The Role of Boundary Conditions on Convergence Properties of Peridynamic Model for Transient Heat Transfer

Abstract

Normally, peridynamic (PD) models for transient heat transfer converge, in the limit of the horizon size going to zero, to the solution of the corresponding PDE-based heat transfer. However, different ways of imposing local boundary conditions have been observed to lead to some interesting properties that may deliver the classical solution at a point in space and time from a series of PD solutions obtained with relatively large horizons. Here, we use analytical derivation of PD solutions to explain how approximations introduced by the one-point Gaussian discretization in space (the so-called “meshfree” PD method) and by specific implementations of boundary conditions lead to the intersection of m-convergence curves at the exact value of the corresponding classical model solution. This leads to a strategy of approximating the local solution better with a sequence of PD models that use relatively large horizons compared to a PD model that uses a small horizon. We analyze this property for transient heat conduction in homogeneous and heterogeneous bars. We find that material interfaces influence the intersection of m-convergence curves for transient heat conduction in a 1D heterogeneous bar.