Browse Technical Reports - Theoretical and Applied Mechanics (TAM) by Author "Fried, Eliot"

  • Kim, Tae-Yeon; Dolbow, John E.; Fried, Eliot (Department of Theoretical and Applied Mechanics (UIUC), 2006-04)
    This work concerns the development of a finite-element method for discretizing a recent second-gradient theory for the flow of incompressible fluids. The new theory gives rise to a flow equation involving higher-order ...

    application/pdf

    application/pdfPDF (7MB)
  • Dolbow, John E.; Fried, Eliot; Ji, Huidi (Department of Theoretical and Applied Mechanics (UIUC), 2004-06)
    We present a strategy for obtaining numerical solutions to a system of nonlinear, coupled evolution equations describing volume transitions in stimulus-responsive hydrogels (SRHs). The theory underlying our sharp-interface ...

    application/pdf

    application/pdfPDF (2MB)
  • Carlson, Donald E.; Fried, Eliot; Tortorelli, Daniel A. (Department of Theoretical and Applied Mechanics (UIUC), 2002-10)
    When a body is subject to simple internal constraints, the deformation gradient must belong to a certain manifold. This is in contrast to the situation in the unconstrained case, where the deformation gradient is in an ...

    application/pdf

    application/pdfPDF (585kB)
  • Fried, Eliot; Sellers, Shaun (Department of Theoretical and Applied Mechanics (UIUC), 2005-05)
    Nematic elastomers exhibit large, spontaneous shape changes at the transition from the high-temperature isotropic phase to the low-temperature nematic phase. These finite deformations are studied here in the context of a ...

    application/pdf

    application/pdfPDF (4MB)
  • Dolbow, John E.; Fried, Eliot; Shen, Amy Q. (Department of Theoretical and Applied Mechanics (UIUC), 2002-02)
    We consider the question of whether compressible nematic gels are capable of sustaining hedgehogs (radially symmetric point defects). As a basis for this work, we rely on a free-energy density that extends the conventional ...

    application/pdf

    application/pdfPDF (736kB)
  • Fried, Eliot; Todres, Russell E. (Department of Theoretical and Applied Mechanics (UIUC), 2001-08)
    The isochoric extension of a cylindrical, nematic-elastomeric specimen is studied. Numerical solutions of the resulting boundary-value problem predict that, for sufficiently large extensions, there exists a region surrounding ...

    application/pdf

    application/pdfPDF (543kB)
  • Chen, Xuemei; Fried, Eliot (Department of Theoretical and Applied Mechanics (UIUC), 2005-10)
    A linear stability analysis of the Rayleigh–Taylor problem for an incompressible fluid undergoing a liquid-liquid phase transformation is presented. Both inviscid and linearly viscous fluids are considered and interfacial ...

    application/pdf

    application/pdfPDF (1MB)
  • Fried, Eliot; Gurtin, Morton E. (Department of Theoretical and Applied Mechanics (UIUC), 2005-04)
    Using a nonstandard version of the principle of virtual power, we develop a gradient theory for incompressible flows at small length scales. In addition to a generalization of the Navier–Stokes equations involving higher-order ...

    application/pdf

    application/pdfPDF (1MB)
  • Fried, Eliot (Department of Theoretical and Applied Mechanics (UIUC), 2006-06)
    We present a sharp-interface theory for phase transformations between the isotropic and uniaxial nematic phases of a flowing liquid crystal. These equations include a supplemental interface condition which expresses the ...

    application/pdf

    application/pdfPDF (449kB)
  • Cermelli, Paolo; Fried, Eliot; Gurtin, Morton E. (Department of Theoretical and Applied Mechanics (UIUC), 2003-12)
    We derive a supplemental evolution equation for an interface between the nematic and isotropic phases of a liquid crystal when flow is neglected. Our approach is based on the notion of configurational force. As an application, ...

    application/pdf

    application/pdfPDF (882kB)
  • Fried, Eliot; Sellers, Shaun (Department of Theoretical and Applied Mechanics (UIUC), 2005-09)
    The occurrence of striped domains in stretched nematic elastomers has been suggested as evidence for soft elasticity. Conversely, the neo-classical model of Bladon, Terentjev and Warner, which displays soft elasticity, ...

    application/pdf

    application/pdfPDF (2MB)
  • Chen, Xuemei; Fried, Eliot (Department of Theoretical and Applied Mechanics (UIUC), 2006-03)
    We consider the RayleighTaylor problem with a phase transformation. For simplicity, we restrict our attention to base states in which the interface convects with the phases, so that mass exchange between the phases occurs ...

    application/pdf

    application/pdfPDF (318kB)
  • Shklyaev, Oleg E.; Fried, Eliot (Department of Theoretical and Applied Mechanics (UIUC), 2006-06)
    We use a newly developed set of boundary conditions to revisit the problem of an evaporating thin liquid film. In particular, instead of the conventional Hertz–Knudsen–Langmuir equation for the evaporation mass flux we ...

    application/pdf

    application/pdfPDF (5MB)
  • Fried, Eliot; Korchagin, Vladimir A. (Department of Theoretical and Applied Mechanics (UIUC), 2001-08)
    We consider a recent experiment of Kundler and Finkelmann (1995), who subjected an aligned specimen of nematic elastomer to uniaxial extension and observed the formation of striped domains. Working with an energy density ...

    application/pdf

    application/pdfPDF (669kB)
  • Fried, Eliot; Gurtin, Morton E.; Shen, Amy Q. (Department of Theoretical and Applied Mechanics (UIUC), 2005-09)
    We develop a complete set of equations governing the evolution of a sharp interface separating a volatile-solvent/nonvolatile-surfactant solution from a vapor atmosphere. In addition to a sorption isotherm equation and the ...

    application/pdf

    application/pdfPDF (1MB)
  • Carlson, Donald E.; Fried, Eliot; Sellers, Shaun (Department of Theoretical and Applied Mechanics (UIUC)Springer, 2002-03)
    The remarkable ability of nematic elastomers to exist in multiple stable equilibrium configurations in the absence of force and energy cost is known as soft elasticity. Here, we determine all of the soft states that are ...

    application/pdf

    application/pdfPDF (539kB)
  • Cermelli, Paolo; Fried, Eliot; Gurtin, Morton E. (Department of Theoretical and Applied Mechanics (UIUC), 2004-09)
    We establish transport relations for integrals over evolving fluid interfaces. These relations make it possible to localize integral balance laws over nonmaterial interfaces separating fluid phases and, therefore, obtain ...

    application/pdf

    application/pdfPDF (1MB)
  • Chen, Yi-Chao; Fried, Eliot (Department of Theoretical and Applied Mechanics (UIUC), 2005-06)
    Using a geometrical approach to treat the constraints associated with the continuum description of uniaxial nematic elastomers, we develop the general constitutive framework for such materials. We also provide a variational ...

    application/pdf

    application/pdfPDF (712kB)
  • Fried, Eliot; Gurtin, Morton E. (Department of Theoretical and Applied Mechanics (UIUC), 2003-05)
    This review presents a unified treatment of several topics at the intersection of continuum mechanics and materials science; the thrust concerns processes involving evolving interfaces, focusing on grain-boundaries, ...

    application/pdf

    application/pdfPDF (2MB)
  • Fried, Eliot; Gurtin, Morton E. (Department of Theoretical and Applied Mechanics (UIUC), 2003-12)
    (1) Introduction: some conditions for nonmaterial interfaces; (2) The need for a configurational force balance; (3) A framework for the study of evolving nonmaterial interfaces; (4) The normal configurational force balance ...

    application/pdf

    application/pdfPDF (504kB)