Generalization of the ordinary state-based peridynamic model for isotropic linear viscoelasticity

Delorme, Rolland; Tabiai, Ilyass; Lebel, Louis Laberge; Lévesque, Martin

doi:10.1007/s11043-017-9342-3

Cited by 24 publications

(15 citation statements)

References 32 publications

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“…energy density Ψ to the classical strain energy density for an arbitrary homogeneous deformation under the infinitesimal strain theory [50]. One finds [20,36,37,45]…”

Section: Resultsmentioning

confidence: 99%

“…The states and their properties are presented in details in App. A of [20]. The main definitions are recalled here.…”

Section: State-based Theorymentioning

confidence: 99%

“…App. B of [20] presents the three PD constitutive models which are the bond-based, the ordinary state-based and non-ordinary state-based theories. In the sequel, only the ordinary state-based approach is used since isotropic linearly elastic materials are considered.…”

Section: State-based Theorymentioning

confidence: 99%

“…where α s and α d are the PD parameters [20]. They are calibrated to the classical isotropic elastic material properties (K and G, the bulk and shear modulus) by equating the PD strain…”

Section: Compliance With Ethical Standardsmentioning

confidence: 99%

“…Many authors have attempted to clarify the horizon concept [7,8] since this is a major PD parameter. In addition, well-known and accepted constitutive theories and meth-ods derived within classical continuum mechanics have yet to be transposed into the PD framework [6,20].…”

Section: Introductionmentioning

confidence: 99%

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Extracting Constitutive Mechanical Parameters in Linear Elasticity Using the Virtual Fields Method Within the Ordinary State-Based Peridynamic Framework

Delorme

Diehl

Tabiai

et al. 2020

J Peridyn Nonlocal Model

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This paper implements the virtual fields method within the ordinary state-based peridynamic framework to identify material properties. The key equations derived in this approach are based on the principle of virtual works written under the ordinary state-based peridynamic formalism for two-dimensional isotropic linear elasticity. In-house codes including a minimization process have also been developed to implement the method. A threepoint bending test and two independent virtual fields arbitrarily chosen are used as a case study throughout the paper. The numerical validation of the virtual fields method has been performed on the case study by simulating the displacement field by finite element analysis. This field has been used to extract the elastic material properties and compared them with those used as input in the finite element model, showing the robustness of the approach. Noise analysis and the effect of the missing displacement fields on the specimen's edges to simulate digital image correlation limitations have also been studied in the numerical part. This work focuses on pre-damage properties to demonstrate the feasibility of the method and provides a new tool for using full-field measurements within peridynamics with a reduced calculation time as there is no need to compute the displacement field. Future works will deal with damage properties which is the main strength of peridynamics.

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“…energy density Ψ to the classical strain energy density for an arbitrary homogeneous deformation under the infinitesimal strain theory [50]. One finds [20,36,37,45]…”

Section: Resultsmentioning

confidence: 99%

“…The states and their properties are presented in details in App. A of [20]. The main definitions are recalled here.…”

Section: State-based Theorymentioning

confidence: 99%

Section: State-based Theorymentioning

confidence: 99%

“…where α s and α d are the PD parameters [20]. They are calibrated to the classical isotropic elastic material properties (K and G, the bulk and shear modulus) by equating the PD strain…”

Section: Compliance With Ethical Standardsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Extracting Constitutive Mechanical Parameters in Linear Elasticity Using the Virtual Fields Method Within the Ordinary State-Based Peridynamic Framework

Delorme

Diehl

Tabiai

et al. 2020

J Peridyn Nonlocal Model

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A nonlocal energy‐informed neural network for isotropic elastic solids with cracks under thermomechanical loads

Zhou

2023

Numerical Meth Engineering

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In this paper, a nonlocal energy‐informed neural network is proposed to characterize the deformation behaviors of elastic solids with cracks subjected to thermomechanical loads in the framework of ordinary state‐based peridynamics. Based on principle of virtual work, a nonlocal energy approach is developed to recast the solution to peridynamic equilibrium equation as a problem of minimizing the potential energy of the system, which automatically satisfies the traction‐free boundary conditions. Meanwhile, the energy representation of physical system can be treated as the loss function for machine learning methods. Therefore, a nonlocal energy‐informed neural network is constructed to approximate the solution of the system. A distinct advantage of the proposed neural network is that the strain energy is expressed in terms of spatial integration instead of spatial derivatives, which avoids the invalidation of automatic differentiation at the crack surfaces in original physics‐informed neural networks. To demonstrate the convergence and accuracy of the proposed neural network, a series of problems in solid and fracture mechanics are conducted, and compared with results from analytical solutions or classical numerical methods. Additionally, for elastic material containing initial cracks, displacement extrapolation method is encoded into the proposed neural network to evaluate the static stress intensity factor.

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Reducing the entry barrier for users and developers of peridynamic high performance computing

Hesse,

Willberg,

Pernatii

2024

Proc Appl Math and Mech

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Over the past two decades, Peridynamics (PD) research has exhibited remarkable diversity, with contributions spanning more than 180 journals and involving over 1000 researchers. Despite its broad applicability, a persistent challenge remains—how to foster widespread adoption. In the engineering domain, classical continuum mechanics, predominantly facilitated by the finite element method, enjoys extensive utilization, supported by a plethora of commercial and open‐source software tools. PD simulation tools often find themselves competing with these well‐established counterparts. In research, custom codes tailored for specific applications are frequently created and applied, with little consideration for their future reuse or third‐party utilization. The complexity is further exacerbated in High‐performance computing (HPC) applications, where a deep understanding of solvers, parallel computing, and PD is imperative for a successful software development. Given the constraints of a typical doctoral thesis, large‐scale problems are often left unexplored, and research tends to be confined to simplistic geometries. This paper aims to elucidate various pathways for the seamless integration and utilization of a PD framework. We will showcase examples that illustrate how the barriers for both users and developers can be significantly lowered, ultimately propelling PD simulation tools to a higher standard of maturity in the medium term.

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Generalization of the ordinary state-based peridynamic model for isotropic linear viscoelasticity

Cited by 24 publications

References 32 publications

Extracting Constitutive Mechanical Parameters in Linear Elasticity Using the Virtual Fields Method Within the Ordinary State-Based Peridynamic Framework

Extracting Constitutive Mechanical Parameters in Linear Elasticity Using the Virtual Fields Method Within the Ordinary State-Based Peridynamic Framework

A nonlocal energy‐informed neural network for isotropic elastic solids with cracks under thermomechanical loads

Reducing the entry barrier for users and developers of peridynamic high performance computing

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