Date of download: 11/4/2017 Copyright © ASME. All rights reserved. From: Wave Dispersion and Basic Concepts of Peridynamics Compared to Classical Nonlocal Damage Models J. Appl. Mech. 2016;83(11):111004-111004-16. doi:10.1115/1.4034319 Figure Legend: (a) Schematic illustration of how particles in a horizon interact through bond forces. (b) Nodal pair vectors in original and deformed position and displacement vectors of paired nodes.

Date of download: 11/4/2017 Copyright © ASME. All rights reserved. From: Wave Dispersion and Basic Concepts of Peridynamics Compared to Classical Nonlocal Damage Models J. Appl. Mech. 2016;83(11):111004-111004-16. doi:10.1115/1.4034319 Figure Legend: Comparison of phase velocity for wave propagation in bond-based peridynamic (PD) continuum: (1) 1D bond-based peridynamic continuum with uniform micromodulus; and (2) 2D bond-based peridynamic continuum with uniform micromodulus. The dashed line corresponds to local model (classical elasticity).

Date of download: 11/4/2017 Copyright © ASME. All rights reserved. From: Wave Dispersion and Basic Concepts of Peridynamics Compared to Classical Nonlocal Damage Models J. Appl. Mech. 2016;83(11):111004-111004-16. doi:10.1115/1.4034319 Figure Legend: Comparison of phase velocity for wave propagation in state-based peridynamic (PD) continua: (1) 1D state-based peridynamic continuum with uniform micromodulus; and (2) 2D state-based peridynamic continuum with uniform micromodulus. The dashed line corresponds to the local model (classical elasticity).

Date of download: 11/4/2017 Copyright © ASME. All rights reserved. From: Wave Dispersion and Basic Concepts of Peridynamics Compared to Classical Nonlocal Damage Models J. Appl. Mech. 2016;83(11):111004-111004-16. doi:10.1115/1.4034319 Figure Legend: Comparison of phase velocity for 1D wave propagation: (1) bond-based peridynamic continuum, and (2) state-based peridynamic continuum (both with uniform micromodulus). The dashed line corresponds to classical elasticity.

Date of download: 11/4/2017 Copyright © ASME. All rights reserved. From: Wave Dispersion and Basic Concepts of Peridynamics Compared to Classical Nonlocal Damage Models J. Appl. Mech. 2016;83(11):111004-111004-16. doi:10.1115/1.4034319 Figure Legend: Comparison of dispersion diagram for 1D wave propagation: (1) bond-based peridynamic (PD) continuum with uniform micromodulus; and (2) state-based peridynamic (PD) continuum. The dashed line corresponds to classical elasticity.

Date of download: 11/4/2017 Copyright © ASME. All rights reserved. From: Wave Dispersion and Basic Concepts of Peridynamics Compared to Classical Nonlocal Damage Models J. Appl. Mech. 2016;83(11):111004-111004-16. doi:10.1115/1.4034319 Figure Legend: Comparison of phase velocity for 1D wave propagation for bond-based and state-based peridynamic (PD) continuum with uniform micromodulus and original nonlocal model for softening damage considering different nonlocal characteristic length l. The dashed line corresponds to a local model (classical elasticity).

Date of download: 11/4/2017 Copyright © ASME. All rights reserved. From: Wave Dispersion and Basic Concepts of Peridynamics Compared to Classical Nonlocal Damage Models J. Appl. Mech. 2016;83(11):111004-111004-16. doi:10.1115/1.4034319 Figure Legend: Phase velocity for 1D bond-based peridynamic model with a uniform micromodulus, considering a uniform grid with 5 points within the horizon. The thick curve represents the phase velocity envelope of the discretized system, and the points on the curve represent the discrete phase velocities of the system. The dashed line represents the phase velocities of linear elastic model.

Date of download: 11/4/2017 Copyright © ASME. All rights reserved. From: Wave Dispersion and Basic Concepts of Peridynamics Compared to Classical Nonlocal Damage Models J. Appl. Mech. 2016;83(11):111004-111004-16. doi:10.1115/1.4034319 Figure Legend: Dispersion diagram for 1D bond-based peridynamic (PD) model with uniform micromodulus considering a uniform grid with 5 points within the horizon. Note that the y -coordinate stands for the magnitude of normalized frequency, |w/w0|, where w=χv. Note that the region −0.5<χ<0.5 in the plot is the reconstruction zone, and the region outside shows the aliasing region.

Date of download: 11/4/2017 Copyright © ASME. All rights reserved. From: Wave Dispersion and Basic Concepts of Peridynamics Compared to Classical Nonlocal Damage Models J. Appl. Mech. 2016;83(11):111004-111004-16. doi:10.1115/1.4034319 Figure Legend: Phase velocity for 1D state-based peridynamic (PD) model considering a uniform grid with 5 points within the horizon. The dashed line represents the continuum solution, while the dotted line represents the classical elasticity solution. The domain −0.5<χ<0.5 is the reconstruction zone.

Date of download: 11/4/2017 Copyright © ASME. All rights reserved. From: Wave Dispersion and Basic Concepts of Peridynamics Compared to Classical Nonlocal Damage Models J. Appl. Mech. 2016;83(11):111004-111004-16. doi:10.1115/1.4034319 Figure Legend: Dispersion diagram for 1D state-based peridynamic (PD) model considering a uniform grid with 5 points within the horizon. The dashed line represents the continuum solution. Note that the shaded region −0.5<χ<0.5 in the plot is the reconstruction zone.

Date of download: 11/4/2017 Copyright © ASME. All rights reserved. From: Wave Dispersion and Basic Concepts of Peridynamics Compared to Classical Nonlocal Damage Models J. Appl. Mech. 2016;83(11):111004-111004-16. doi:10.1115/1.4034319 Figure Legend: Wave propagation in an elastic bar

Date of download: 11/4/2017 Copyright © ASME. All rights reserved. From: Wave Dispersion and Basic Concepts of Peridynamics Compared to Classical Nonlocal Damage Models J. Appl. Mech. 2016;83(11):111004-111004-16. doi:10.1115/1.4034319 Figure Legend: (a) Direct long-range interparticle interactions in a peridynamic continuum, (b) indirect interactions between particles through intergranular forces, (c) three common cases of micromodulus distribution, (d) micromodulus with a Dirac delta function at |ξ|=δ, (e) approximation of the Dirac delta function at |ξ|=δ, (f) Burt and Dougill's constitutive model for progressive failure of heterogeneous media