Analysis grid strain

Martin, T.A., Christie, G.R. and Bhattacharyya, D. (1997) Grid strain analysis and its application in composite sheet forming, in Composite Sheet Forming, Vol. 11, (ed. D. Bhattacharyya), Composite Materials Series, Elsevier, Amsterdam, pp. 217-246. 

Keywords grid strain analysis, Plytron , trellis effect, kinematic approach, finite-element approach (I M), analytical approach, anisotropy, hyperelastic, interply slip, intraply slip, thermoforming, modelling sheet forming, composite laminates, continuous fiber-reinforced composites. 

Sheet forming tools can benefit from real-time monitoring for clamping pressure, vacuum level between diaphragms, forming rate and consolidation. Trial runs can combine grid strain analysis (Krebs et aL, 1997) with finite element methods to validate performance. 

Conformational isomers represent minima on an energy surface, and all structures and the corresponding strain energies can be obtained by a careful analysis. This can be performed manually (such as in Sections 17.3 and 17.4) or automatically. An automatic procedure may involve a systematic search (grid search methods), a stochastic search (e.g., torsional Monte Carlo or cartesian stochastic, i.e., the random kick method) or molecular dynamics (see Chapter 5 and Section 16.5). Implemented in MOMEC is a random kick stochastic search module, and this has been shown to lead to excellent results, not only for conformational equilibria, but also for distributions of configurational isomers[37]. 

Fig 1 4 25 Plane-strain bending in 50 mm (2 in.) thick 5051-T5 Al. (a) Parent metal bent to 27°, with cracks initiating on the ten-" sile surface, (b) Friction stir processed 5051-T5 Al bent to 85° without cracking. Circle grid analysis of the surface strains showed that the negative minor strain at the crown was less than 1 %. 

The visioplasticity method introduced by Thomsen et al. (1959) is a combination of experiments and analysis. In this method, a velocity field is obtained from a series of photographs of the instantaneous grid pattern during a metal-forming process. The strain rate, and strain and stress fields can then be obtained by kinematical, equilibrium, and constitutive equations. The calculations involved are time-consuming, and method has lost importance with the advent of other computational methods. 

Structural mechanical calculations such as finite-element analysis (FEA) are used to analyze both the inflated and loaded deflected shapes of a tire cross-section and the resulting stress-strain relationships in the belt area. Such studies permit both quantitative analysis and qualitative comparisons of the range of belt configuration options. Figure 14.9 shows a heavy-duty truck tire in the loaded and unloaded states. The density of grids is designed so as to preserve... 

Similar to the belt area of the tire, the bead region also lends itself to finite-element analysis. Switching grid details to the bead enables analysis of the ply end strains on inflation as well as in a loaded state as the tire makes a complete revolution. By viewing Figure 14.11, it is possible to evaluate strains caused by tire inflation and cyclic deformation via FEA quantitatively, whereas without such tools, tire building and testing are required. 

The experimental distribution of the major and minor true strains obtained from circle grid analysis in the principal strain space is shown in Figure 8.6. The open markers refer to experimental strains that were taken along the meridional direction of the SPIF benchmark parts while the solid markers refer to experimental strains at failure. The latter were obtained from grid-elements placed just outside the crack since they represent the condition of the thinned sheet at the onset of fracture. 

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