Classical and Computational Solid Mechanics

By Y. Fung, Pin Tong, S. Bechtel. 2001

544 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/21c9c39381a2c246cd9e84edcbc85b8629fc2ee2

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In Biomedical Engineering

Citations in the corpus

On Simple Formulations of Weakly-Singular Traction {\&} Displacement BIE, and Their Solutions through Petrov-Galerkin Approaches (2003, unknown): “It is well-known [Fung and Tong (2001)] that the displacement solution corresponding to this unit point load is given by the Galerkin vector displacement potential: ϕ∗p = (1−υ)F∗ep (20) where F∗ = r 8πµ(1−υ) for 3D problems (21a) and F∗ = −r2 lnr 8πµ(1−υ) for 2D problems (21b) wherer = ‖ξ −x‖…”
Computational fluid dynamics of dispersed two-phase flows at high phase fractions (2003, background): “Examples include computational solid mechanics [201, 107] and molecular dynamics simulations [198].”
Three-dimensional analysis of transient thermal stresses in functionally graded plates (2003, methodology): “The constitutive equations for a linear isotropic thermoelastic material are (e.g. see Fung and Tong, 2001 )”
A framework for multiplicative elastoplasticity with kinematic hardening coupled to anisotropic damage (2005, methodology): “For a detailed outline we refer the reader to the monographs by Haupt (2000), Marsden and Hughes (1994), Lodge (1974) or Eringen (1962).”
Development of a cell centred upwind finite volume algorithm for a new conservation law formulation in structural dynamics (2013, background): “3), typically involve a considerable change of shape and are often accompanied by nonlinear material behaviour [3, 4, 6, 7].”
Reformulation of Mindlin–Reissner governing equations of functionally graded circular plates (2008, methodology): “Upon substitution of Eq. (11) into the linear strain-displacement relations of elasticity [ 26 ] the strain components are obtained as follows: er ¼ e 0 þ zk1; eh ¼ e 0 þ zk2; ez ¼ 0; chz ¼ k4; crz ¼ k5; crh ¼ e 0 þ zk6; ð12Þ”
NONLINEAR REDUCED ORDER MODELING OF ISOTROPIC AND FUNCTIONALLY GRADED PLATES (2008, unknown): “see [30,31], summation over repeated indices assumed)”
Scaling, dimensional analysis, and indentation measurements (2004, background): “The stress–strain relationships of isotropic linear elastic materials can be expressed in two equations by separating the deviatoric stress and strain, sij and dij, from the dilatational stress and strain, sii and eii, as follows [78]: sij 1⁄4 2Gdij sii 1⁄4 3Keii; (8)”
Internal lattice relaxation of single-layer graphene under in-plane deformation (2008, background): “In classical continuum mechanics (e.g., Marsden and Hughes, 1983; Fung and Tong, 2001 ), the deformation gradient, F ¼ H þ I, maps an infinitesimal vector dX from a reference state to dx in a deformed state, i.e., dx ¼ F dX, where I is the identity tensor.”
A non-classical Mindlin plate model based on a modified couple stress theory (2011, background): “, [25,26]), while the third constraint on the new material length scale parameter l in Eq.”
Macroscopic equilibrium domain structure and geometric compatibility in elastic phase transition of thin plates (2010, methodology): “Newton–Raphson iteration method [25] is a common method to solve such nonlinear equations.”