Peridynamics for multiscale materials modeling

By E. Askari, Florin Bobaru, R. Lehoucq, Michael L. Parks, Stewart A. Silling, Olaf Weckner. 2008

276 citations recorded by the source corpus.

The paper presents an overview of peridynamics, a continuum theory that employs a nonlocal model of force interaction. Specifically, the stress/strain relationship of classical elasticity is replaced by an integral operator that sums internal forces separated by a finite distance. This integral operator is not a function of the deformation gradient, allowing for a more general notion of deformation than in classical elasticity that is well aligned with the kinematic assumptions of molecular dynamics. Peridynamics effectiveness has been demonstrated in several applications, including fracture and failure of composites, nanofiber networks, and polycrystal fracture. These suggest that peridynamics is a viable multiscale material model for length scales ranging from molecular dynamics to those of classical elasticity.

Subfields: Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ea37486267684043bb6805f88d24a851ac068faf

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In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Viscoplasticity using peridynamics (2010, methodology): “finite element method), these partial derivatives must only be defined in a weak sense in order for F to exist; we will not even make this restriction in the peridynamic formulation [14].”
An extended constitutive correspondence formulation of peridynamics based on nonlinear bond-strain measures (2014, background): “A key feature of peridynamics is the ability to naturally describe discontinuities such as cracks [2, 3, 4, 5, 6, 7] and phase transition boundaries [8] within a single continuum framework.”
Dual‐horizon peridynamics (2015, background): “Refined PD was developed in [19, 16, 17, 18, 20], however it is restricted to BB-PD formulation and to the authors knowledge, has only been used for one- and twodimensional problems.”
An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis (2015, background): “Some representative research works using the bond-based PD model include the dynamic fracture of homogeneous and heterogeneous bar [6–8], damage and fracture of membranes and fibers [9,10], brittle fracture of polycrystals [11,12] and quenched glass [13], failure analysis of composites [14,15], and ”
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”
Peridynamic Theory of Solid Mechanics (2010, unknown): “Preliminary work is reported in [5].”
A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials (2013, background): “the analysis of polycrystalline microstructures and their failure processes, both in two and three dimensions [5]: among different approaches, multiscale methods appear to be the most promising, as they are able to bring together and link the diverse scales acting in the initiation and evolution of ”
A force-based coupling scheme for peridynamics and classical elasticity (2013, methodology): “Therefore, PD is suitable for multiscale modeling [1, 2, 11, 19, 26, 31].”
At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola (2013, background): “with the discrete theories of particles bound to the nodes of a lattice. How deep was the insight of Piola can be understood by looking at the literature about the subject which includes for instance [2], [35], [36], [37], [38], [39], [63], [111], [120], [121], [122]. 7.4 Appendix D. On an expressio”
ON THE ROLE OF THE INFLUENCE FUNCTION IN THE PERIDYNAMIC THEORY (2011, background): “First, like all nonlocal models, peridynamic models possess length scales and are thus suitable for multiscale modeling (Askari et al. (2008)).”
A peridynamic material model for the analysis of dynamic crack propagation in orthotropic media (2014, background): “Peridynamic predictions of inter/trans-granular fracture within a polycrystal with cubic symmetry (Benedetti and Aliabadi 2013b) have been presented in (Askari et al. 2008).”