Browsing by Author "Reynolds, Daniel R."

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    A Nonlinear Thermodynamic Model for Phase Transitions in Shape Memory Alloy Wires
    (2003-05) Reynolds, Daniel R.
    Through a mathematical and computational model of the physical behavior of shape memory alloy wires, this study shows that localized heating and cooling of such materials provides an effective means of damping vibrational energy. The thermally induced pseudo-elastic behavior of a shape memory wire is modeled using a continuum thermodynamic description based on an improved Landau-Devonshire potential. Our construction of the potential function allows the model to account for particular alloys as well as the general solid-state phase transformation, improving over traditional potentials that idealize many of the material properties or focus only on individual processes. The material's thermodynamic response is modeled using a nonlinear conservation of momentum and a nonlinear heat equation. The heat equation introduces an inhomogeneous version of the Fourier heat flux, thereby describing the discontinuous heat flow associated with shape memory materials more thoroughly than standard, continuous heat dissipation mechanisms do. This continuum thermodynamic model is then solved computationally to determine the resulting state of the wire in time. Continuous time Galerkin methods and affine finite elements treat the temporal and spatial discretizations of the model, respectively. Traditional methods for solution of the resulting finite-dimensional, nonlinear, nonconvex system of equations must introduce a significant artificial dissipation to achieve existence of solutions. The solution of the discrete system here uses a novel combination of the damped Newton method and a homotopy method for minimizing the artificial dissipation. This combination, inspired by the well-known Method of Vanishing Viscosity for the solution of scalar hyperbolic conservation laws, reduces the artificial dissipation errors introduced by traditional approaches for such nonlinear, nonconvex thermomechanical models. Computational tests show that the proposed model successfully describes the relevant physical processes inherent in shape memory alloy behavior. Further computational experiments then confirm that up to 80% of an initial shock of vibrational energy can be eliminated at the onset of a thermally-induced phase transformation.
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    Vibration damping and heat transfer using material phase changes
    (2009-03-24) Kloucek, Petr; Reynolds, Daniel R.; Rice University; United States Patent and Trademark Office
    A method and apparatus wherein phase changes in a material can dampen vibrational energy, dampen noise and facilitate heat transfer. One embodiment includes a method for damping vibrational energy in a body. The method comprises attaching a material to the body, wherein the material comprises a substrate, a shape memory alloy layer, and a plurality of temperature change elements. The method further comprises sensing vibrations in the body. In addition, the method comprises indicating to at least a portion of the temperature change elements to provide a temperature change in the shape memory alloy layer, wherein the temperature change is sufficient to provide a phase change in at least a portion of the shape memory alloy layer, and further wherein the phase change consumes a sufficient amount of kinetic energy to dampen at least a portion of the vibrational energy in the body. In other embodiments, the shape memory alloy layer is a thin film. Additional embodiments include a sensor connected to the material.