A new finite element integration scheme. Application to a simple shear test of anisotropic material

Finite element simulations involving large strains and large displacements imply the setting up of a precise kinematics for the integration scheme. Moreover, anisotropic mechanical behaviours have to be expressed in an appropriate local reference frame. In the present paper, a computational procedure is derived from a particular velocity gradient definition. Its implementation in a finite element code is described. Application to a simple shear test is proposed. For anisotropic materials, a sinusoidal behaviour of the shear stress component is emphasized. This is due to the anisotropic yield locus and appears in the case of a saturated isotropic hardening law. Copyright © 2007 John Wiley & Sons, Ltd.     

Unfolded partial least-squares with residual quadrilinearization: A new multivariate algorithm for processing five-way data achieving the second-order advantage. Application to fourth-order excitation-emission-kinetic-pH fluorescence analytical data

Unfolded partial least-squares in combination with residual quadrilinearization (U-PLS/RQL), is developed as a new latent structured algorithm for the processing of fourth-order instrumental data. In order to check its analytical predictive ability, fluorescence excitation-emission-kinetic-pH data were measured and processed. The concentration of the fluorescent pesticide carbaryl was determined in the presence of the pesticides fuberidazole and thiabendazole as uncalibrated interferents, in the first example of fourth-order multivariate calibration. The hydrolysis of the analyte was followed at different pH values using a fast-scanning spectrofluorimeter, recording the excitation-emission fluorescence matrices during its evolution to produce 1-naphthol, which does also emit fluorescence. A set of test samples containing the above mentioned fluorescent contaminants was analyzed with the new model, comparing the results with those from parallel factor analysis (PARAFAC). The newly developed U-PLS/RQL model provides better figures of merit for analyte quantitation (average prediction error, 7 μg L⁻¹, relative prediction error, 5%, calibration range, 50-250 μg L⁻¹), and is considerably simpler than PARAFAC in its implementation. The latter, however, furnishes important physicochemical information regarding the chemical process under study, although this requires the data to be unfolded into an array of lower dimensions, due to the lack of quadrilinearity of the experimental data.