Peridynamics has attractive features for solving several fracture mechanics problems. On the other hand, to ensure the accuracy, a great deal of particles (material points) is required. Introduction of variable horizon is an alternative approach by changing the horizon size over the problem domain. In the present study, we propose a novel variable horizon concept. It is known that undesired “ghost” force arises along the transition region of different horizons. In order to suppress the ghost force, the gradual variation of the horizon size over a certain region, called smoothing length, is introduced between the different scale particle distributions. Efficiency of the smoothed variable horizon peridynamics is demonstrated through several numerical studies employing the ordinary statebased peridynamics. As a basic case, a linear displacement field is considered. It is observed that the proposed approach significantly reduces the ghost forces along the interface of different spatial discretizations. Additionally, the dynamic stress intensity factors of stationary cracks are carefully examined. The path independence of the fracture parameters in the variable horizon peridynamics is ensured. Efficiency of the presented method is then discussed. It is monitored that introduction of the smoothing length concept significantly reduces the computational costs in the peridynamic modeling.
Last. Erkan Oterkus(University of Strathclyde)H-Index: 26
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Functionally graded materials are regarded as a special kind of composites capable of eliminating material interfaces and the delamination problems. Stress discontinuity can be avoided owing to smooth composition of the functionally graded ingredients. In this study, a recently emerged effective non-local continuum theory for solving fracture problems in solids and structures, peridynamics, is employed to simulate dynamic wave propagation as well as crack propagation in functionally graded mater...
Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54
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Abstract A meshfree approach for analyzing the fracture mechanics parameters in cracked curved shells is presented. The reproducing kernel (RK) meshfree method and mapping technique are employed to approximate cracked curvilinear surfaces and field variables. In order to model the crack segment, the meshfree discretization techniques are used. The stabilized conforming nodal integration (SCNI) and sub-domain stabilized conforming integration (SSCI) techniques are adopted to accurately integrate ...
Abstract Geometrically nonlinear analysis of flat, curved and folded shells under finite rotations is performed by enhanced six degrees of freedom (6-DOFs) meshfree formulation. Curvilinear surfaces are dealt with the concept of convected coordinates. Equilibrium equations are derived by total Lagrangian formulation with Green–Lagrange strain and Second Piola–Kirchhoff stress. Both shell geometry and its deformation are approximated by Reproducing Kernels (RKs). Transverse shear strains are cons...
Last. Erkan Oterkus(University of Strathclyde)H-Index: 26
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Dynamic fracture analysis for the crack arrest phenomenon is performed by ordinary state-based peridynamics formulation and discretization employing transition bond concept. Double cantilever beam specimen is chosen for our numerical evidence purpose. The analysis consists of two main phases namely, generation and application (prediction) phases. In the generation phase, the dynamic stress intensity factors of propagating and arrested cracks are estimated by the present formulation for given cra...
Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54
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Abstract Several numerical examples for cracked folded structures are analyzed to investigate the mixed-mode stress resultant intensity factors (SRIFs). The kinematic formulations of structures are derived by the first order shear deformation plate theory. A Galerkin meshfree six degrees of freedom (6DOFs) flat shell is employed, in which the reproducing kernel (RK) is used as the meshfree interpolant. A diffraction method, visibility criterion and enriched basis are introduced to model the thro...
Recently, Khodabakhshi et al. (Meccanica 51(12):3129–3147, 2016. https://doi.org/10.1007/s11012-016-0560-6) presented a new method (by the name GraFEA) capable of studying fracture based on edge breakage within a classical FEA scheme which combines the best features of FEA and bond-breakage methods in a single framework. In this study, an attempt is made to investigate the mesh dependency of GraFEA by a set of numerical examples, and it is shown that using a local fracture criterion for edge fai...
A coupling extended multiscale finite element and peridynamic method is developed for the quasi-static mechanical analysis of large-scale structures with crack propagation. Firstly, a novel incremental peridynamic (PD) formulation based on the ordinary state-based PD model is derived utilizing the Taylor expansion technique. To combine the high computational efficiency of the EMsFEM and advantages of dealing with discontinuous problems of the PD, a coupling strategy based on the numerical base f...
Abstract Peridynamics is a nonlocal reformulation of solid mechanics which can reproduce the solution of classical continuum mechanics as its horizon approaches zero. Taking this idea into consideration, we proposed a new coupling approach between meshfree peridynamics and finite element method. An intermediate variable horizon element called “morakkab” is introduced to transfer force and momentum between peridynamic and FEM regions. In the original peridynamic formulation, artificial ghost forc...
Abstract The recently developed ordinary state-based peridynamics (OSPD) is further enhanced to study elastodynamic propagating crack based on the dynamic stress intensity factors (DSIFs). The displacement discontinuity such as a crack surface is represented by a bond-failure. Variations of the mixed-mode DSIFs with time are evaluated by the interaction integral method for the dynamic crack propagation. In terms of OSPD fracture modeling, numerical oscillation of DSIFs becomes a critical issue d...
The forces in the ‘arms’ joining the particles in a peridynamic analysis depend upon the state of stress in the equivalent continuum and the orientation, length and density of the arms. Short and long arms carry less force than medium length arms as controlled by the weighting kernel. We introduce an intermediate step of imagining a mat of long fibres in which the fibre forces only depend upon the stress, the fibre orientation and the length of fibres per unit volume without the added complexity...