The finite element method (FEM) is computationally robust and very effective for modeling structures with complex geometries and different materials under general loading conditions. Its computational model requires an explicit representation of cracks for the prediction of crack initiation and growth.&nbsp; However, the stresses at the crack tips are mathematically singular because of the undefined spatial derivatives of displacements.Peridynamic (PD) is a non-local reformulation of the equation of motions in classical continuum mechanics and does not contain any spatial derivatives of displacements. Therefore, the PD governing equations are always defined at the fracture surfaces. This feature allows crack initiation and propagation at multiple sites without resorting to external crack growth criteria. The original PD formulation was called “bond-based (BB)” which is established based on the assumption of pair-wise interactions of the same magnitude in the same domains of interaction. The BB PD does not distinguish between dilatation and distortional parts of deformation with a constraint on the Poisson’s ratio (1/3 for 2D and 1/4 for 3D). Ordinary state-based (OSB) PD theory eliminates the limitations of the BB PD theory. In the OSB PD, the two interacting points have their own domains of interaction without such constraints.The PD material parameters are determined by equating the classical strain energy density (SED) under simple loading conditions to that of PD at a point with a complete domain of interaction. However, these PD parameters are not valid if the material point is located near a surface because of its incomplete domain of interaction. Therefore, they require a correction procedure due to surface effects. Moreover, the PD analysis requires volume integration over the interaction domain which must conform to the geometry of the integration domain for determining the PD material parameters. In the PD analysis, a volumetric correction procedure is required due to the use of circular or spherical analytical integration of interaction domains.The PD equations are entirely consistent with the fundamentals of FEM. This study presents an ordinary state-based PD truss element. The PD interactions among the nodes are achieved through a truss element. The present PD element permits the use of non-uniform domain discretization leading to a domain of interaction with an arbitrary shape and a variable horizon. The PD material parameters are determined based on the discretized computational model; thus, the volume and surface correction procedures are not required. The non-uniform PD discretization is generated using standard FE mesh generation software that enables the construction of computational models to represent specific geometries. The accuracy of this element is verified by considering a plate with and without a pre-existing crack under tension. In the presence of a crack, its solution is achieved by employing an implicit algorithm until crack growth begins, and then continuing with an explicit algorithm.

A Truss Element for Ordinary State-Based Peridynamic Analysis With Uniform or Non-Uniform Discretization

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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