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Research by Andy Hansen
General Research Interests
General research interests lie in the area of theoretical solid mechanics with an emphasis on multiphase materials. Examples include high performance structural materials such as composites, as well as geophysical materials such as snow and sea ice. Although applications in geophysical problems and high performance composites are substantially different, the characterization of their behavior relies on a solid understanding of the behavior of multiphase materials. In this regard, the materials present similar analytical problems whose solutions rely on advanced continuum theories such as multicontinuum theories (axiomatic continuum mixture theories) and/or microphysical approaches.
MCT, Multicontinuum Theories for Composite Structural Analysis
Composite material systems are constantly being developed for increasingly severe thermo-mechanical environments and generally exhibit nonlinear behavior under such conditions. The inelastic behavior is severely complicated by the existence of two distinct phases. Standard practice treats a composite as a single homogenized continuum, However, nonlinearities, damage, fiber matrix debonding, and fracture initiate at the constituent level. Current research in this area treats the composite as a multiphase continuum in which the constituents retain their identity in a general structural analysis. This allows one to extract constituent stresses and the interactions between constituents. Such information is enormously useful for predicting the initiation and evolution of nonlinearities, damage, fracture, debonding, and other related phenomena.
Continuum Mixture Theories
An approach to analyzing high performance composite materials is to develop an immiscible mixture theory to describe the nonlinear behavior of the material. By immiscible, it is meant that the constituents remain physically separate and hence give the material some form of local microstructure. It is precisely this local microstructure which give rise to material anisotropy. The goal of the theory is to develop accurate expression for the interaction terms between individual constituents in terms of the local morphology. Substantial progress has been made in applying mixture theory to composites. In doing so, some fundamental problems with modern mixture theory formulation have been expose. Work is continuing of the general development of modern mixture theory as well as its application to composite materials.
Temperature Gradient Metamorphism of Snow
The stratigraphy of an alpine snowpack can be very complex and variable due to different environmental conditions during and after deposition. Melt/freeze cycles, solar radiation, equi-temperature metamorphism, and temperature gradient metamorphism working in concert with the thermodynamically unstable state of snow contribute to this variability. Temperature gradients which commonly occur near the earth's surface cause the formation of low strength snow which can lead to an unstable snowpack and avalanches. Low strength snow is also of concern in the construction and maintenance of polar runways and highways. Modern mixture theory is used model temperature gradient metamorphism and to provide a stepping stone for a comprehensive treatment of the microstructural changes that occur in natural snowpacks.
Impact of Snow Microstructure on the Macroscopic Thermo-mechanical Properties of Snow
The thermo-mechanical properties of snow are strongly influenced by the microstructure. Advanced constitutive models for snow must reflect this dependence. A viable approach for analyzing microstructural effects is to generate and use computer generated unit cells. Such cells must contain a random distribution of grains and bonds in sufficient number to be statistically meaningful. Using such cells will allow for the identification of microstructure parameters that significantly contribute to the thermo-mechanical properties of snow and track their evolution during deformation. Numerical results will enhance and direct experimental efforts to predict the response of snow (and other material with random microstructure) under a variety of thermomechanical conditions.