incremental region of inclusion / inhomogeneity with transformation strain, and, consequently, the evolution of these regions under dynamic loading. The static counter-part of the phenomenon is the "Eshelby inclusion" and inhomogeneity, which constitutes the most cited paper in Solid Mechanics in the last fifty years. The theoretical predictions will be used in the analytical modeling of experimental results regarding the microstructural evolution of phase transformations in shape memory alloys due to stress wave loading.
The applications and impact of these dynamic solutions are wide in the characterization of materials in terms of the dynamic evolution of their microstructure, such as the one of shape memory alloys widely used in biomedical devices, as well as in the geophysical modeling of earthquake sources. The research effort will have an impact on the graduate education program in the dynamical properties and microstructural evolution of materials at UCSD (University of California - San Diego) and nationwide.
