A peridynamic failure analysis of fiber-reinforced composite laminates using finite element discontinuous Galerkin approximations

Ren, Bo; Wu, C. T.; Seleson, Pablo; Zeng, Deliang; Lyu, Dandan

doi:10.1007/s10704-018-0317-4

Cited by 27 publications

(28 citation statements)

References 34 publications

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“…In small-strain formulation, the elementary rotation matrices shown in Eq. (3.19) are given by X (1,1) = 1, X ( [2,3,4], [2,3,4]) (α) = r p (α), X ( [5,6], [5,6] 4,9], [4,9]) (β) = X f ( [5,8], [5,8] for an arbitrary angle θ.…”

Section: Appendix a Elementary Rotation Matricesmentioning

confidence: 99%

“…) (α) = r v (α); (A.1) Y (2,2) = 1, Y ([1,3,5],[1,3,5]) (β) = r p (−β), Y ([4,6],[4,6]) (β) = r v (−β); Z (3,3) = 1, Z ([1,2,6],[1,2,6]) (γ) = r p (γ), Z ([4,5],[4,5]) (γ) = r v (γ).The in-plane and output-plane rotation matrices r p and r v for an arbitrary angle θ are defined in Mandel notation asr p (θ) =   − sin 2 θ    , r v (θ) = cos θ − sin θ sin θ cos θ . (A.2)In finite-strain formulation, the elementary rotation matrices shown in Eq.…”

mentioning

confidence: 99%

“…(A.2)In finite-strain formulation, the elementary rotation matrices shown in Eq. (3.41 are given byX f (1,1) = 1, X f ([2,3,4,5],[2,3,4,5]) (α) = r pf (α), X f ([6,8],[6,8]) (α) = X f ([7,9],[7,9]) (α) = r vf (α); (A.3) Y f (2,2) = 1, X f ([1,3,6,7],[1,3,6,7]) (β) = r pf (−β), Y f ([…”

mentioning

confidence: 99%

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Exploring the 3D architectures of deep material network in data-driven multiscale mechanics

Liu

2019

Journal of the Mechanics and Physics of Solids

147

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This paper extends the deep material network (DMN) proposed by Liu et al. (2019) [1] to tackle general 3-dimensional (3D) problems with arbitrary material and geometric nonlinearities. It discovers a new way of describing multiscale heterogeneous materials by a multi-layer network structure and mechanistic building blocks. The data-driven framework of DMN is discussed in detail about the offline training and online extrapolation stages. Analytical solutions of the 3D building block with a two-layer structure in both small-and finite-strain formulations are derived based on interfacial equilibrium conditions and kinematic constraints. With linear elastic data generated by direct numerical simulations on a representative volume element (RVE), the network can be effectively trained in the offline stage using stochastic gradient descent and advanced model compression algorithms. Efficiency and accuracy of DMN on addressing the long-standing 3D RVE challenges with complex morphologies and material laws are validated through numerical experiments, including 1) hyperelastic particle-reinforced rubber composite with Mullins effect; 2) polycrystalline materials with rate-dependent crystal plasticity; 3) carbon fiber reinforced polymer (CFRP) composites with fiber anisotropic elasticity and matrix plasticity. In particular, we demonstrate a threescale homogenization procedure of CFRP system by concatenating the microscale and mesoscale material networks. The complete learning and extrapolation procedures of DMN establish a reliable data-driven framework for multiscale material modeling and design.anisotropic responses, and may require burdensome calibration to find the model parameters. As a result, homogenization based on the concept of representative volume element (RVE) [11] has become an important approach to model multiscale materials [12]. Many analytical methods have been proposed, which adopt some micromechanics assumptions to simplify the full-field RVE problem, such as Hashin-Shtrikman bounds [13,14], the Mori-Tanaka method [15] and self-consistent methods [16]. Since most analytical methods are derived based on the solution for regular geometries and simple material models (e.g. Eshelby's solution for isotropic elastic materials [17]), it is usually difficult for them to consider complex microstructural morphologies, history-dependent materials and large deformations. Additionally, direct numerical simulation (DNS) tools, such as finite element [18], meshfree [19,20] and fast Fourier transform (FFT)-based micromechanics methods [21,22], are both flexible and accurate. However, a DNS model involves a detailed meshing of the RVE microstructures and requires tremendous computational cost, especially for 3D problems. Therefore, one of the fundamental issues in multiscale material modeling and design is how to find an accurate low-dimensional representation of the RVE for arbitrary morphologies and nonlinearities.In the past decade, a plethora of data-driven material modeling methods have been proposed based on exist...

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Section: Appendix a Elementary Rotation Matricesmentioning

confidence: 99%

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confidence: 99%

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Exploring the 3D architectures of deep material network in data-driven multiscale mechanics

Liu

2019

Journal of the Mechanics and Physics of Solids

147

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“…Accordingly, literature concerning peridynamic theory is quite exhaustive and abundant. In the past two decades, several peridynamic studies pertaining to elastic deformation and fracture solids [2,[26][27][28], brittle fracture [29][30][31][32][33], fatigue failure [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49], and PD application of damage in composites [33,43,[50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65] have been reported. Studies related to crack initiation and propagation using peridynamics can be found in [30,[66][67][68][69].…”

Section: Review Of Peridynamic Theorymentioning

confidence: 99%

A Review of Peridynamics (PD) Theory of Diffusion Based Problems

Zeleke

Ageze

2021

Journal of Engineering

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The study of heat conduction phenomena using peridynamic (PD) theory has a paramount significance on the development of computational heat transfer. This is because PD theory has got an interesting feature to deal with the inherent nonlocal nature of heat transfer processes. Since the revolutionary work on PD theory by Silling (2000), extensive investigations have been devoted to PD theory. This paper provides a survey on the recent developments of PD theory mainly focusing on diffusion based peridynamic (PD) formulation. Both the bond-based and state-based PD formulations are revisited, and numerical examples of two-dimensional problems are presented.

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“…Peridynamics is a version of the non-local theory which was first introduced by Eringen and Edelen [17] and Kroner [18]. Peridynamics has been applied for the solution of many different problems and material systems including crack branching [19], plasticity [20], viscoelasticity [21], viscoplasticity [22], composite materials [23,24], nanowires [25], and bounded and unbounded domains [26].…”

Section: Introductionmentioning

confidence: 99%

Peridynamic Simulations of Nanoindentation Tests to Determine Elastic Modulus of Polymer Thin Films

Çelik

Öterkuş

Guven

2019

J Peridyn Nonlocal Model

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This study combines atomic force microscope (AFM) nanoindentation tests and peridynamic (PD) simulations to extract the elastic moduli of polystyrene (PS) films with varying thicknesses. AFM nanoindentation tests are applied to relatively hard PS thin films deposited on soft polymer (polydimethylsiloxane (PDMS)) substrates. Linear force versus deformation response was observed in nanoindentation experiments and numerical simulations since the soft PDMS substrate under the stiff PS films allowed bending of thin PS films instead of penetration of AFM tip towards the PS films. The elastic moduli of PS thin films are found to be increasing with increasing film thickness. The validity of both the simulation and experimental results is established by comparison against those previously published in the literature.

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A peridynamic failure analysis of fiber-reinforced composite laminates using finite element discontinuous Galerkin approximations

Cited by 27 publications

References 34 publications

Exploring the 3D architectures of deep material network in data-driven multiscale mechanics

Exploring the 3D architectures of deep material network in data-driven multiscale mechanics

A Review of Peridynamics (PD) Theory of Diffusion Based Problems

Peridynamic Simulations of Nanoindentation Tests to Determine Elastic Modulus of Polymer Thin Films

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