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## PeridynamicsPeridynamics is a formulation of continuum mechanics that is oriented toward deformations with discontinuities, especially fractures. ## Additional recommended knowledgeThe peridynamic theory is based on integral equations, in contrast with the classical theory of continuum mechanics, which is based on partial differential equations. Since partial derivatives do not exist on crack surfaces and other singularities, the classical equations of continuum mechanics cannot be applied directly when such features are present in a deformation. The integral equations of the peridynamic theory can be applied directly, because they do not require partial derivatives. The ability to apply the same equations directly at all points in a mathematical model of a deforming structure helps the peridynamic approach avoid the need for the special techniques of fracture mechanics. For example, in peridynamics, there is no need for a separate crack growth law based on a stress intensity factor. The basic equation of peridynamics is the following equation of motion:
The vector valued function The interaction between any
The term "peridynamic," an adjective, was proposed in the year 2000 and comes from the prefix ## Pairwise force functionsUsing the abbreviated notation
## DamageDamage is incorporated in the pairwise force function by allowing bonds to break when their elongation exceeds some prescribed value. After a bond breaks, it no longer sustains any force, and the endpoints are effectively disconnected from each other. When a bond breaks, the force it was carrying is redistributed to other bonds that have not yet broken. This increased load makes it more likely that these other bonds will break. The process of bond breakage and load redistribution, leading to further breakage, is how cracks grow in the peridynamic model. ## Bibliography♦ S. A. Silling, "Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces," Journal of the Mechanics and Physics of Solids, Vol. 48 (2000) 175-209. DOI: 10.1016/S0022-5096(99)00029-0 ♦ S. A. Silling, M. Zimmermann, and R. Abeyaratne, "Deformation of a Peridynamic Bar," Journal of Elasticity, Vol. 73 (2003) 173-190. DOI: 10.1023/B:ELAS.0000029931.03844.4f ♦ S. A. Silling and F. Bobaru, "Peridynamic Modeling of Membranes and Fibers," International Journal of Non-Linear Mechanics, Vol. 40 (2005) 395-409. DOI:10.1016/j.ijnonlinmec.2004.08.004 ♦ O. Weckner and R. Abeyaratne, "The Effect of Long-Range Forces on the Dynamics of a Bar," Journal of the Mechanics and Physics of Solids, Vol. 53 (2005) 705-728. DOI: 10.1016/j.jmps.2004.08.006 ♦ S. A. Silling and E. Askari, "A Meshfree Method Based on the Peridynamic Model of Solid Mechanics," Computers and Structures, Vol. 83 (2005) 1526-1535. DOI:10.1016/j.compstruc.2004.11.026 ♦ K. Dayal and K. Bhattacharya, "Kinetics of Phase Transformations in the Peridynamic Formulation of Continuum Mechanics," Journal of the Mechanics and Physics of Solids, Vol. 54 (2006) 1811-1842. DOI: I0.1016/j.jmps.2006.04.001 ♦ W. Gerstle, N. Sau, and S. Silling, "Peridynamic Modeling of Concrete Structures," Nuclear Engineering and Design, Vol. 237 (2007) 1250-1258. DOI: 10.1016/j.nucengdes.2006.10.002 ♦ S. A. Silling, M. Epton, O. Weckner, J. Xu and E. Askari, "Peridynamic States and Constitutive Modeling," Journal of Elasticity, Vol. 88 (2007) 151-184. DOI: 10.1007/s10659-007-9125-1 ♦ F. Bobaru, "Influence of van der Waals forces on increasing the strength and toughness in dynamic fracture of nanofibre networks: a peridynamic approach," Modelling and Simulation in Materials Science and Engineering, Vol. 15 (2007) 397-417. DOI: 10.1088/0965-0393/15/5/002 |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Peridynamics". A list of authors is available in Wikipedia. |