Parameter optimization in modeling static deformations of elastic membranes with TensorFlow 2.0

23.11.2023, 16:00  –  Haus 9, Raum 0.14
Forschungsseminar Differentialgeometrie

Claudia Grabs

The solution of a boundary value problem for static deformations of hyperelastic membranes depends on some constant material parameters describing the elastic properties of the material. These can be optimized with TensorFlow using experimental data in order to obtain optimal simulation results. Experiments were performed for rotationally symmetric deformations of elastic annuli cut from silicone film. In that symmetric setting, the equilibrium equations are quasi-linear ordinary differential equations and solving the boundary value problem can be achieved numerically by reducing it with the shooting method to solving initial value problems. The search for the optimal initial values can be done using a quasi-Newton method. Having implemented all this in TensorFlow, one can start to train the material parameters with the experimental data to minimize the distance of the experiment and the simulation. After many training loops hopefully some convergence to optimal parameters can be achieved. Unfortunately, I encountered some problems - these I want to explain and discuss in the talk.

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