A dynamic hybrid local/nonlocal continuum model for wave propagation

Abstract

In this work, we develop a dynamic hybrid local/nonlocal continuum model to study wave propagations in a linear elastic solid. The developed hybrid model couples, in the dynamic regime, a classical continuum mechanics model with a bond-based peridynamic model using the Morphing coupling method that introduced in a previous study (Lubineau et al., J Mech Phys Solids 60(6):1088-1102. The classical continuum mechanical model is known as a local continuum model, while the peridynamic model is known as a nonlocal continuum model. This dynamic hybrid model aims to introduce the nonlocal model into the key structural domain, in which the dispersions or crack nucleations may occur due to flaws, while applying the local model to the rest of the structural domain. Both the local and nonlocal continuum domains are overlapped in the coupled subdomain. We study the speeds and angular frequencies of the plane waves, with small and large wavenumbers obtained by the hybrid model and compare them to purely local and purely nonlocal solutions. The error of the hybrid model is discussed by analyzing the ghost forces, and the work done by the ghost forces is considered equivalent to the energy of spurious reflections. One-and two-dimensional numerical examples illustrate the validity and accuracy of the proposed approach. We show that this dynamic hybrid local/nonlocal continuum model can be successfully applied to simulate wave propagations and crack nucleations induced by waves.

Element‐based coupling modeling of peridynamics and classical continuum mechanics for dynamic brittle fracture

“…c 0 (𝝃) is the peridynamic micromodulus function which is defined as c 0 (𝝃) = ĉe −|𝝃|∕l , in this paper, both ĉ and l are chosen as a constant. 39 Substituting Equation ( 7) into Equation ( 5) yields…”

“…The hybrid model based on the Morphing coupling method has been used to analyze the deformation and fracture under the quasi-static loadings 37 and the damage caused by the wave propagation. 39 Note that the peridynamic model used in this hybrid model is still a kind of bond-based peridynamic model, which means the limitation of the fixed Poisson's ratio still remains. To overcome this limitation, many modified bond-based peridynamic models have been developed, such as the conjugated bond-pair-based peridynamic model, 40 which will be furtherly used in the hybrid model.…”

“…Although the coupling artifacts of the hybrid model have been analytically studied by estimating the ghost forces, 29,39 the ability of the hybrid model for dynamic crack propagation problems has not been fully proved yet. In addition, to enhance the applicability of the hybrid model within the finite element software platform, it is necessary to implement the hybrid model within a finite element method framework.…”

“…A hybrid peridynamic and classical continuum mechanical model is established in the transition domain with the help of the Morphing function. The hybrid model based on the Morphing coupling method has been used to analyze the deformation and fracture under the quasi‐static loadings 37 and the damage caused by the wave propagation 39 . Note that the peridynamic model used in this hybrid model is still a kind of bond‐based peridynamic model, which means the limitation of the fixed Poisson's ratio still remains.…”

Peridynamic Simulation of Dynamic Fracture Process of Engineered Cementitious Composites (ECC) with Different Curing Ages

“…Zhang et al [ 28 ] proposed an angle-based bond damage criterion for type II and mixed-mode fractures and developed a peridynamics model for mixed-mode fracture analysis, which was validated for fractures at mixed-mode interfaces and homogeneous materials. Han et al [ 29 ] developed a dynamic mixed classical continuum mechanics and peridynamics medium model to study wave propagation in a linear elastic solid, and successfully simulated wave propagation and wave-induced crack nucleation. Wu et al [ 30 ] investigated the fracture mode of laminated glass panels under drop weight loading by reconstructing a classical viscoelastic model within the framework of ordinary state-based peridynamics theory.…”