Project head:
Prof. Dr. Etienne Emmrich
TU Berlin, Institut für Mathematik,
Straße des 17. Juni 136,
10623 Berlin
e-mail: emmrich@math.tu-berlin.de

Graduate assistants:
Henrik Büsing
Stephan Kusche
Address as above
e-mail: {buesing,kusche}@math.tu-berlin.de

Support:
The Boeing Company
Also associated with MATHEON.
(Find MATHEON Poster here.)

Duration:
February 2006 - June 2007

Project description:
The Mathematics and Engineering Analysis unit of The Boeing Company supports this research project on the development and implementation of numerical methods for peridynamic modeling. It is intended to help modeling structural damage and crack growth in complex materials. It is part of Boeing's commercial aircraft programs.

The peridynamic model is rather a new approach in non-local elasticity theory to cope with discontinuities. The governing equation is a nonlinear partial integro-differential equation without spatial derivatives that has to be solved numerically. Relying on the quadrature formula method, an improved meshfree spatial approximation shall be constructed and tested within this project. The new numerical method shall then enhance an existing parallel code that is employed in simulations of aircraft material damages due to hail impact, bird strike or similar impacts.

Related references:

E. Emmrich and O. Weckner: On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity. Commun. Math. Sci. 5 (2007) 4, pp. 851-864.

E. Emmrich and O. Weckner: Analysis and numerical approximation of an integro-differential equation modelling non-local effects in linear elasticity. Math. Mech. Solids. 12 (2007) 4, pp. 363-384.

E. Emmrich and O. Weckner: The peridynamic equation and its spatial discretisation. Math. Model. Anal. 12 (2007) 1, pp. 17-27.

E. Emmrich and O. Weckner: The peridynamic model in non-local elasticity theory.  PAMM 6 (2006) 1, pp. 155-156.

E. Emmrich and O. Weckner: The peridynamic equation of motion in non-local elasticity theory. In: C. A. Mota Soares et al. (eds.), III European Conference on Computational Mechanics. Solids, Structures and Coupled Problems in Engineering (Lisbon, June 2006), Springer, 2006, 19 p.

O. Weckner and E. Emmrich: Numerical simulation of the dynamics of a nonlocal, inhomogeneous, infinite bar. J. Comp. Appl. Mech. 6 (2005) 2, pp. 311 - 319.

_{Disclaimer: Der Autor zeichnet nur für den Inhalt dieser Seite verantwortlich, nicht aber für den Inhalt von Seiten, auf die hier nur verwiesen wird. Für den Inhalt derartiger fremder Seiten ist ausschließlich der jeweilige Anbieter verantwortlich. (Prof. Dr. Etienne Emmrich 07/04/08)}

Analysis of Discretization Methods for Nonlinear Evolution Equations
Teilprojekt B7 im SFB 701

The mathematical modeling of time-dependent processes in science and engineering leads to in general nonlinear evolution equations of first or second order. The highest spatial derivatives appearing can often be described by a monotone and coercive operator; semilinearities are then treated as a strongly continuous perturbation of the principle part. Relying upon the variational approach and the theory of monotone operators, the numerical solution of such evolution problems is studied with a focus on time discretization methods on equidistant as well as non-uniform meshes and their convergence. The results apply in particular to fluid flow problems.

The Research Group Linkage programme (Institutspartnerschaft) is supported by the Alexander von Humboldt Foundation.

2013-2015

Topic: Nonlinear differential equations: analysis, discretization
methods and applications

Cooperation partners:

Etienne Emmrich (TU Berlin)
Petra Wittbold (U Duisburg-Essen)
Piotr Gwiazda (U Warsaw)

Participating researchers:

Aleksandra Zimmermann (U Duisburg-Essen)
Piotr B. Mucha (U Warsaw)
Aneta Wróblewska-Kamińska (U Warsaw)
Ewelina Zatorska (U Warsaw)
Agnieszka Świerczewska-Gwiazda (U Warsaw)
Piotr Minakowski (U Warsaw)

German-Polish Workshop
Nonlinear differential equations: analysis, discretization methods and applications

Analytical and Numerical Aspects of Evolution Equations - Link
Spring school (gemeinsam mit Prof. Dr. Petra Wittbold)
Gefördert von der VolkswagenStiftung

Analysis und Numerik des Flusses Newtonscher und nicht-Newtonscher Fluide durch poröse Medien unter Berücksichtigung des Strömungsverhaltens auf mikroskopischer Ebene - Link
Beschäftigungsplanungsmittel (gemeinsam mit Prof. Dr. Petra Wittbold)
Gefördert von der TU Berlin

Analytical and numerical aspects of partial differential equations - Link
Vorlesungsreihe mit Gastwissenschaftlern aus Frankreich (gemeinsam mit Prof. Dr. Petra Wittbold)
Gefördert von der Stiftung Luftbrückendank

Diskretisierung nichtlinearer Evolutionsgleichungen erster Ordnung
Reisebeihilfen für einen Austausch mit Prof. Dr. Mechthild Thalhammer (Innsbruck)
Gefördert von der Deutschen Forschungsgemeinschaft

Aktive Mathematik - Link
Studienreformprojekt für die Lehrerausbildung (gemeinsam mit Prof. Dr. Andreas Unterreiter)
Gefördert von der TU Berlin