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2 Computer Assisted Mechanics and Engineering Sciences

2 2001

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Splines in physicochemical studies of liquid binary mixtures

Iwanow Z., Bauer J., Jelińska-Kazimierczuk M.

Computer Assisted Mechanics and Engineering Sciences

2001

Vol. 8, No. 1

169-182

Physicochemical studies of the organic-water mixtures show that their properties are not linear functions of their concentration but depend on the mixture composition in various ways. The evaluation of the measurement results requires an interpolation of the experimental data and the derivatives of a mixture property with respect to concentration should be known as well. The results of measurements are disturbed by experimental error which causes the scatter of the approximated function values and oscillations of the approximating function derivatives. In the paper an application of the 3rd degree splines for the calculation of derivative and the interpolation for a non-uniform mesh are considered. Smoothing methods of an approximating function by means of splines are proposed. Some numerical examples illustrating the efficiency of the smoothing method and its applications are presented.

Simulation of instabilities in non-softening Drucker-Prager plasticity

Stankiewicz A., Pamin J.

Computer Assisted Mechanics and Engineering Sciences

2001

Vol. 8, No. 1

183-204

The problem of instability and strain localization in a hardening non-associative Drucker-Prager plasticity theory is analyzed. The classical and gradient-enhanced versions of the theory are reviewed and instability indicators are summarized. The regularizing properties of the gradient-enhancement are shown. The classical plane strain biaxial compression test is analyzed in terms of the analytical prediction of ellipticity loss and numerical simulation of the process of shear band formation and evolution. The influence of material model parameters, especially of the degree of non-associativity and the gradient influence,