This paper presents the development of 5th order 6-point scheme for high-order precision computation scheme based on the characteristic curve method. As this scheme does not meet TVD conditions, it is newly developed for translation into the conservative form in order to apply the flux limiter and discriminator. It is defined as a 5th order conservative 6-point scheme. This proposed scheme is adapted and cleared one or two dimension problems in addition to the multiple dimensions. It is proved that the proposed scheme can be achieved excellent results from computer simulations.

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 This paper presents a finite strain isotropic damage model for finite deformation FE analyses of crack propagations in concrete and reinforced concrete. The modified von-Mises criterion is extended to finite deformation problem for evaluating damage. The evolution of the damage variables is defined as the traction — separation law which is based on fracture mechanics for concrete. We first show the formulation of the proposed finite strain damage model with the modified von-Mises criterion. Several numerical experiments are presented for verification and validation of the proposed model. The mesh sensitivity in crack propagation FE analyses is verified in 1-D and 3-D problems. The FE numerical results with the damage model are then compared with the own experimental test results of 4-point bend test of RC beam without shear reinforcements.

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 By comparing the two physically different shearing constitutive relations of the Timoshenko beam in finite displacement, the characteristics of the Jaumann rate of the Cauchy stress are examined. Numerical calculations by two representative hypoelastic models using the Jaumann rate and the Truesdell stress rate are compared in the fundamental elastic problems of deep beams and short columns. The column buckling loads numerically obtained indicate that the Jaumann rate of the Cauchy stress cannot take the effect of shear deformation into account properly even at the level of relatively small rotations. Also, the critical stress at the incipience of the plastically localized deformation predicted by the model using the Truesdell stress rate becomes smaller than that predicted by the Jaumann rate. Eventually, the characteristics of the hypoelastic model using the Truesdell stress rate are clarified. Also, the co-rotational stress rates seem to be appropriate to describe the material properties with relatively small elastic shear deformation like single crystals.

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 This paper proposes a stochastic model to evaluate behaviour of non-linear elasto-plastic bodies with uncertain properties. This model is achieved by applying the first order spectral expansion to the return mapping algorithm, and is readily implemented in Spectral Stochastic Finite Element Method. The stochastic stress-strain relation is simulated and compared with a Monte-Carlo simulation to examine the validity of the proposed model. It is shown that this model enables efficient evaluations of the mean and variance of stochastic yielding.

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