• Fibers and Polymers
• /
• v.7 no.3
• /
• pp.276-285
• /
• 2006

Development and numerical implementation for an elastoplastic constitutive model for anisotropic and asymmetric materials are presented in this paper. The Coulomb-Mohr yield criterion was modified to consider both the anisotropic and asymmetric properties. The modified yield criterion is an isotropic function of the principal values of a symmetric matrix which is linearly transformed from the Cauchy stress space. In addition to the constitutive equation, the numerical treatment for the singularity in the vertex region of yield surface and stress integration algorithm based on elastoplasticity were presented. In order to assess the accuracy of numerical algorithm, isoerror maps were considered. Also, extension of a strip with a circular hole was simulated and results compared with those obtained using the (smooth) Mises yield criterion to validate stress output for a complex stress state.

• Structural Engineering and Mechanics
• /
• v.66 no.3
• /
• pp.329-341
• /
• 2018

This paper considers the smooth receding contact problem between a homogeneous half-plane and a composite laminate composed of an inhomogeneously coated elastic layer. The inhomogeneity of the elastic modulus of the coating is approximated by an exponential function along the thickness dimension. The three-component structure is pressed together by either a concentrated force or uniform pressures applied at the top surface of the composite laminate. Both semianalytical and finite element analysis are performed to solve for the extent of contact and the contact pressure. In the semianalytical formulation, Fourier integral transformation of governing equations and boundary conditions leads to a singular integral equation of Cauchy-type, which can be numerically integrated by Gauss-Chebyshev quadrature to a desired degree of accuracy. In the finite element modeling, the functionally graded coating is divided into homogeneous sublayers and the shear modulus of each sublayer is assigned at its lower boundary following the predefined exponential variation. In postprocessing, the stresses of any node belonging to sublayer interfaces are averaged over its surrounding elements. The results obtained from the semianalytical analysis are successfully validated against literature results and those of the finite element modeling. Extensive parametric studies suggest the practicability of optimizing the receding contact peak stress and the extent of contact in multilayered structures by the introduction of functionally graded coatings.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.20 no.4
• /
• pp.1275-1289
• /
• 1996

The plane elasticity problem of collinear cracks in a layered medium is investigated. The medium is modeled as bonded structure constituted from a surface layer and a semi-infinite substrate. Along the bond line between the two dissimilar homegeneous constituents, it is assumed that as interfacial zone having the functionally graded, nonhomogeneous elastic modulus exists. The layered medium contains three collinear cracks, one in each constituent material oriented perpendicular to the nominal interfaces. The stiffness matrix formulation is utilized and a set of homogeneous conditions relevant to the given problem is readily satisfied. The proposed mixed boundary value problem is then represented in the form of a system of integral equations with Cauchy-type singular kernels. The stress intensity factors are defined from the crack-tip stress fields possessing the standard square-root singular behavior. The resulting values of stress intensity factors mainly address the interactions among the cracks for various crack sizes and material combinations.

• Journal of the Korean Crystal Growth and Crystal Technology
• /
• v.16 no.4
• /
• pp.133-140
• /
• 2006

The growth characteristics and properties of large size $SrAlF_5$ single crystals are described and compared with those of $BaMgF_4$. Transmission spectra in the vacuum ultraviolet wavelength region indicate a high transparency of $SrAlF_5$ (about 90% without considering surface reflection loses) down to 150 nm, on contrast to the optical loses observed for $BaMgF_4$. The ferroelectric character of $SrAlF_5$ is evidenced by the reversal of the spontaneous polarization in a hysteresis loop. The higher potential of $SrAlF_5$ in comparison with $BaMgF_4$ for the realization of all-solid-state lasers in the ultraviolet wavelength region by the quasi-phase matching (QPM) technique is pointed out. $SrAlF_5$, besides a higher grade of transparency, shows a nonlinear effective coefficient similar to that of quartz and uniaxial nature, on contrast to the one order smaller nonlinear coefficient and biaxial character of $BaMgF_4$. The refractive index of $SrAlF_5$ from the ultraviolet to the near-infrared wavelength region is measured by the minimum deviation method. The Sellmeier and Cauchy coefficients are obtained from the fits to the curves of the ordinary and extraordinary refractive indices, and the grating period for the first order QPM is estimated as a function of the wavelength. The poling periodicity for 193 nm SHG from 386 nm is $4{\mu}m$.

• Journal of the Society of Naval Architects of Korea
• /
• v.29 no.4
• /
• pp.114-131
• /
• 1992

In the present work, a two-dimensional boundary-value problem for a large amplitude motion is treated as an initial-value problem by satisfying the exact body-boundary and nonlinear free-surface boundary conditions. The present nonlinear numerical scheme is similar to that described by Vinje and Brevig(1981) who utilized the Cauchy's theorem and assumed the periodicity in the horizontal coordinate. In the present thesis, however, the periodicity in the horizontal coordinate is not assumed. Thus the present method can treat more realistic problems, which allow radiating waves to infinities. In the present method of solution, the original infinite fluid domain, is divided into two subdomains ; ie the inner and outer subdomains which are a local nonlinear subdomain and the truncated infinite linear subdomain, respectively. By imposing an appropriate matching condition, the computation is carried out only in the inner domain which includes the body. Here we adopt the nonlinear scheme of Vinje & Brevig only in the inner domain and respresent the solution in the truncated infinite subdomains by distributing the time-dependent Green function on the matching boundaries. The matching condition is that the velocity potential and stream function are required to be continuous across the matching boundary. In the computations we used, if necessary, a regriding algorithm on the free surface which could give converged stable solutions successfully even for the breaking waves. In harmonic oscillation problem, each harmonic component and time-mean force are obtained by the Fourier transform of the computed forces in the time domain. The numerical calculations are made for the following problems. $\cdot$ Forced harmonic large-amplitude oscillation(${\omega}{\neq}0,\;U=0$) $\cdot$ Translation with a uniform speed(${\omega}=0,\;U{\neq}0$) The computed results are compared with available experimental data and other analytical results.