Publications

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The peridynamic model was introduced by Silling in 1998. In this paper, we demonstrate the application of the quasistatic peridynamic model to two-dimensional, linear elastic, plane stress and plane strain problems, with special attention to the modeling of plain and reinforced concrete structures. We consider just one deviation from linearity--that which arises due to the irreversible sudden breaking of bonds between particles. The peridynamic model starts with the assumption that Newton's second law holds true on every infinitesimally small free body (or particle) within the domain of analysis. A specified force density function, called the pairwise force function, (with units of force per unit volume per unit volume) between each pair of infinitesimally small particles is postulated to act if the particles are closer together than some finite distance, called the material horizon. The pairwise force function may be assumed to be a function of the relative position and the relative displacement between the two particles. In this paper, we assume that for two particles closer together than the specified 'material horizon' the pairwise force function increases linearly with respect to the stretch, but at some specified stretch, the pairwise force function is irreversibly reduced to zero.

An alternative theory of solid mechanics, known as the peridynamic theory, formulates problems in terms of integral equations rather than partial differential equations. This theory assumes that particles in a continuum interact with each other across a finite distance, as in molecular dynamics. Damage is incorporated in the theory at the level of these two-particle interactions, so localization and fracture occur as a natural outgrowth of the equation of motion and constitutive models. A numerical method for solving dynamic problems within the peridynamic theory is described. Accuracy and numerical stability are discussed. Examples illustrate the properties of the method for modeling brittle dynamic crack growth.

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The peridynamic theory of continuum mechanics allows damage, fracture, and long-range forces to be treated as natural components of the deformation of a material. In this paper, the peridynamic approach is applied to small thickness two- and one-dimensional structures. For membranes, a constitutive model is described appropriate for rubbery sheets that can form cracks. This model is used to perform numerical simulations of the stretching and dynamic tearing of membranes. A similar approach is applied to one-dimensional string like structures that undergrow stretching, bending, and failure. Long-range forces similar to van der Waals interactions at the nanoscale influence the equilibrium configurations of these structures, how they deform, and possibly self-assembly.

The deformation of an infinite bar subjected to a self-equilibrated load distribution is investigated using the peridynamic formulation of elasticity theory. The peridynamic theory differs from the classical theory and other nonlocal theories in that it does not involve spatial derivatives of the displacement field. The bar problem is formulated as a linear Fredholm integral equation and solved using Fourier transform methods. The solution is shown to exhibit, in general, features that are not found in the classical result. Among these are decaying oscillations in the displacement field and progressively weakening discontinuities that propagate outside of the loading region. These features, when present, are guaranteed to decay provided that the wave speeds are real. This leads to a one-dimensional version of St. Venant's principle for peridynamic materials that ensures the increasing smoothness of the displacement field remotely from the loading region. The peridynamic result converges to the classical result in the limit of short-range forces. An example gives the solution to the concentrated load problem, and hence provides the Green's function for general loading problems.

Some materials may naturally form discontinuities such as cracks as a result of deformation. As an aid to the modeling of such materials, a new framework for the basic equations of continuum mechanics, called the 'peridynamic' formulation, is proposed. The propagation of linear stress waves in the new theory is discussed, and wave dispersion relations are derived. Material stability and its connection with wave propagation is investigated. It is demonstrated by an example that the reformulated approach permits the solution of fracture problems using the same equations either on or off the crack surface or crack tip. This is an advantage for modeling problems in which the location of a crack is not known in advance. © 1999 Elsevier Science Ltd. All rights reserved.

Funded as a laboratory-directed research and development (LDRD) project, the work reported here focuses on the development of a computational methodology to determine the dynamic response of heterogeneous solids on the basis of their composition and microstructural morphology. Using the solid dynamics wavecode CTH, material response is simulated on a scale sufficiently fine to explicitly represent the material`s microstructure. Conducting {open_quotes}numerical experiments{close_quotes} on this scale, the authors explore the influence that the microstructure exerts on the material`s overall response. These results are used in the development of constitutive models that take into account the effects of microstructure without explicit representation of its features. Applying this methodology to a glass-reinforced plastic (GRP) composite, the authors examined the influence of various aspects of the composite`s microstructure on its response in a loading regime typical of impact and penetration. As a prerequisite to the microscale modeling effort, they conducted extensive materials testing on the constituents, S-2 glass and epoxy resin (UF-3283), obtaining the first Hugoniot and spall data for these materials. The results of this work are used in the development of constitutive models for GRP materials in transient-dynamics computer wavecodes.

The numerical stability and truncation error of a family of differencing schemes for viscoplastic constitutive relations in wavecodes is investigated. A von Neumann stability analysis is performed for a one-dimensional model problem. This analysis identifies two differencing methods that have no restriction on the time step size beyond the usual Courant-Friedrichs-Lewy condition. One of these methods is first-order accurate, and the other is second-order accurate. Implementation of one of these methods in the three-dimensional wavecode CTH is discussed. © 1993 Academic Press. All rights reserved.

A new algorithm for the treatment of sliding interfaces between solids with or without friction in an Eulerian wavecode is described. The algorithm has been implemented in the two-dimensional version of the CTH code. The code was used to simulate penetration and perforation of aluminum plates by rigid, conical-nosed tungsten projectiles. Comparison with experimental data is provided.