Constitutive relations, plastics mechanical

The OSL model was constructed in order to explain curious observations reporting that the maximum pressure P in a sandpile was not necessarily directly below the pile s peak but, rather, could occur on a ring of nonzero radius [49-52] (see also Savage [53]). In some cases, the pressure at the base was actually reported to have a local minimum under the peak, the so-called stress dip phenomenon. The 2D OSL model has a Janssen-like constitutive relation of the form (Jxx = ( zz + where z is the vertical and x is the horizontal direction. When coupled with the constraint of stress balance, this leads to the proposal that (static) stresses within a granular material satisfy a hyperbolic PDF in the spatial variables, x and z. Bouchaud et al. then showed that this model could predict a stress dip. Savage [53] argued that soil mechanics models [14] can also account for a stress dip. Elasto-plastic soil mechanics models [ 14] are elastic below yield and are described in this case by elliptic equations (above yield, they are characterized by hyperbolic equations). Hence, the OSL and soil mechanics approaches are inherently different types of models. 

The dependence of mechanical behavior on constitution in Zr02-Ni system results from the variation of microstructure and its distribution. In the regions rich in Ni or PSZ, the mechanical performance is controlled by continuous matrix component and displays elasto-plastic or linear elastic characteristics, respectively. The non-linear elastic behavior at 60 vol% PSZ is related to the connectivity transition of matrix component. 

This situation changed substantially when in April 1921, Kurt H. Meyer was appointed leader of the Central Research Laboratory. Although an organic chemist, Meyer was interested in the emerging field of physical chemistry. In the years from 1921 to 1932 he extended the research topics of his laboratory from dyestuffs chemistry into the field of natural and synthetic fibres, plastics, and related intermediates. But for the purpose of this paper, his attitude towards fundamental questions such as the constitution of natural and synthetic polymers, and the mechanisms of catalytic reactions is more significant. Meyer inaugurated a short period of basic research in the Central Research Laboratory. 

If this deformation field does not fulfill the geometrical compatibility, a strain tensor related to stress is generated. The constitutive equation, which represents the mechanical behavior of the material, relates this strain tensor and the stress tensor. Due to the memory effect of wood, this tensor has to be divided into two parts (1) an elastic strain, connected to the actual stress tensor and (2) a memory strain, which includes all the strain due to the history of that point (e can deal with plasticity, creep, mechanosorption, etc.). 

As a general rale, visco-plastic material behavior is specified for FEM simulation of chip removal. Thermo-mechanically coupled calculations are used. For describing material behavior, the use of the Johnson-Cook equation (Eq. 4) is preferred. Another semiempiiical model presented by Zerilli and Armstrong considers micro-mechanical effects in relation to the thermal activation behavior of face-centered (fee) and body-centered cubic (bcc) structures of the workpiece material. Other constitutive material laws are formulated by Oxley, Clifton Hensel-Spittel, and El-Magd, respectively, whereas the stress s is determined by different linear or exponential procedures within the equation terms. 

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