An In-depth Investigation of Bimaterial Interface Modeling Using Ordinary State-based Peridynamics

Nguyen, Huy Anh; Wang, Hanlin; Tanaka, Satoyuki; Oterkus, Selda; Öterkuş, Erkan

doi:10.1007/s42102-021-00058-x

Cited by 23 publications

(7 citation statements)

References 66 publications

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“…We note that in some studies the harmonic mean formulation is employed for the averaged fracture energy (see[47] and references therein), which would make the interfacial bonds relatively weaker than what we proposed here. However, as studied in[90], in bimaterial problems the interfacial bond strength depends on the interfacial adhesion strength, which should be provided by experiments.…”

mentioning

confidence: 84%

“…Specifically, we consider the interaction between x and y as a series of two springs connecting the two points, and then the equivalent total spring constant will be the harmonic mean of the two spring constants [47,51,87]:…”

Section: Deterministic Peridynamics Problem With Heterogeneous Materi...mentioning

confidence: 99%

“…In particular, we employ the linear peridynamic solid (LPS) model [44] as a prototypical state-based model appropriate for brittle fracture, and propose a heterogeneous LPS formulation where twopoint function formulations are used to describe the heterogeneous material properties. Although such an averaged two-point function formulation were developed for nonlocal diffusion [45,46] and peridynamics [47][48][49][50][51] models, we have for the first time provided rigorous mathematical analysis for the well-posedness of this formulation in a heterogeneous LPS model. Furthermore, an important feature of peridynamics is that when classical continuum models still apply, peridynamics revert back to classical continuum models as its horizon size δ → 0.…”

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confidence: 99%

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A Meshfree Peridynamic Model for Brittle Fracture in Randomly Heterogeneous Materials

Fan¹,

You²,

Tian³

et al. 2022

Preprint

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In this work we aim to develop a unified mathematical framework and a reliable computational approach to model the brittle fracture in heterogeneous materials with variability in material microstructures, and to provide statistic metrics for quantities of interest, such as the fracture toughness. To depict the material responses and naturally describe the nucleation and growth of fractures, we consider the peridynamics model.In particular, a stochastic state-based peridynamic model is developed, where the micromechanical parameters are modeled by a finite-dimensional random vector, or a combination of random variables truncating the Karhunen-Loève decomposition or the principle component analysis (PCA). To solve this stochastic peridynamic problem, probabilistic collocation method (PCM) is employed to sample the random field representing the micromechanical parameters. For each sample, the deterministic peridynamic problem is discretized with an optimization-based meshfree quadrature rule. We present rigorous analysis for the proposed scheme and demonstrate its convergence for a number of benchmark problems, showing that it sustains the asymptotic compatibility spatially and achieves an algebraic or sub-exponential convergence rate in the random space as the number of collocation points grows. Finally, to validate the applicability of this approach on real-world fracture problems, we consider the problem of crystallization toughening in glass-ceramic materials, in which the material at the microstructural scale contains both amorphous glass and crystalline phases. The proposed stochastic peridynamic solver is employed to capture the crack initiation and growth for glass-ceramics with different crystal volume fractions, and the averaged fracture toughness are calculated. The numerical estimates of fracture toughness show good consistency with experimental measurements.

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confidence: 84%

Section: Deterministic Peridynamics Problem With Heterogeneous Materi...mentioning

confidence: 99%

mentioning

confidence: 99%

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A Meshfree Peridynamic Model for Brittle Fracture in Randomly Heterogeneous Materials

Fan¹,

You²,

Tian³

et al. 2022

Preprint

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“…Recent work on bi-material interface modeling has also concluded that the harmonic mean of properties yields the best solution compared to FEM. 54 Since effective macroscale properties, such as fracture toughness, are strongly dependent on the microstructure, it is important to incorporate the stochastic nature of the microstructure. Computational costs can limit the feasible size of the microstructural representative volume element; the stochastic nature of the material can be considered by simulating multiple realizations of the material at each crystal volume fraction of interest.…”

Section: Glass Ceramicmentioning

confidence: 99%

“…For the current work, a harmonic mean of both the stiffness and fracture properties are specified to reflect these observations. Recent work on bi‐material interface modeling has also concluded that the harmonic mean of properties yields the best solution compared to FEM 54 …”

Section: Computational Detailsmentioning

confidence: 99%

Investigation of microscale fracture mechanisms in glass–ceramics using peridynamics simulations

et al. 2022

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Glass–ceramics (GCs), obtained by controlled crystallization of a specially formulated precursor glass, are interesting materials that show great promise in obtaining superior properties compared to those of the precursor glass. Controlled crystallization enables creation of a microstructure with multiple phases which impacts macroscale properties in interesting ways. The present work develops microstructure‐scale computational models using the theory of peridynamics to investigate the increase in fracture toughness of GCs compared to traditional glass. Computational modeling is a promising tool to probe microstructural mechanics, but such studies in the literature are scarce. In this work, the theory of peridynamics, a non‐local theory of continuum mechanics, is applied to simulate crack propagation through microstructural realizations of a model lithium‐disilicate glass–ceramic. The crystalline and glassy phases within the microstructure are explicitly considered, with the size and shape of crystals inspired by experimental data. Multiple toughening mechanisms are revealed, which are functions of crystallinity and morphology, and the impact on fracture toughness is demonstrated. Crack path tortuosity is studied, and it is found that an optimum level of crack path tortuosity can be obtained in the range of 0.6–0.8 crystallinity. Numerical results are shown to agree well with previously published experimental and modeling results.

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A nonlocal interface approach to peridynamics exemplified by continuum‐kinematics‐inspired peridynamics

Laurien

Javili

Steinmann

2022

Numerical Meth Engineering

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In this contribution, we present a novel approach on how to treat material interfaces in nonlocal models based on peridynamics (PD) and in particular continuum-kinematics-inspired peridynamics (CPD), a novel variationally consistent peridynamic formulation. Our method relies on a nonlocal interface where the material subdomains overlap. Within this region, a kinematic coupling of the two constituents is enforced. The contact is purely geometrical as interaction forces act only between points of the same material. We provide a detailed description of the computational implementation within the framework of CPD, that is in principle applicable to all formulations of PD. A variety of numerical examples for modeling bimaterial interfaces illustrate the utility of the technique for both two-dimensional and three-dimensional problems, including examples at large deformations. Our model approaches a local model when the nonlocality parameter, the horizon size, is decreased. The proposed methodology offers a viable alternative to previous approaches in PD, which are essentially imposing mixture rules for the interfacial material parameters.

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An In-depth Investigation of Bimaterial Interface Modeling Using Ordinary State-based Peridynamics

Cited by 23 publications

References 66 publications

A Meshfree Peridynamic Model for Brittle Fracture in Randomly Heterogeneous Materials

A Meshfree Peridynamic Model for Brittle Fracture in Randomly Heterogeneous Materials

Investigation of microscale fracture mechanisms in glass–ceramics using peridynamics simulations

A nonlocal interface approach to peridynamics exemplified by continuum‐kinematics‐inspired peridynamics

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