Journal ArticleDOI
The effect of long-range forces on the dynamics of a bar
Olaf Weckner,Rohan Abeyaratne +1 more
TLDR
In this paper, the authors considered the one-dimensional dynamic response of an infinite bar composed of a linear "microelastic material" and examined the effects of long-range forces.Abstract:
The one-dimensional dynamic response of an infinite bar composed of a linear “microelastic material” is examined. The principal physical characteristic of this constitutive model is that it accounts for the effects of long-range forces. The general theory that describes our setting, including the accompanying equation of motion, was developed independently by Kunin (Elastic Media with Microstructure I, 1982), Rogula (Nonlocal Theory of Material Media, 1982) and Silling (J. Mech. Phys. Solids 48 (2000) 175), and is called the peridynamic theory. The general initial-value problem is solved and the motion is found to be dispersive as a consequence of the long-range forces. The result converges, in the limit of short-range forces, to the classical result for a linearly elastic medium. Explicit solutions in elementary form are given in a broad class of special cases. The most striking observations arise in the Riemann-like problem corresponding to a constant initial displacement field and a piecewise constant initial velocity field. Even though, initially, the displacement field is continuous, it involves a jump discontinuity for all later times, the Lagrangian location of which remains stationary. For some materials the magnitude of the discontinuity-jump oscillates about an average value, while for others it grows monotonically, presumably fracturing the material when it exceeds some critical level.read more
Citations
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Journal ArticleDOI
A meshfree method based on the peridynamic model of solid mechanics
TL;DR: In this article, a numerical method for solving dynamic problems within the peridynamic theory is described, and the properties of the method for modeling brittle dynamic crack growth are discussed, as well as its accuracy and numerical stability.
Journal ArticleDOI
Peridynamic States and Constitutive Modeling
TL;DR: In this article, a generalization of the original peridynamic framework for solid mechanics is proposed, which allows the response of a material at a point to depend collectively on the deformation of all bonds connected to the point.
Book ChapterDOI
Peridynamic Theory of Solid Mechanics
TL;DR: The classical theory of solid mechanics is based on the assumption of a continuous distribution of mass within a body and all internal forces are contact forces that act across zero distance as discussed by the authors, however, the classical theory has been demonstrated to provide a good approximation to the response of real materials down to small length scales, particularly in single crystals, provided these assumptions are met.
Journal ArticleDOI
Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
TL;DR: It is shown that fractional Laplacian and fractional derivative models for anomalous diffusion are special cases of the nonlocal model for diffusion that the authors consider.
Journal ArticleDOI
Peridynamics via finite element analysis
TL;DR: In this paper, the authors describe how the peridynamic model can also be implemented in a conventional finite element analysis (FEA) code using truss elements, and demonstrate the utility and robustness of the method for problems involving fracture, damage and penetration.
References
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Book
Linear and Nonlinear Waves
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Journal ArticleDOI
Linear and Nonlinear Waves
G. B. Whitham,T. C. T. Ting +1 more
TL;DR: In this paper, a reference record was created on 2005-11-18, modified on 2016-08-08 and used for the purpose of ondes ; chocs ; onde de : choc reference record.
Journal ArticleDOI
Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces
TL;DR: In this paper, a peridynamic formulation for the basic equations of continuum mechanics is proposed, and the propagation of linear stress waves in the new theory is discussed, and wave dispersion relations are derived.
Journal ArticleDOI
Deformation of a Peridynamic Bar
TL;DR: In this paper, the deformation of an infinite bar subjected to a self-equilibrated load distribution is investigated using the peridynamic formulation of elasticity theory, which does not involve spatial derivatives of the displacement field.