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Numerical Methods in the Peridynamic Theory

Project head:
Prof. Dr. Etienne Emmrich
TU Berlin, Institut für Mathematik,
Straße des 17. Juni 136,
10623 Berlin
Graduate assistants:
Henrik Büsing
Stephan Kusche
Address as above
e-mail: {buesing,kusche}@math.tu-berlin.de
The Boeing Company
Also associated with MATHEON.
(Find MATHEON Poster here.)
Feb 2006 - Jun 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.


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