CAE-Companion-2018-2019

Modeling of Materials & Connections WISSEN CAE

Curve matching metric The objective of a parameter identification problem is to minimize the mismatch between the target curve and the simulation curve. To judge on the mismatch between two curves, a curve matching metric is required. The commonly appliedMean Squared Error uses the vertical coordinate distance between two specified curves to compute the matching error. The mismatch is quantified by the sum of the squares of the distances in the y-coordinate between the target points and the interpolated points on the computed curve. Thus, the mismatch of the abscissa is not explicitly included. = 1 ∑ ( ( ) − ) 2 =1 = 1 ∑ ( ( ) ) 2 =1

An important criterion for choosing a strategy is also whether the user wants to build the metamodel and solve the prob- lem iteratively or he has a “simulation budget”, i.e. a certain number of simulations he wants to use as effectively as pos- sible to build a metamodel and obtain as much information about the design as possible. In case of iterative solving polynomial response surfaces are typically used, together with the strategy “Sequential Response SurfaceMethod with domain reduction” (SRSM). In case of a “simulation budget” or of complex problem descriptions Feedforward Neural Networks or Radial Basis Function Networks are used more often nowadays. To solve parameter identification problems, SRSM is usually used.

Figure 5: Mean Squared Error Amajor difficulty with ordinate-based curve matching is that steep parts of the curve are difficult to incorporate in the matching. Failure material models have the characteristic of a steep decline of the stress-strain curve towards the end of the curve while steep curves also feature in models in which part of the behavior (the leading part of the curve) is linear. In case of curve hysteresis the ordinate values of the curve are not unique. To solve this problem one can use time dependent measurement descriptions, which are unique or a different curve matching algorithm has to be used, e.g. Partial CurveMapping.

Figure 3: Sequential Response Surface Method

Figure 4: Material characterization of the yield behavior based on a three point bending test (4a impetus process).

Figure 6: Partial Curve Mapping

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