# Events

**Date:**12.04.2018

**Time:**4:00 p.m.

**Place:**IC 04 408

*Norbert Huber*, Materials Mechanics Division, Helmholtz-Zentrum Geesthacht, Geesthacht, Germany

Problems in mechanics and materials science can be relatively easy approached by experiments or computational methods, as long as the solution is needed only pointwise, i.e. as long as a the material response should be determined for a certain set of input parameters as a simple forward problem. An extension of the understanding on the underlying relationship is commonly achieved by systematic variation of some or all of the independent input parameters. This can dramatically increase the complexity of the problem. Reasons are the large number of experiments or simulations caused by the number of variations and parameters in the problem or the – still unknown – complexity of the relationship. Also the combination of both often appears. The higher the complexity (e.g. caused by nonlinearities), the more dense the parameters space needs to be filled for having sufficient information. All these issues can make a conventional analysis of the problem extremely expensive or impossible to solve. They already occur in forward problems, where the unknown relationship is connecting the independent parameters with the dependent material response. In inverse problems, additional questions need to be included concerning the existence and uniqueness of the inverse solution as well as the completeness of the information from the available input data.

Artificial neural networks can principally solve such problems or at least give valuable indications about the solvability or origins of the opposite. This is done by approximating the unknown relationship via training of the neural network using patterns produced pointwise either from experiments or computer simulations. Despite their powerful generalization capabilities, they are however still of approximate nature and the validity and accuracy of their output needs to be carefully analyzed. The talk will summarize the common limitations and techniques will be discussed that can enable artificial neural networks to manage problems in mechanics and materials science, where results of high accuracy are expected. Best results can be achieved by hybrid approaches where a priori knowledge is combined with artificial neural networks as corrector. Presented examples will touch forward as well as inverse problems.

References:

N. Huber: Anwendung Neuronaler Netze bei nichtlinearen Problemen der Mechanik, Wissenschaftliche Berichte, FZKA-6504 (August 2000), Forschungszentrum Karlsruhe, zugleich Habilitationsschrift, Universität Karlsruhe, 2000. KITopen ID: 200047982, Link: https://publikationen.bibliothek.kit.edu/200047982/3813968

N. Huber, Ch. Tsakmakis: A neural network tool for identifying the material parameters of a finite deformation viscoplasticity model with static recovery, Computer Methods in Applied Mechanics and Engineering, Vol. 191, pp. 353-384, 2001.

N. Huber, W.D. Nix, H. Gao: Identification of elastic-plastic material parameters from pyramidal indentation of thin films, Proceedings of the Royal Society London A, Vol. 458, pp. 1593-1620, 2002.

N. Huber, E. Tyulyukovskiy: A new loading history for identification of viscoplastic properties by spherical indentation, Journal of Materials Research, Vol. 19, pp. 101-113, 2004.

E. Tyulyukovskiy, N. Huber: Identification of viscoplastic material parameters from spherical indentation data. Part I: Neural networks, J. Mater. Res, Vol. 21, pp. 664-676, 2006.

D. Klötzer, Ch. Ullner, E. Tyulyukovskiy, N. Huber: Identification of viscoplastic material parameters from spherical indentation data. Part II: Experimental validation of the method, J. Mater. Res, Vol. 21, pp. 677-684, 2006.

E. Tyulyukovskiy, N. Huber: Neural networks for tip correction of spherical indentation curves from bulk metals and thin metal films, J. Mech. Phys. Solids, Vol. 55, pp. 391-418, 2007.

N. Huber, E. Tyulyukovskiy, H. C. Schneider, R. Rolli: An indentation device for determination of viscoplastic stress-strain behaviour of small metal volumes before and after irradiation, J. Nuclear Materials, Vol. 377, pp. 352-358, 2008.

N. Huber, J. Heerens: On the effect of a general residual stress state in indentation and hardness testing, Acta Mat., Acta Mater Vol. 56, pp. 6205-6213, 2008.

J. Hilgert, J.F. dos Santos, N. Huber: Shear layer modelling for bobbin tool friction stir welding, Science and Technology of Welding and Joining, Vol. 17, pp. 454-459, 2012.

R. Willumeit, F. Feyerabend, N. Huber: Magnesium degradation as determined by artificial neural networks. In: Acta Biomaterialia. Vol. 9 (2013) 10, 8722 - 8729.

S. Chupakhin, N. Kashaev, N. Huber: Effect of elasto-plastic material behaviour on determination of residual stress profiles using the hole drilling method. In: Journal of Strain Analysis for Engineering Design. Vol. 51 (2016) 8, 572 - 581.