Onto resolving spurious wave reflection problem with changing nonlocality among various length scales

•The wave reflection can be mitigated between different nonlocal models by using fraction power law based kernel.•Seamless local/nonlocal bridging can be established by incorporating power law based handshake region.•Heterogeneous materials at different length scale can be modeled using power law based kernels without having any spurious wave reflection problem.

In this work an effective method was proposed in order to resolve the wave reflection problems between local/nonlocal models as well as multiple nonlocal models with varying nonlocality. Spurious   wave reflection has been a primary concern in developing a robust multiscale–multiresolution model. In the current work a power-law based nonlocal peridynamic model has been proposed in order to mitigate this issue in a versatile manner. The fractional power-law eliminates the spurious wave reflection at the interfaces between local/nonlocal regions or regions with different nonlocalities. By controlling the exponent of the power-law it is possible to vary the frequency components of short or long waves without requiring a large handshake region. Using this underlying idea, 1|x−x′|1+α,∀0<α<2 can be used as a kernel function in order to define nonlocal interaction between x and x′. It was shown that by controlling α it is possible to change the nature of nonlocal interaction within any given cutoff range. Besides power law, Gaussian kernel is another good choice in minimizing the wave reflection issue. However, Gaussian function has some limitations with large variation in nonlocality or waves with higher frequency. In that context the proposed model demonstrated its effectiveness by removing any spurious wave reflections originated in various cases.