# Basic Peridynamics Question

LAMMPS Users,

I am beginning to dabble with some larger scale modeling and I was hoping to try a peridynamics model. I have gone through the user guide many times but I am still a little confused about a couple of things:

1. I am having a hard time understanding exactly how to choose the values for s00 and alpha for a given material. I understand that together they define the critical bond stretch, but I am a little unclear about what the s_min in the user guide actually means.
2. When choosing between the two models (pmb and lps), is the difference that with the pmb model is a subset of the lps model to describe very brittle materials?

Any clarification with these questions would be greatly appreciated.

Thanks,
Max

Steve

Max,

Thanks for your interest in peridynamics.

1. The critical stretch damage model uses is described in this paper (see equations (27), (28)). S00 can be derived from an experimentally measurable quantity.

S.A. Silling, E. Askari, A meshfree method based on the peridynamic model of solid mechanics, Computers & Structures, Volume 83, Issues 17–18, June 2005, Pages 1526-1535

http://dx.doi.org/10.1016/j.compstruc.2004.11.026

1. Peridynamics models can be broadly classed in two forms: “state-based” and “bond-based.” The LPS model is a state-based model, the PMB model is a bond-based model. While the implementation details differ somewhat, the primary distinction is that state-based models are more general. All bond-based models describe materials with a Poisson’s ratio of 1/4 (in 3D), which is somewhat limiting. Bond-based models are conceptually simpler, and can still be useful in some circumstances. State-based models (including the LPS model, the linearized peridynamic solid model) are described in this paper (see section 15):

S. A. Silling, M. Epton, O. Weckner, J. Xu, E. Askari, Peridynamic States and Constitutive Modeling, Journal of Elasticity, August 2007, Volume 88, Issue 2, pp 151-184.

http://dx.doi.org/10.1007/s10659-007-9125-1

Shortcomings of the bond-based theory are found on page 153. The bond-based theory is a special case of the state-based theory; see equation (47).

You may also be interested in a separate peridynamics code called “Peridigm.” See https://software.sandia.gov/trac/peridigm for more.

Best regards,

• Mike