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Peridynamic theory vs. classical continuum theory

Dr. Stewart Silling has provided me with a copy of his talk on Peridynamic theory that he presented at McMat 2007.  The PDF file of the talk is attached below.

In order to deal with classical material models and volume constraints, Dr. Silling has modified the original theory to allow for forces that are not necessarily pairwise. A bit on that is included in the talk.

You can find more information on peridynamics including a bit on Dr. Silling's code (EMU) at (though it's slightly out of date).  Dr. Silling promises to update the site in the near future.

PDF icon Silling_Peridynamic_McMat07.pdf2.89 MB


Shuozhi Xu's picture

Thank you so much for your information,  I checked out the web and found that maybe it can help me to simulate sth I want, thus I will be appreciated if you could tell me how to get this code called "EMU", I didn't find any download link on that site.

Another question is whether this code can be coupled with sandia's another code "LAMMPS"? So that one can do some multiscale modeling.

Thanks again~


Xu Shuozhi

Kaushik Dayal's picture

Regarding your second question, this paper describes an implementation that couples peridynamics to LAMMPS: 

Shuozhi Xu's picture

Thank you~It is helpful.

Shuozhi Xu's picture

Dear Dayal:

I read that paper today and found that peridunamic is a powerful tool for solving discrete problem, e.g. crack propagation.

I found that a command in lammps called "fix peri", I read that command and find out the peridynamics is used indepently in lammps, not coupled with MD like most other multiscale methods, e.g. qc, bsm ,bd, etc.

I also noticed that in the following paper:

PD is going to be a multiscale method, and what I am interested is that whether and when will PD becomes a real and handful multiscale theory, not just a continuum one, and is there any possiblity that some free code about PD could be released in the near future? Thus one can use it to do some dynamics simulation, coupled with MD.

Thank you~

Erkan Oterkus's picture

Hello Xu,

If you have an access to a finite element software, you can implement peridynamic theory within that software by using truss elements. This paper might be useful for this purpose:

R. W. Macek and S. A. Silling, "Peridynamics via finite element
analysis," Finite Elements in Analysis and Design, Vol. 43, Issue 15,
(2007) 1169-1178. DOI: 10.1016/j.finel.2007.08.012

For taking into account some nano-scale effects such as van der Waals forces within the peridynamic framework, then this paper might be useful:

 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




Shuozhi Xu's picture


Thank you, I will read these paper.



nowruzpour's picture

Can anyone send me EMU code of peridynamic?

The link does not work. any help will be greatly appreciated 

Erkan Oterkus's picture

Dear Nowruzpour,

As far as I know, EMU peridynamics code is not available to the public. However, Sandia provides another open source peridynamics code, peridigm. Here is the link of peridigm webpage:


If you want to also develop your own codes, you can start by using the fortran codes that we provided with the Peridynamic Theory and Its Applications book. If your university has access to it, you can download the book from this website:


For the codes, you should go to website and insert the following ISBN code: 978-1-4614-8464-6

Once you click on go, you can download all codes for the problems which are given in chapters 8, 9 and 10 of the peridynamics book.

Best Regards,





nowruzpour's picture

I appreciate your help. 

Hi Team,


I have gone through some papers on Peridynamics which tell that in Peridyanamics the ideas of " force per unit area" and "stress tensor" are not used. Then which are the quantified values can we calculate from the Peridynamics simulation.

Help will be appreciated.

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