Strong Local-Nonlocal Coupling for Integrated Fracture Modeling

Abstract

Peridynamics, a nonlocal extension of continuum mechanics, is unique in its ability to capture pervasive material failure. Its use in the majority of system-level analyses carried out at Sandia, however, is severely limited, due in large part to computational expense and the challenge posed by the imposition of nonlocal boundary conditions. Combined analyses in which peridynamics is employed only in regions susceptible to material failure are therefore highly desirable, yet available coupling strategies have remained severely limited. This report is a summary of the Laboratory Directed Research and Development (LDRD) project "Strong Local-Nonlocal Coupling for Integrated Fracture Modeling," completed within the Computing and Information Sciences (CIS) Investment Area at Sandia National Laboratories. A number of challenges inherent to coupling local and nonlocal models are addressed. A primary result is the extension of peridynamics to facilitate a variable nonlocal length scale. This approach, termed the peridynamic partial stress, can greatly reduce the mathematical incompatibility between local and nonlocal equations through reduction of the peridynamic horizon in the vicinity of a model interface. A second result is the formulation of a blending-based coupling approach that may be applied either as the primary coupling strategy, or in combination with the peridynamic partial stress. This blending-based approach is distinct from general blending methods, such as the Arlequin approach, in that it is specific to the coupling of peridynamics and classical continuum mechanics. Facilitating the coupling of peridynamics and classical continuum mechanics has also required innovations aimed directly at peridynamic models. Specifically, the properties of peridynamic constitutive models near domain boundaries and shortcomings in available discretization strategies have been addressed. The results are a class of position-aware peridynamic constitutive laws for dramatically improved consistency at domain boundaries, and an enhancement to the meshfree discretization applied to peridynamic models that removes irregularities at the limit of the nonlocal length scale and dramatically improves convergence behavior. Finally, a novel approach for modeling ductile failure has been developed, motivated by the desire to apply coupled local-nonlocal models to a wide variety of materials, including ductile metals, which have received minimal attention in the peridynamic literature. Software implementation of the partial-stress coupling strategy, the position-aware peridynamic constitutive models, and the strategies for improving the convergence behavior of peridynamic models was completed within the Peridigm and Albany codes, developed at Sandia National Laboratories and made publicly available under the open-source 3-clause BSD license.

Stent Fracture Predictions With Peridynamics

“…Deformation and fracture dynamics of the stent made from a 7075-T651 aluminum alloy were performed. A fitting coefficient of 1.9x10 3 and a fitting degree of 2.8 required for computing the remaining life in Equation (2) was obtained by developing an analytical fit to the strain ratio versus cycle dependence reported in [9]. The obtained fit is shown in Figure 2.…”

“…Displacements rather than displacement derivatives are used in the peridynamic governing equations, which provide ample advantages to peridynamics over the FEM in the case of complex materials with heterogeneities and discontinuities. Specifically, the peridynamic equation of deformation is given by [3] ,…”

A review of Local-to-Nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics

“…A basic desired property of a LtN coupling method is patch-test consistency, which is established when such a method passes the so-called patch test or consistency test [72,76,84]. The main idea is as follows: if for a certain class of problems the local and nonlocal solutions, u l and u nl , respectively, coincide, then "patching" the two problems by coupling the corresponding models should still return the same problem solution.…”

An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems

“…In recent years, there has been great interest in using nonlocal integro-differential equations (IDEs) as a means to describe physical systems, due to their natural ability to describe physical phenomena at small scales and their reduced regularity requirements which lead to greater flexibility [3, 9, 15-17, 20, 21, 25, 26, 29, 31, 34-36, 42, 47, 48, 55, 58, 60, 69, 70]. In particular, nonlocal problems with Neumann-type boundary constraints have received particular attention [1,7,8,18,19,23,27,28,30,32,39,41,52,53,57,61,69] due to their prevalence in describing problems related to: interfaces [2], free boundaries, and multiscale/multiphysics coupling problems [5,6,43,59,68]. Unlike classical PDE models, in the nonlocal IDEs the boundary conditions must be defined on a region with non-zero volume outside the surface [19,28,61], in contrast to more traditional engineering scenarios where boundary conditions are typically imposed on a sharp co-dimension one surface.…”