GraFEA: a graph-based finite element approach for the study of damage and fracture in brittle materials

Khodabakhshi, Parisa; Reddy, J. N.; Srinivasa, Arun R.

doi:10.1007/s11012-016-0560-6

Cited by 29 publications

(15 citation statements)

References 37 publications

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“…It is worth to note that there exists a large literature on discrete models of fracture that abstract a continuum domain using a lattice representation, such as Lattice Discrete Particle Modeling [56], Graph-based Finite Element Analysis GraFEA [57], and Virtual bond model [58]. A major difference between the QC approach and these methods is that the discrete component of the QC model is physical and represents an actual networked material with a well defined failure criterion at the discrete elements scale.…”

Section: Discussionmentioning

confidence: 99%

An adaptive quasicontinuum approach for modeling fracture in networked materials: Application to modeling of polymer networks

Ghareeb

Elbanna

2020

Journal of the Mechanics and Physics of Solids

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Materials with network-like microstructure, including polymers, are the backbone for many natural and human-made materials such as gels, biological tissues, metamaterials, and rubbers. Fracture processes in these networked materials are intrinsically multiscale, and it is computationally prohibitive to adopt a fully discrete approach for large scale systems. To overcome such a challenge, we introduce an adaptive numerical algorithm for modeling fracture in this class of materials, with a primary application to polymer networks, using an extended version of the Quasi-Continuum method that accounts for both material and geometric nonlinearities. In regions of high interest, for example near crack tips, explicit representation of the local topology is retained where each polymer chain is idealized using the worm like chain model. Away from these imperfections, the degrees of freedom are limited to a fraction of the network nodes and the network structure is computationally homogenized, using the micromacro energy consistency condition, to yield an anisotropic material tensor consistent with the underlying network structure. A nonlinear finite element framework including both material and geometric nonlinearities is used to solve the system where dynamic adaptivity allows transition between the continuum and discrete scales. The method enables accurate modelling of crack propagation without a priori constraint on the fracture energy while maintaining the influence of large-scale elastic loading in the bulk. We demonstrate the accuracy and efficiency of the method by applying it to study the fracture in different examples of network structures. We further use the method to investigate the effects of network topology and disorder on its fracture characteristics. We discuss the implications of our method for multiscale analysis of fracture in networked material as they arise in different applications in biology and engineering.

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Section: Discussionmentioning

confidence: 99%

An adaptive quasicontinuum approach for modeling fracture in networked materials: Application to modeling of polymer networks

Ghareeb

Elbanna

2020

Journal of the Mechanics and Physics of Solids

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“…Extensions to higher-strain rates and other modes of failure will be considered in our future works. Lastly, our method can be coupled with other machine learning and graph-based methods [92][93][94][95] for increased accuracy of failure paths prediction, which is our future work.…”

Section: Discussionmentioning

confidence: 99%

Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials

et al. 2019

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In brittle fracture applications, failure paths, regions where the failure occurs and damage statistics, are some of the key quantities of interest (QoI). High-fidelity models for brittle failure that accurately predict these QoI exist but are highly computationally intensive, making them infeasible to incorporate in upscaling and uncertainty quantification frameworks. The goal of this paper is to provide a fast heuristic to reasonably estimate quantities such as failure path and damage in the process of brittle failure. Towards this goal, we first present a method to predict failure paths under tensile loading conditions and low-strain rates. The method uses a k-nearest neighbors algorithm built on fracture process zone theory, and identifies the set of all possible pre-existing cracks that are likely to join early to form a large crack. The method then identifies zone of failure and failure paths using weighted graphs algorithms. We compare these failure paths to those computed with a high-fidelity fracture mechanics model called the Hybrid Optimization Software Simulation Suite (HOSS). A probabilistic evolution model for average damage in a system is also developed that is trained using 150 HOSS simulations and tested on 40 simulations. A non-parametric approach based on confidence intervals is used to determine the damage evolution over time along the dominant failure path. For upscaling, damage is the key QoI needed as an input by the continuum models. This needs to be informed accurately by the surrogate models for calculating effective moduli at continuum-scale. We show that for the proposed average damage evolution model, the prediction accuracy on the test data is more than 90%. In terms of the computational time, the proposed models are ≈ O ( 10 6 ) times faster compared to high-fidelity fracture simulations by HOSS. These aspects make the proposed surrogate model attractive for upscaling damage from micro-scale models to continuum models. We would like to emphasize that the surrogate models are not a replacement of physical understanding of fracture propagation. The proposed method in this paper is limited to tensile loading conditions at low-strain rates. This loading condition corresponds to a dominant fracture perpendicular to tensile direction. The proposed method is not applicable for in-plane shear, out-of-plane shear, and higher strain rate loading conditions.

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“…Work in finite element analysis literature by Reddy et al [Reddy and Srinivasa 2015] proposes a solution based on classical FEM to show that for any hyper-elasticity problem, the magnitude of the nodal forces can be written completely in terms of strain energy density along the edges composing the elements, while force directions are along the unit vectors corresponding to the edges. Using this idea in subsequent work, authors [Khodabakhshi et al 2016] introduce Graph-based Finite Element Analysis (Gra-FEA) where a damage variable corresponding to the edges of composing elements is used. It is based on the strain threshold and thus can simulate the fracture of an object by weakening the material.…”

Section: Graph-based Finite Element Methodsmentioning

confidence: 99%

“…It has been shown in earlier work that the nodal forces of a discretized hyper-elastic FEM system can be completely represented in terms of a function of strain energy density along the edges of the induced graph [Reddy and Srinivasa 2015]. We use this fact and follow prior work in structural mechanics [Khodabakhshi et al 2016] to define a purely edge based damage variable, which describes the extent of damage for any edge in the graph. We build over prior work to reformulate the strain energy of damaged elements in 3D volumetric object meshes and then simulate independent movement of the fractured pieces.…”

Section: Introductionmentioning

confidence: 99%

Remeshing-Free Graph-Based Finite Element Method for Ductile and Brittle Fracture

Mandal¹,

Chaudhuri²,

Chaudhuri³

2021

Preprint

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GraFEA: a graph-based finite element approach for the study of damage and fracture in brittle materials

Cited by 29 publications

References 37 publications

An adaptive quasicontinuum approach for modeling fracture in networked materials: Application to modeling of polymer networks

An adaptive quasicontinuum approach for modeling fracture in networked materials: Application to modeling of polymer networks

Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials

Remeshing-Free Graph-Based Finite Element Method for Ductile and Brittle Fracture

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