The original peridynamics formulation uses a constant nonlocal region, the horizon, over the entire domain. We propose here adaptive refinement algorithms for the bond-based peridynamic model for solving statics problems in two dimensions that involve a variable horizon size. Adaptive refinement is an essential ingredient in concurrent multiscale modeling, and in peridynamics changing the horizon is directly related to multiscale modeling. We do not use any special conditions for the “coupling” of the large and small horizon regions, in contrast with other multiscale coupling methods like atomistic-to-continuum coupling, which require special conditions at the interface to eliminate ghost forces in equilibrium problems. We formulate, and implement in two dimensions, the peridynamic theory with a variable horizon size and we show convergence results (to the solutions of problems solved via the classical partial differential equations theories of solid mechanics in the limit of the horizon going to zero) for a number of test cases. Our refinement is triggered by the value of the nonlocal strain energy density. We apply the boundary conditions in a manner similar to the way these conditions are enforced in, for example, the finite-element method, only on the nodes on the boundary. This, in addition to the peridynamic material being effectively “softer” near the boundary (the so-called “skin effect”) leads to strain energy concentration zones on the loaded boundaries. Because of this, refinement is also triggered around the loaded boundaries, in contrast to what happens in, for example, adaptive finite-element methods.

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Adaptive refinement and multiscalemodeling in 2d peridynamics

Peridynamic investigation on thermal fracturing behavior of ceramic nuclear fuel pellets under power cycles

An adaptive thermo-mechanical peridynamic model for fracture analysis in ceramics

A coupled contact heat transfer and thermal cracking model for discontinuous and granular media

A refined thermo-mechanical fully coupled peridynamics with application to concrete cracking

The effects of moderate intensity ‘hot’ or ‘cold’ shock in brittle solids have been extensively studied, while much less is known about thermal shock response during large temperature variations. In this study, a combined finite element – peridynamics numerical procedure is proposed for the simulation of cracking in ceramic materials, undergoing severe thermal shock. Initially, Finite Element nonlinear heat transfer analysis is conducted. The effects of surface convection and radiation heat exchange are also included. Subsequently, the interpolated temperature field is used to formulate a varying temperature induced action for a bond-based peridynamics model. The present model, which is weakly coupled, is found to reproduce accurately previous numerical and experimental results regarding the case of a ‘cold’ shock. Through several numerical experiments it is established that ‘cold’ and ‘hot’ shock conditions give rise to different failure modes and that large temperature variations lead to intensified damage evolution.

https://bura.brunel.ac.uk/bitstream/2438/18296/1/FullText.pdf

Simulation of thermal shock cracking in ceramics using bond-based peridynamics and FEM

A peridynamics (PD)–extended finite element method (XFEM) coupling strategy for brittle fracture simulation is presented. The proposed methodology combines a small PD patch, restricted near the crack tip area, with the XFEM that captures the crack body geometry outside the domain of the localised PD grid. The feasibility and effectiveness of the proposed method on a Mode I crack opening problem is examined. The study focuses on comparisons of the J integral values between the new coupling strategy, full PD grids and the commercial software Abaqus. It is demonstrated that the proposed approach outperforms full PD grids in terms of computational resources required to obtain a certain degree of accuracy. This finding promises significant computational savings when crack propagation problems are considered, as the efficiency of FEM and XFEM is combined with the inherent ability of PD to simulate fracture.

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Coupling XFEM and peridynamics for brittle fracture simulation—part I: feasibility and effectiveness

Digital clone testing platform for the assessment of SHM systems under uncertainty

/pdf/digital-clone-testing-platform-for-the-assessment-of-shm-3awnsmkc.pdf

Correspondence Theodosios K. Papathanasiou, Department of Civil and Environmental Engineering, Brunel University London, Uxbridge UB8 3PH, UK. Email: theodosios.papathanasiou@brunel.ac.uk 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.

/pdf/wave-reflection-and-cut-off-frequencies-in-coupled-fe-auy4x0srsr.pdf

Ilias N. Giannakeas

Papers

Simulation of thermal shock cracking in ceramics using bond-based peridynamics and FEM

Coupling XFEM and peridynamics for brittle fracture simulation—part I: feasibility and effectiveness

Digital clone testing platform for the assessment of SHM systems under uncertainty

Digital clone testing platform for the assessment of SHM systems under uncertainty

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