Coupling three‐dimensional peridynamics and high‐order one‐dimensional finite elements based on local elasticity for the linear static analysis of solid beams and thin‐walled reinforced structures

Pagani, Alfonso; Carrera, Erasmo

doi:10.1002/nme.6510

Cited by 32 publications

(17 citation statements)

References 36 publications

(45 reference statements)

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“…These analyses show that the solution is not affected by the theory of the FE model employed. This conclusion was already proven in Reference 27 , where simple linear static analysis were performed.…”

Section: Numerical Resultssupporting

confidence: 59%

“…The cross‐section is discretized with a single L9 element. This discretization has been chosen because it demonstrated to be the most accurate for a similar traction problem, investigated in Reference 27 . Nevertheless, TE models are also employed in order to study the influence of the 1D theory on the model's accuracy.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…This coupling has been realized between three‐dimensional PD grids and higher‐order one‐dimensional finite elements through the well‐known CUF. This method has proven to have a very high accuracy along with a significant reduction of the computational cost, 27 allowing to deal with complex and representative problems. The failure algorithm introduced in the model is based on the so‐called “bond stretch criterion.” 37 First, a pre‐cracked bar under traction has been investigated.…”

Section: Discussionmentioning

confidence: 99%

“…For further information about the proposed coupling model, interested readers can refer to Reference 27 . This method is valid for 1D finite elements of any order.…”

Section: High Order 1d Finite Elementsmentioning

confidence: 99%

“…Note that most of the coupling methods in the literature involve dimensionally consistent domains: 1D FEM with 1D PD grid, 2D with 2D, and 3D with 3D. The work by Pagani and Carrera 27 proposed a coupling method between refined 1D FEs and 3D PD grids, based on Lagrange multipliers. This model allowed to deal with complex 3D problems while reducing the computational cost of the analysis.…”

Section: Introductionmentioning

confidence: 99%

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Quasi‐static fracture analysis by coupled three‐dimensional peridynamics and high order one‐dimensional finite elements based on local elasticity

Pagani

Enea

Carrera

2021

Numerical Meth Engineering

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This work investigates quasi-static crack propagation in specimens made of brittle materials by combining local and non-local elasticity models. The portion of the domain where the failure initiates and then propagates is modeled via three-dimensional bond-based peridynamics (PD). On the other hand, the remaining regions of the structure are analyzed with high order one-dimensional finite elements based on the Carrera unified formulation (CUF). The coupling between the two zones is realized by using Lagrange multipliers. Static solutions of different fracture problems are provided by a sequential linear analysis. The proposed approach is demonstrated to combine the advantages of the CUF-based classical continuum mechanics models and PD by providing, in an efficient manner, both the failure load and the shape of the crack pattern, even for three-dimensional problems.

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Section: Numerical Resultssupporting

confidence: 59%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…For further information about the proposed coupling model, interested readers can refer to Reference 27 . This method is valid for 1D finite elements of any order.…”

Section: High Order 1d Finite Elementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quasi‐static fracture analysis by coupled three‐dimensional peridynamics and high order one‐dimensional finite elements based on local elasticity

Pagani

Enea

Carrera

2021

Numerical Meth Engineering

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An improved coupling of 3D state‐based peridynamics with high‐order 1D finite elements to reduce spurious effects at interfaces

Scabbia

Enea

2023

Numerical Meth Engineering

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Peridynamics (PD) is a nonlocal continuum theory capable of handling fracture mechanisms with ease. However, its use involves high computational costs. On the other hand, Carrera Unified Formulation (CUF) allows one to use one‐dimensional high‐order finite elements, resulting in excellent accuracy while improving computational efficiency. To address the high computational cost of solving fracture problems, a coupling technique between these two theories is necessary. Various approaches have been proposed to couple peridynamic grids with finite element meshes in the literature. However, most of these approaches are affected by arbitrary choices of blending functions and tuning parameters or exhibit spurious effects at the interfaces. To overcome these issues, we propose a simple coupling technique based on overlapping PD/CUF regions and continuity of the displacement field at the interfaces. This approach is verified through static analysis of classical beams and thin‐walled structures with applications in the aerospace industry.

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A computational approach to integrate three-dimensional peridynamics and two-dimensional higher-order classical elasticity theory for fracture analysis

Zhang,

Enea,

Pagani

et al. 2024

Engineering with Computers

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As a nonlocal alternative of classical continuum theory, peridynamics (PD) is mathematically compatible to discontinuities, making it particularly attractive for failure prediction. The PD theory on the other side can be computationally demanding due to its nonlocal interactions. A coupling between PD and refined higher-order finite element method (FEM) integrates their salient features. The present study proposes a computational approach to couple three-dimensional peridynamics with two-dimensional higher-order finite elements based on classical elasticity. The bond-based PD modeling is considered in a region where damage might appear while refined finite element modeling is used for the remaining region. The refined finite elements employed in this study are based on the 2D Carrera Unified Formulation (CUF), which provides 3D-like accuracy with optimized computational efficiency. The coupling between PD and FEM is achieved through the Lagrange multiplier method which permits physical consistency and compatibility at the interface domain. An adaptive convergence check algorithm is also proposed to achieve predetermined accuracy in the solution with minimum computational effort. Simulations of quasi-static tension tests, wedge splitting tests and L-plate cracking tests are carried out for verification. In-depth analysis shows that the present approach can reproduce the linear deformation, material degradation and crack propagation in an effective way.

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Coupling three‐dimensional peridynamics and high‐order one‐dimensional finite elements based on local elasticity for the linear static analysis of solid beams and thin‐walled reinforced structures

Cited by 32 publications

References 36 publications

Quasi‐static fracture analysis by coupled three‐dimensional peridynamics and high order one‐dimensional finite elements based on local elasticity

Quasi‐static fracture analysis by coupled three‐dimensional peridynamics and high order one‐dimensional finite elements based on local elasticity

An improved coupling of 3D state‐based peridynamics with high‐order 1D finite elements to reduce spurious effects at interfaces

A computational approach to integrate three-dimensional peridynamics and two-dimensional higher-order classical elasticity theory for fracture analysis

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