Peridynamic modeling of membranes and fibers

By Stewart A. Silling, Florin Bobaru. 2004

448 citations recorded by the source corpus.

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.

Subfields: Civil and Structural Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/72890bc28f8bfcfda78676a518158c767fc52049

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In Civil and Structural Engineering

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Crack nucleation in a peridynamic solid (2010, background): “Propagation, as opposed to nucleation, of cracks within the peridynamic model has been described elsewhere (Silling and Askari 2005) and has been applied to a number of problems involving complex patterns of fracture (Silling 2003; Silling and Bobaru 2005; Askari et al. 2006; Bobaru 2007; Xu et al. ”
Implementing peridynamics within a molecular dynamics code (2007, background): “The reader is referred to [16,2,15] for information describing PD 2 modeling in several applications at length and timescales up to meters and seconds, respectively.”
Peridynamic Theory of Solid Mechanics (2010, methodology): “Among applications of the peridynamic model to real systems, Bobaru [10] [9] demonstrated the application of a numerical model to small scale structures, including nanofibers and nanotubes.”
On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity (2007, background): “[22, 23], Silling [34], Silling & Askari [36, 35], Silling & Bobaru [37], Silling et al.”
A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities (2012, background): “The mechanical peridynamic theory ([78], [82]) has been successfully applied to model brittle fracture ([79], [80], [62], [71]), rupture of membranes and nanofiber networks ([81], [10]), spallation [95], damage in composite materials and polycrystalline ceramics ([96], [5]), phase transformations [3”
Convergence, adaptive refinement, and scaling in 1D peridynamics (2009, methodology): “Peridynamics differs from other integral non-local methods in at least two crucial aspects: (1) spatial derivatives are eliminated while other methods average infinitesimal stresses over a certain area and (2) the way damage and fracture are introduced in the method (see [26]).”
Convergence of Peridynamics to Classical Elasticity Theory (2008, background): “If it is additionally required to reproduce effects controlled by small-scale behavior, such as dispersion curves, then δ must be chosen to reflect the relevant physical length scale [5, 6, 7].”