Browsing by Author "Jusuf, Vincent"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Algorithms for branch-following and critical point identification in the presence of symmetry
    (2010-04) Jusuf, Vincent
    The objective of this work is to present techniques that can be used to study steady state solutions to systems generically described by the equation F(x; #21;) = dx dt = 0, where x 2 RN is the set of degrees of freedom (DOFs) of the system and #21; 2 R is a loading parameter. In particular, the implications of the presence of discrete and continuous symmetry to systems described by F(x; #21;) = 0 will be explored. Additionally, numerical techniques that can be used to “path-follow” the evolution of the DOFs as the loading parameter #21; is varied will be presented along with schemes to increase the computationally efficiency of the path following algorithms. These techniques can be used to obtain solutions to F(x; #21;) = 0 around regular and singular points. Additionally, methods to detect, and compute singular points of F will be presented. Finally, the benefits of these techniques will be illustrated through the computation of solutions to two typical problems.
  • Thumbnail Image
    Item
    A new framework for the interpretation of modulated martensites in shape memory alloys
    (2013-06) Jusuf, Vincent
    Shape memory alloys (SMAs) are a class of materials with unusual properties that have been attributed to the material undergoing a martensitic phase transformation (MPT). An MPT consists of the material's crystal structure evolving in a coordinated fashion from a high symmetry austenite phase to a low symmetry martensite phase. Often in SMAs, the austenite is a B2 cubic configuration that transforms into a Modulated Martensite (MM) phase. MMs are long-period stacking order structures consisting of cubic (110) basal planes. First-principles computational results have shown that the minimum energy phase for these materials is not a MM, but a short-period structure called the ground state martensite. It is commonly argued that energy contributions associated with kinematic compatibility constraints at the austenite-martensite interface explain the experimental observation of meta-stable MMs, as opposed to the expected ground state martensite phase. To date, a general approach for predicting the properties of the MM structure that will be observed for a particular material has not been available. In this work, we develop a new framework for the interpretation of MMs as natural features of the material's energy landscape (expressed as a function of the lattice parameters and individual atomic positions within a perfect infinite crystal). From this energy-based framework, a new understanding of MMs as a mixture of two short-period base martensite phases is developed. Using only a small set of input data associated with the two base martensites, this Modulated Martensite Mixture Model is capable of accurately predicting the energy, lattice constants, and structural details of an arbitrary modulated martensite phase. This is demonstrated by comparing the Modulated Martensite Mixture Model predictions to computational results from a particular empirical atomistic model.