Strain, two-dimensional

In their early work, Adams and Peppiatt (1974) used constant strain, two-dimensional, triangular elements which give the stress at the centroid of the element. Since joints tend to be wide compared with the thickness, the problem was considered to be one of plane strain. This assumption should be satisfactory for the adhesive layer, but less so for the adherend. The spew fillet was approximated to a 45° triangular fillet of varying size. The restraints used in their models are shown in Fig. 18 and a typical mesh in Fig. 19. 

Figure 7-5. Two-dimensional representation of Koshland s induced fit model of the active site of a lyase. Binding of the substrate A—B induces conformational changes In the enzyme that aligns catalytic residues which participate in catalysis and strains the bond between A and B, facilitating its cleavage.

Under internal pressure a vessel will expand slightly. The radial growth can be calculated from the elastic strain in the radial direction. The principal strains in a two-dimensional system are related to the principal stresses by ... 

Proteome profiling allows quantitative and global examination of the changes in protein expression in different strains or cells under different conditions. Two-dimensional gel... 

In textbooks, plastic deformation is often described as a two-dimensional process. However, it is intrinsically three-dimensional, and cannot be adequately described in terms of two-dimensions. Hardness indentation is a case in point. For many years this process was described in terms of two-dimensional slip-line fields (Tabor, 1951). This approach, developed by Hill (1950) and others, indicated that the hardness number should be about three times the yield stress. Various shortcomings of this theory were discussed by Shaw (1973). He showed that the experimental flow pattern under a spherical indenter bears little resemblance to the prediction of slip-line theory. He attributes this discrepancy to the neglect of elastic strains in slip-line theory. However, the cause of the discrepancy has a different source as will be discussed here. Slip-lines arise from deformation-softening which is related to the principal mechanism of dislocation multiplication a three-dimensional process. The plastic zone determined by Shaw, and his colleagues is determined by strain-hardening. This is a good example of the confusion that results from inadequate understanding of the physics of a process such as plasticity. 

Fig. 15 Initiation of fibre fracture by a crack oriented parallel to the chain direction in a domain. It is proposed that a circular crack with a radius q releases the strain energy in a sphere around the crack with the same radius. Note that in this two-dimensional drawing only the circular crack is shown in perspective...

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