Simulating concrete failure using the Microplane (M7) constitutive model in correspondence-based peridynamics: Validation for classical fracture tests and extension to discrete fracture

Bazilevs, Yuri; Behzadinasab, Masoud; Foster, Janet

doi:10.1016/j.jmps.2022.104947

Cited by 19 publications

(6 citation statements)

References 65 publications

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“…Bond‐associated correspondence PD formulation from References 8,10 serves as a stabilization technique for the PD formulation presented in the previous section. Here, numerical quadrature of the Galerkin form is carried out using bonds .…”

Section: Continuum Solid and Its Pd Approximationmentioning

confidence: 99%

“…4 Several, mostly ad-hoc approaches were developed to mitigate these instabilities (see, e.g., References 5,6), including the more recently proposed bond-associated methods. [7][8][9][10] While bond-associated methods brought the necessary stability and accuracy to correspondence-based PD, they also came with additional computational costs. These costs emanate from having to carry out additional sums over the neighboring nodes and to store the internal variables (e.g., plastic strains) at bonds for history-dependent materials.…”

Section: Introductionmentioning

confidence: 99%

“…However, correspondence‐based PD approaches were plagued by numerical instabilities emanating from spurious low‐energy modes of the internal force operator leading to non‐convergent results, especially for non‐uniform meshes 4 . Several, mostly ad‐hoc approaches were developed to mitigate these instabilities (see, e.g., References 5,6), including the more recently proposed bond‐associated methods 7–10 . While bond‐associated methods brought the necessary stability and accuracy to correspondence‐based PD, they also came with additional computational costs.…”

Section: Introductionmentioning

confidence: 99%

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A stable formulation of correspondence‐based peridynamics with a computational structure of a method using nodal integration

Wang,

Behzadinasab,

et al. 2024

Numerical Meth Engineering

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SummaryIn this paper, we lay out a variational framework for correspondence‐based peridynamic (PD) formulations of solid mechanics. Using the framework, we address the numerical instabilities of the original version of correspondence‐based PD by developing a natural stabilization technique that avoids costly bond‐associated approaches and retains the structure of a method with nodal integration. Accuracy, robustness, and efficiency of the proposed naturally stabilized correspondence‐based PD are demonstrated on several computational test cases ranging from linear elastostatics to large deformation elasto‐plasticity. The computational methodology developed is particularly effective for handling materials undergoing nearly‐incompressible deformations.

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Section: Continuum Solid and Its Pd Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A stable formulation of correspondence‐based peridynamics with a computational structure of a method using nodal integration

Wang,

Behzadinasab,

et al. 2024

Numerical Meth Engineering

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“…By employing the nonlocal deformation gradient, it becomes possible to calculate classical strain and stress measures for the entire nonlocal domain. More recently, this approach has been extended even to the bond level [3].…”

Section: Introductionmentioning

confidence: 99%

Why develop twice? Integration of continuum mechanical material models in Peridynamics

Willberg,

Hesse,

Pernatii

et al. 2024

Proc Appl Math and Mech

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To harvest the full potential of the peridynamic approach, the state‐of‐the‐art material models should be usable without redeveloping or reimplementing them from classical continuum mechanics theory. User materials (UMAT) in finite element codes allow the researchers or engineers to apply their own material routines. Simple interfaces are specified to allow the utilization of material behaviors in software. In order to use these already existing and often validated models with Peridynamics, a UMAT interface is presented. It allows the simplified use of already existing material routines in the peridynamic framework Peridigm. The interface is based on the finite element (FE) software Abaqus UMAT definition and allows the integration of Fortran routines directly into Peridigm. In addition, the same material model implementations are applicable in finite element applications as well as peridynamic simulations. In the presentation, the interface is presented and various material models are utilized and compared between Peridynamics and FE methods. The effect of the horizon and nonlocal boundaries are analyzed and discussed.

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“…In the literature two main PD streams can be found: the native-based modelling approach and the correspondence-based modelling approach [25]. The first approach consists of developing new constitutive models, tailored directly for PD.…”

Section: Introductionmentioning

confidence: 99%

A peridynamics approach to flexible multibody dynamics for fracture analysis of mechanical systems

Vieira,

Pagaimo,

Magalhães

et al. 2023

Multibody Syst Dyn

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The classical theory of continuum mechanics is formulated using partial differential equations (PDEs) that fail to describe structural discontinuities, such as cracks. This limitation motivated the development of peridynamics, reformulating the classical PDEs into integral-differential equations. In this theory, each material point interacts with its neighbours inside a characteristic length-scale through bond-interaction forces. However, while peridynamics can simulate complex multi-physics phenomena, its integration in the study of mechanical systems is still limited. This work presents a methodology that incorporates a peridynamics formulation into a planar multibody dynamics (MBD) formulation to allow the integration of flexible structures described by peridynamics into mechanical systems. A flexible body is described by a collection of point masses, in analogy with the meshless collocation scheme commonly used for peridynamics discretisations. Each point mass interacts with other point masses through nonlinear forces governed by a bond-based peridynamics (BBPD) formulation. The virtual bodies methodology enables the definition of kinematic joints connecting the flexible body with the neighbouring bodies. The implementation of the methodology proposed is illustrated using various mechanisms with different levels of complexity. Notched plates subjected to different loading conditions are compared with the results presented in the literature of the peridynamics field. The deformations of a flexible slider-crank mechanism compare well with the results obtained using a classical flexible MBD formulation. Additionally, three scenarios involving a rotating pendulum illustrate how the methodology proposed allows simulating impact scenarios. The results demonstrate how this methodology is capable to successfully simulate highly nonlinear phenomena, including crack propagation, in a multibody framework.

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Simulating concrete failure using the Microplane (M7) constitutive model in correspondence-based peridynamics: Validation for classical fracture tests and extension to discrete fracture

Cited by 19 publications

References 65 publications

A stable formulation of correspondence‐based peridynamics with a computational structure of a method using nodal integration

A stable formulation of correspondence‐based peridynamics with a computational structure of a method using nodal integration

Why develop twice? Integration of continuum mechanical material models in Peridynamics

A peridynamics approach to flexible multibody dynamics for fracture analysis of mechanical systems

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