A unified, stable and accurate meshfree framework for peridynamic correspondence modeling. Part II: wave propagation and enforcement of stress boundary conditions

by   Masoud Behzadinasab, et al.

The overarching goal of this work is to develop an accurate, robust, and stable methodology for finite deformation modeling using strong-form peridynamics (PD) and the correspondence modeling framework. We adopt recently developed methods that make use of higher-order corrections to improve the computation of integrals in the correspondence formulation. A unified approach is presented that incorporates the reproducing kernel (RK) and generalized moving least square (GMLS) approximations in PD to obtain higher-order gradients. We show, however, that the improved quadrature rule does not suffice to handle correspondence-modeling instability issues. In Part I of this paper, a bond-associative, higher-order core formulation is developed that naturally provides stability. Numerical examples are provided to study the convergence of RK-PD, GMLS-PD, and their bond-associated versions to a local counterpart, as the degree of non-locality approaches zero. It is shown that the bond-associative approach improves the robustness of RK-PD and GMLS-PD formulations, which is essential for practical applications. The higher-order, bond-associated model can obtain second-order convergence for smooth problems and first-order convergence for problems involving field discontinuities, such as curvilinear free surfaces. In Part II of this paper we use our unified PD framework to: (a) study wave propagation phenomena, which have proven problematic for the state-based correspondence PD framework; (b) propose a new methodology to enforce natural boundary conditions in correspondence PD formulations, which should be particularly appealing to coupled problems. Our results indicate that bond-associative formulations accompanied by higher-order gradient correction provide the key ingredients to obtain the necessary accuracy, stability, and robustness characteristics needed for engineering-scale simulations.



page 9

page 14

page 19


A unified, stable and accurate meshfree framework for peridynamic correspondence modeling. Part I: core methods

The overarching goal of this work is to develop an accurate, robust, and...

A Consistent Higher-Order Isogeometric Shell Formulation

Shell analysis is a well-established field, but achieving optimal higher...

Higher-order generalized-α methods for parabolic problems

We propose a new class of high-order time-marching schemes with dissipat...

A General-Purpose, Inelastic, Rotation-Free Kirchhoff-Love Shell Formulation for Peridynamics

We present a comprehensive rotation-free Kirchhoff-Love (KL) shell formu...

A continuum and computational framework for viscoelastodynamics: finite deformation linear models

This work concerns the continuum basis and numerical formulation for def...

A complete and consistent second-order hydrodynamic model for floating structures with large horizontal motions

Floating offshore structures often exhibit low-frequency oscillatory mot...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.