Papers by Author: Nobutada Ohno

Abstract: In this study, the elastic buckling strength of cubic open-cell foams subjected to uniaxial compression is investigated using the homogenization framework developed by the present authors (Ohno et al., JMPS 2002; Okumura et al., JMPS 2004). First of all, based on the framework, the microscopic bifurcation and macroscopic instability of cubic open-cell foams are numerically analyzed by performing finite element analysis. It is thus shown that long wavelength buckling is the primary mode and occurs just after the onset of macroscopic instability. Then, a solution for predicting the stress of long wavelength buckling is analytically derived from the onset condition of macroscopic instability. The validity of this analytical solution is demonstrated by the finite element results.

Abstract: In this study, to determine incremental, perturbed displacement fields in periodic elastic-viscoplastic solids, an incremental homogenization problem is fully implicitly formulated using a linearized constitutive relation, a micro/macro-kinematic relation, and a stress balance equation. It is shown that the homogenization problem can be iteratively solved with quadratic convergences by successively updating strain increments in unit cells, and that the present formulation allows versatility in the initial setting of strain increments in contrast to Terada-Kikuchi (2001) and Miehe (2002). This homogenization algorithm is then examined by analyzing a holed plate, with an elastic-viscoplastic micro-structure, subjected to tensile loading. It is thus demonstrated that the convergence in iteratively solving the homogenization problem strongly depends on the initial setting of strain increments in unit cells, and that quick convergences can be attained if the initial setting of strain increments is appropriate.

Abstract: In this study, the elastic buckling strength of cubic open-cell foams subjected to uniaxial compression is investigated using the homogenization framework developed by the present authors (Ohno et al., JMPS 2002; Okumura et al., JMPS 2004). First of all, based on the framework, the microscopic bifurcation and macroscopic instability of cubic open-cell foams are numerically analyzed by performing finite element analysis. It is thus shown that long wavelength buckling is the primary mode and occurs just after the onset of macroscopic instability. Then, a solution for predicting the stress of long wavelength buckling is analytically derived from the onset condition of macroscopic instability. The validity of this analytical solution is demonstrated by the finite element results.

Abstract: In this study, to determine incremental, perturbed displacement fields in periodic elastoplastic solids, an incremental homogenization problem is fully implicitly formulated, and an algorithm is developed to solve the homogenization problem. It is shown that the homogenization problem can be iteratively solved with quadratic convergences by successively updating strain increments in unit cells, and that the present formulation allows versatility in the initial setting of strain increments in contrast to previous studies. The homogenization algorithm developed is then examined by analyzing a holed plate, with an elastoplastic micro-structure, subjected to tensile loading. It is thus demonstrated that the convergence in iteratively solving the homogenization problem strongly depends on the initial setting of strain increments in unit cells, and that quick convergences can be attained if the initial setting of strain increments is appropriate.

Abstract: Microscopic stress distributions at an interlaminar area in a CFRP cross-ply laminate are analyzed three-dimensionally using a homogenization theory in order to investigate microscopic interaction between 0°- and 90°-plies. It is first shown that a cross-ply laminate has a point-symmetric internal structure on the assumption that each ply in the laminate has a square array of long fibers. Next, the point-symmetry is utilized to reduce the domain of homogenization analysis by half. Moreover, the substructure method is combined with the homogenization theory for reducing consumption of computational resources. The present method is then employed for analyzing stress distributions at an interlaminar area in a carbon fiber/epoxy cross-ply laminate under in-plane off-axis tensile loading. It is thus shown that microscopic shear stress significantly occurs at the interface between 0°- and 90°-plies. It is also shown that the microscopic interaction between two plies is observed only in the vicinity of the interface.

Abstract: In this study, a linearization approach is used to develop an implicit integration scheme for high-temperature inelastic constitutive models based on non-linear kinematic hardening. A non-unified model is considered in which inelastic strain rate is divided into the transient and steady parts driven, respectively, by effective stress and applied stress. By discretizing the constitutive relations using the backward Euler method, and by linearizing the resulting discretized relations, a tensor equation is derived to iteratively achieve the implicit integration of constitutive variables. The integration scheme is then programmed as a subroutine in a finite element code and applied to a lead-free solder joint analysis. It is thus demonstrated that the integration scheme affords the quadratic convergence of iteration even for considerably large increments.

Abstract: The monotonic tensile and creep deformations of a directionally solidified (DS) superalloy are investigated for several loading directions. The material exhibits remarkable anisotropy under elastic and creep loading conditions, whereas it shows isotropy under loading conditions of high strain rates. Tension-torsion creep tests are also conducted to investigate the deformation under multiaxial stress conditions. Referring to the observed behavior, a unified constitutive model, which has two features, is developed for the DS superalloy. One is a static recovery term of back stresses that is prescribed as a transversely isotropic property, which is supposed to have an effect on the deformation behavior under creep loading conditions. The other is the division of inelastic strain into two components, which represent octahedral and cubic slip system deformations, so as to describe multiaxial creep deformation. Calculation results obtained using the constitutive model are compared with the uniaxial and multiaxial experimental results to evaluate the validity of the model.