Coupling of FEM meshes with Peridynamic grids

Summary Reflections are typically observed when pulses propagate across interfaces. Accordingly, spurious reflections might occur at the interfaces between different models used to simulate the same medium. Examples of such coupled models include classical continuum descriptions with molecular dynamics or peridynamic (PD) grids. In this work, three different coupling approaches are implemented to couple bond‐based PDs with finite element (FE) solvers for solid mechanics. It is observed that incorporation of an overlapping zone, over which the coupling between FE and PD occurs, can lead to minimization of the reflected energy compared to a standard force coupling at the FE domain/PD grid interface. However, coupling with other existing methodologies, like the addition of ghost particles, achieves comparable accuracy at lower computational cost. Furthermore, the prudent selection of the discretization parameters is of pivotal importance as they control the high frequency cut‐off limit. Mismatch between the cut‐off frequencies of the different descriptions can lead to unrealistic results.

Section: Coupling Approachesmentioning

confidence: 91%

Section: Coupling Approachesmentioning

confidence: 97%

Section: Coupling Approachesmentioning

confidence: 99%

Section: Reflection‐transmission In a 1d Continuum‐pd Barmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Wave reflection and cut‐off frequencies in coupled FE‐peridynamic grids

Giannakeas

Papathanasiou

Bahai

2019

A continuous‐discontinuous model for crack branching

Tamayo-Mas

Feliu‐Fabà

Casado‐Antolin

et al. 2019

Summary A new continuous‐discontinuous model for fracture that accounts for crack branching in a natural manner is presented. It combines a gradient‐enhanced damage model based on nonlocal displacements to describe diffuse cracks and the extended finite element method (X‐FEM) for sharp cracks. Its most distinct feature is a global crack tracking strategy based on the geometrical notion of medial axis: the sharp crack propagates following the direction dictated by the medial axis of a damage isoline. This means that, if the damage field branches, the medial axis automatically detects this bifurcation, and a branching sharp crack is thus easily obtained. In contrast to other existing models, no special crack‐tip criteria are required to trigger branching. Complex crack patterns may also be described with this approach, since the X‐FEM enrichment of the displacement field can be recursively applied by adding one extra term at each branching event. The proposed approach is also equipped with a crack‐fluid pressure, a relevant feature in applications such as hydraulic fracturing or leakage‐related events. The capabilities of the model to handle propagation and branching of cracks are illustrated by means of different two‐dimensional numerical examples.

An implicit dual‐based approach to couple peridynamics with classical continuum mechanics

Bie

She

et al. 2019

Summary A general local/nonlocal implicit coupling technique called the dual‐based approach is proposed to couple peridynamics (PD) with classical continuum mechanics. In the present method, physical information is transmitted mutually from local to nonlocal regions through the coupling elements; no transition region is introduced. For different mesh discretizations, two coupling methods are achieved with simplicity and effectivity. To obtain the stiffness matrix of the coupled model, without loss of generality, the implicit dual‐horizon ordinary state‐based peridynamic model is proposed, in which the linearization of dual‐horizon ordinary state‐based PD is derived and the dual assembly algorithm of the peridynamic stiffness matrix is developed. It will be seen that the implicit dual‐based coupling approach provides a new implicit coupling method that is easy to implement and makes full use of the internal connection between PD and classical continuum mechanics. Several numerical examples involving static crack propagation are investigated, and the satisfactory results show both quantitative and qualitative agreement with either the analytic solution or the available experiment.