7 research outputs found

    Solid-fluid dynamics of yield-stress fluids

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    On the example of two-phase continua experiencing stress induced solid-fluid phase transitions we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the time evolution equations possessing it are compatible with mechanics and with thermodynamics. The former compatibility means that the equations are local conservation laws of the Godunov type and the latter compatibility means that the entropy does not decrease during the time evolution. In numerical illustrations, in which the one-dimensional Riemann problem is explored, we require that the Euler structure is also preserved in the discretization.Comment: 51 pages, 7 figure

    Nucleation of Cavities in Gels

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    University of Minnesota Ph.D. dissertation. August 2017. Major: Mathematics. Advisor: Ronald Siegel. 1 computer file (PDF); viii, 94 pages.Many implantable devices are made of synthetic polymers which upon insertion absorb water, causing the polymer to swell and form a gel (mixture of solid and fluid). Since the swelling leads to an expansion of the polymer, a gel is considered to be a compressible material. A high concentration of stress due to the swelling may lead to the nucleation and growth of cavities within the gel, which is likely to cause the debonding of the material from the support it is attached to. In this dissertation, we focus on the cavitation in a gel occupying a spherical domain, subject to either displacement boundary conditions or free swelling. We consider a total free energy of the gel accounting for the elasticity of the polymer and for the mixing between polymer and fluid, called the Flory-Huggins energy. In addition to penalizing gel deformation, the free energy represents competing effects of entropy that favours mixing, polymer-polymer and fluid-fluid interaction forces. We study the material properties necessary to allow for a nucleation of cavities and analyze radially symmetric deformations

    Incipient Dynamics of Swelling of Gels

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