Homogenization of the 1D Peri-static/dynamic Bar with Triangular Micromodulus

In peridynamics, boundary effects generally appear due to nonlocality of interparticle forces; in particular, end effects are found in 1D bars. In a previous work by Eriksson and Stenström ( J Peridyn Nonlocal Model 2(2):205–228, 2020 ), a simple method to remove end effects in certain types of 1D bars, or to homogenize such bars, was presented for bars with constant micromodulus. In this work, which is a continuation of Eriksson and Stenström ( J Peridyn Nonlocal Model 2(2):205–228, 2020 ), the homogenizing procedure is applied to bars with a linear, or “triangular,” micromodulus. For the examples studied, common in practice, the linear elastic behavior of a homogenized bar, is identical to that of a corresponding classical continuum mechanics bar, independently of the interparticle force range and total number of material points of the bar.