Peridynamics LPS and PMB model

Hello,

I made a simulation using PMB model. I had results.
Then I wanted to use the LPS model. I took 0.25 for the poisson’s ratio
and the influence function equal to 1/r. But the results doesn’t match those of PMB.
Do you have an idea why?

Hugo

A question for the PD experts (CCd).

Steve

Hugo,

This is a good question. Analytically, the two models are identical, although the implementations are different. The LPS model is a state-based model, whereas the PMB model is bond-based. Practical implementation differences require the state-based model to communicate information a distance of 2 \delta every timestep (in the course of computing the dilatation) while the bond based model doesn’t have to do this. This will lead to slight differences in numerical results.

– Mike

I think Mike got the most exact answer. I’ll add couple of things. In the bond based PD the force is merely “pairwise”. On the other hand “force state” in the state based PD is some way refers to the stress tensor of continuum mechanics. So the force state and pairwise force is not exactly the same thing. Theoretically it is expected that for same material with Poisson’s ratio=0.25 both PMB and LPS should give the same result but these two terms are mathematically different (see Stewart Silling’s paper: Peridynamic States and Constitutive Modeling). For ease of understanding, a weak analogy could be Lennard-Jones potential (PMB) and EAM potential (LPS).

A question for the PD experts (CCd).

Steve