2017/11/20 by Pelech, Petr · 1 citation
#74A10 #Classical Physics (physics.class-ph) #FOS: Physical sciences
paper · doi:10.48550/arxiv.1711.08445
We re-examine the notion of stress in peridynamics. Based on the idea of traction we define two new peridynamic stress tensors Py and P which stand, respectively, for analogues of the Cauchy and 1st Piola-Kirchhoff stress tensors from classical elasticity. We show that the tensor P differs from the earlier defined peridynamic stress tensor ν; though their divergence is equal. We address the question of symmetry of the tensor Py which proves to be symmetric in case of bond-based peridynamics; as opposed to the inverse Piola transform of ν (corresponding to the analogue of Cauchy stress tensor) which fails to be symmetric in general. We also derive a general formula of the force-flux in peridynamics and compute the limit of P for vanishing non-locality, denoted by P0. We show that this tensor P0 surprisingly coincides with the collapsed tensor ν0, a limit of the original tensor ν. At the end, using this flux-formula, we suggest an explanation why the collapsed tensor P0 (and hence ν0) can be indeed identified with the 1st Piola-Kirchhoff stress tensor.