Showing papers by "Stewart A. Silling published in 2004"
01 Aug 2004
TL;DR: 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 as discussed by the authors, and a constitutive model is described appropriate for rubbery sheets that can form cracks.
Abstract: 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.
260 citations
01 Jan 2004
TL;DR: The peridynamic theory as discussed by the authors is an alternative formulation of continuum mechanics oriented toward modeling discontinuites such as cracks, which is formulated in terms of integral equations, whose validity is not affected by the presence of discontinuities.
Abstract: The peridynamic theory is an alternative formulation of continuum mechanics oriented toward modeling discontinuites such as cracks. It differs from the classical theory and most nonlocal theories in that it does not involve spatial derivatives of the displacement field. Instead, it is formulated in terms of integral equations, whose validity is not affected by the presence of discontinuities such as cracks. It may be thought of as a “continuum version of molecular dynamics” in that particles interact directly with each other across a finite distance. This paper outlines the basis of the peridynamic theory and its numerical implementation in a three-dimensional code called EMU. Examples include simulations of a Charpy V-notch test, accumulated damage in concrete due to multiple impacts, and crack fragmentation of a glass plate.Copyright © 2004 by ASME
74 citations
09 Jul 2004
TL;DR: In this article, a peridynamic formulation (PF) is proposed to capture nucleation and propagation of defects and discontinuities without ad hoc assumptions or special treatments needed by classical continuum theory.
Abstract: Here we employ a reformulation of the continuum mechanics theory, the peridynamic formulation (PF) in an integral form that, at the discretized level, resembles molecular dynamics (MD). The peridynamic theory is based on a continuum formulation and can capture nucleation and propagation of defects and discontinuities without ad‐hoc assumptions or special treatments needed by classical continuum theory. We analyze nanofiber networks and CNT‐reinforced polymer composites. We treat all crossovers contacts between fibers as perfect bonds. The use of repulsive short‐range forces eliminates the need for complex contact detection algorithms. We generate the fibers as 3D curves with random orientation, with or without preferred directionality. We use an object‐oriented code written in Fortran 90/95 to define the geometrical entities. The PF can capture the deformation and complex fracture behavior in fully 3D dynamic simulations. van der Waals forces are included in these calculations. The strength of the bonds between the polymer chains and the CNTs, as well as among the chains, is controllable.
37 citations
01 May 2004
TL;DR: In this article, the authors present developments in two categories of multiscale mathematics and analysis: continuum-to-continuum (CtC) and atomistic-tocontinuity (AtC).
Abstract: This report is a collection of documents written as part of the Laboratory Directed Research and Development (LDRD) project A Mathematical Framework for Multiscale Science and Engineering: The Variational Multiscale Method and Interscale Transfer Operators. We present developments in two categories of multiscale mathematics and analysis. The first, continuum-to-continuum (CtC) multiscale, includes problems that allow application of the same continuum model at all scales with the primary barrier to simulation being computing resources. The second, atomistic-to-continuum (AtC) multiscale, represents applications where detailed physics at the atomistic or molecular level must be simulated to resolve the small scales, but the effect on and coupling to the continuum level is frequently unclear.
18 citations