Godding, Robert 
  
3.2 Nodal strain analysis 
The determination of the principal elongations and principal strains ¢; and @, from nodal points is clearly tedious if 
performed manually. A fast computer-based strain analysis using square grids or any array of nodal points requires 
more complex algorithms compared with circle grid analysis. Although, the identification of square grids - and this is 
the essential advantage — can easier be automated using photogrammetry and image processing techniques, which 
reduces processing speed significantly. In previous papers /10-15/ different methodologies for measuring large strain 
fields, based on these techniques are described. 
Plasticity analysis should be done incrementally since pure proportional deformation may not always be assumed. 
Because the strain is locally inhomogeneous extensive calculations are required. Several methodologies are supposed 
with different approaches /16-19/. 
One possible evaluation method is the "modified tangent method" /20/, which is based on the "coefficient method" /21/ 
applied for strain determination of distorted square grids. The main advantages are that the forming history is taken into 
consideration, which is important in case of changing principle strain directions and local forming inhomogeneities /22/. 
Based on the calculation of angles and distances in an arbitrary three-dimensional space as represented in Figure 7 the 
principal strains @; and @, are determined. 
a) b) 
  
  
  
  
  
  
  
  
Figure 7: Square grid on the undeformed blank (a), deformed grid measured in the u,v-plane (b) 
4 SETUP OF ANEW PHOTOGRAMMETRIC MEASURING SYSTEM PROTOTYPE 
Digital image processing combined with photogrammetric algorithms is a powerful tool for a quick and accurate 
measurement of surface geometry and strain-states. The new system allows the measuring of strains as well as the 
determination of 3D-surfaces of the formed sheet metals. While for strain measurements a grid is printed to the sheet 
metal directly, the optical surface measurement requires any kind of texture on the surface which can be either a 
projected pattern or a fixed pattern. This surface marking is necessary for the identification of discrete points whose 3D 
co-ordinates can be derived by photogrammetric methods /23-25/. The accuracy of the 3D coordinates depends on the 
size of the object and the resolution of the digital image capturing device. 
A prototype of the newly developed measuring system was installed at IFUM in Hanover (Figure 8). 
photogrammetric 
    
calculated points 
| — on part surface 
  
  
   
—. deformed 
square elements 
  
Figure 8: Photogrammetric measurement system 
  
294 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000.