Example 5: Inverse modeling of indenter test

In an experiment, a plate (size 1 by 1) is clamped at the bottom and loaded at the middle top point by a concentrated load ($-0.000\,1$ in $y$-direction)

The $y$-displacement at the point of loading is measured ($-0.000\,25571$) and used to estimate the Young's modulus of the material. Four quadratic elements are used to model the indenter test. Initially, the Young's modulus is estimated to be $0.2$. The top force and the measured displacement are such that the Young's modulus should become 1 in the inverse iteration process (with this element mesh). The table below shows the estimated Young's modulus versus the inverse iteration number

iteration	Young's modulus
0	0.200
1	0.276
2	0.371
3	0.487
4	0.619
5	0.760
6	0.887
7	0.970
8	0.998
9	1.000