CAE-Companion-2018-2019

Modeling of Materials & Connections WISSEN CAE

= 0 ( ) ̇ = 0 ( ) [1 + ( ̇ ) 1 ] = 0 ( ) [1 + ⁡ ̇ ̇ 0 ] = 0 ( ) [1 + 1 ̇ ̇ 0 + 2 ( ̇ ̇ 0 ) 2 ]

Partial CurveMapping normalizes the curves to the test (experimental) curve to avoid problems with different magnitudes for abscissa and ordinate. It maps the short curve onto the long curve so that the lengths are equal. The error is defined by the area between the short curve and the mapped curve. The sum of the volumes representing the individual segment errors is the criterion which is minimized in the optimization process. Formulation of the material “parameter” law Typical material cards in commercial solvers for elastic viscoplastic material behavior are defined by true stress- true strain curves for different strain rates. Internally the com- mercial solvers are using a table lookup algorithm to get the current material state during an explicit simulation. To use reverse engineering for material characterization, the curves σ(ε,έ) have to be described by a parameterized material law. Before simulating each loadcase the material card has to be created by a script using the design parameter values submitted by the optimizer. Well known material laws for describing the yield behavior can be found in Table 1, those describing the strainrate behavior in Table 2.

PowerLaw

Cowper Symonds

Johnson Cook

Kang

Table 2: Strain rate dependence Evaluation of optimization results

Since parameter identification problems have target values or curves, the easiest way to judge on the quality of the optimi- zation result is to compare the optimal simulation results and the target. If the fit is not good enough, the following issues could be a reason among others: First the convergence of the optimization algorithm should be checked. If a sensitive parameter still varies, the results can be improved by continuing the optimization. If the optimum is found at a bound for one or more parameters, those vari- able ranges should be enlarged. In case that not any of the curves found in the optimization process fits the test curves quite well, the material model might not be appropriate and should be changed.

= 0 + ∙ = +

Bi-Linear

Ludwik

= + √1 − exp⁡(−0.5⁡ ⁡) = 0 + · (1 − − · ) · ℎ· = [ + · ( ) ] · [1 − ( ∗ ) ] = · ( + )

Bergström

G’sell Jonas

Johnson Cook

Swift

Voce = + ( − ) · − ∗ 4a three parameter = 0 + · · [1 − 1 · ] Table 1: Material laws for yield curves

Figure 7: Optimization History Further information: http://impetus.4a.co.at http://www.lsoptsupport.com CAEWissen by courtesy of 4a engineering GmbH, Austria (www.4a-engineering.at) and Dynamore GmbH, Stuttgart (www.dynamore.de)

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