Marlon Franke

Adaptive local model networks with higher degree polynomials

A new adaptation method for local model networks with higher degree polynomials which are trained by the polynomial model tree (POLYMOT) algorithm is presented in this paper. Usually the local models are linearly parameterized and those parameters are typically adapted by a recursive least squares approach. For the utilization of higher degree polynomials a subset selection method, which is a part of the POLYMOT algorithm, selects and estimates the most significant parameters from a huge parameter matrix. This matrix contains one parameter wi, nx for each input ulp up to the maximal polynomial degree and for all the combinations of the inputs. It is created during the training procedure of the local model network. For the online adaptation of the trained local model network only the selected parameters should be used. Otherwise the local model network would be too flexible and the idea of subset selection would be lost. Therefore the presented adaptation method generates at first a new parameter matrix with the selected and most significant parameters which are unequal to zero. Afterwards the local model parameters can be adapted with the aid of a standard recursive least squares method.

A higher order phase-field approach to fracture for finite-deformation contact problems

The present contribution provides a comprehensive computational framework for large deformational contact and phase-fracture analysis and is based on the recently appeared publication [16]. A phase-field approach to fracture allows for the efficient numerical treatment of complex fracture patterns for three dimensional problems. Recently, the fracture phase-field approach has been extended to finite deformations (see [18] for more details). In a nutshell, the phase-field approach relies on a regularization of the sharp (fracture-) interface. Besides a second-order Allen-Cahn phase-field model, a more accurate fourth-order Cahn-Hilliard phase-field model is considered as regularization functional. For the former standard finite element analysis (FEA) is sufficient. The latter requires global C continuity (see [3]), for which we provide a suitable isogeometric analysis (IGA) framework. Furthermore, to account for different local physical phenomena, like the contact zone, the fracture region or stress peak areas, a newly developed hierarchical refinement scheme is employed (see [19] for more details). For the numerical treatment of the contact boundaries we use the variational consistent Mortar method. The Mortar method passes the patch-test and is known to be the most accurate numerical contact method. It can be extended, in a straightforward manner, to transient phasefield fracture problems. The performance of the proposed methods will be examined in several representative numerical examples.