Multiscale Continuous and Discontinuous Modeling of Heterogeneous Materials: A Review on Recent Developments

Nguyen, Vinh Phu; Stroeven, Martijn; Sluys, L.J.

doi:10.1142/s1756973711000509

Cited by 153 publications

(89 citation statements)

References 143 publications

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“…The availability of a microstructural model allows one to get rid of the assumptions at the macro-scale, as the cracks are initiated at the micro-scale and then transferred to the macro-scale when damage has spread beyond a certain threshold. The conceptual development and numerical implementation of such aspects, in the framework of a multiscale modelling approach to material degradation and fracture of polycrystalline materials [35,37,38], will be the focus of further studies. It is worth mentioning that, in a multiscale context, the proposed formulation can be used as a microscale model to estimate material degradation or plastic deformation in a macroscale FE model, according to what has been proposed in [35].…”

Section: Discussion and Further Developmentsmentioning

confidence: 99%

“…the analysis of polycrystalline microstructures and their failure processes, both in two and three dimensions [5]: among different approaches, multiscale methods appear to be the most promising, as they are able to bring together and link the diverse scales acting in the initiation and evolution of fracture [34,35,36,37,38]. Several techniques have been developed and used for studying the crack initiation and propagation in heterogeneous or polycrystalline microstructures.…”

Section: Introductionmentioning

confidence: 99%

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A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

Benedetti

Aliabadi

2013

Computer Methods in Applied Mechanics and Engineering

113

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In this study, a novel three-dimensional micro-mechanical crystal-level model for the analysis of intergranular degradation and failure in polycrystalline materials is presented. The polycrystalline microstructures are generated as Voronoi tessellations, that are able to retain the main statistical features of polycrystalline aggregates. The formulation is based on a grain-boundary integral representation of the elastic problem for the aggregate crystals, that are modeled as threedimensional anisotropic elastic domains with random orientation in the three-dimensional space. The boundary integral representation involves only intergranular variables, namely interface displacement discontinuities and interface tractions, that play an important role in the micromechanics of polycrystals. The integrity of the aggregate is restored by enforcing suitable interface conditions, at the interface between adjacent grains. The onset and evolution of damage at the grain boundaries is modeled using an extrinsic non-potential irreversible cohesive linear law, able to address mixed-mode failure conditions. The derivation of the traction-separation law and its relation with potential-based laws is discussed. Upon interface failure, a non-linear frictional contact analysis is used, to address separation, sliding or sticking between micro-crack surfaces. To avoid a sudden transition between cohesive and contact laws, when interface failure happens under compressive loading conditions, the concept of cohesive-frictional law is introduced, to model the smooth onset of friction during the mode II decohesion process. The incrementaliterative algorithm for tracking the degradation and micro-cracking evolution is presented and discussed. Several numerical tests on pseudo-and fully three-dimensional polycrystalline microstructures have been performed. The influence of several intergranular parameters, such as cohesive strength, fracture toughness and friction, on the microcracking patterns and on the aggregate response of the polycrystals has been analyzed. The tests have demonstrated the capability of the formulation to track the nucleation, evolution and coalescence of multiple damage and cracks, under either tensile or compressive loads.

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Section: Discussion and Further Developmentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

Benedetti

Aliabadi

2013

Computer Methods in Applied Mechanics and Engineering

113

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“…Detailed reviews on computational homogenization can be found in Refs. [197] and [198]. One of the widely used approaches in modeling heterogeneous materials is the unit-cell method which leads to a global macroscopic constitutive model for a heterogeneous material based on detailed modeling of the microstructure [199][200][201][202][203].…”

Section: Computational Homogenizationmentioning

confidence: 99%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

178

138

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The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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“…Different kinds of boundary conditions [58,59,60,33] can be used to transfer macrostrains to the micro-RVEs for material homogenization [3]. Periodic boundary conditions Figure 3: Application of the micro-RVE processing algorithm: a) example micro-RVE morphology; b) intergranular damage evolution; c) micro-cracking; d ) homogenized stresses provided to the macro-scale [41].…”

Section: Rve's Boundary Conditions: Down-scalingmentioning

confidence: 99%

“…Geers et al [32] analyzed recent trends and challenges in multiscale computational homogenization, briefly reviewing first-order techniques for mechanical problems, the concepts of second-order, continuous-discontinuous and multiphysics homogenization, applications to thin structures and problems involving interface and cohesive problems. A review on multiscale models for localization problems has been recently given by Nguyen et al [33], who focused, among other topics, on continuous and discontinuous computational homogenization for adhesive/cohesive crack modelling and cohesive failures. Multiscale models have been developed for the analysis of different classes of materials.…”

Section: Introductionmentioning

confidence: 99%

Multiscale modeling of polycrystalline materials: A boundary element approach to material degradation and fracture

Benedetti

Aliabadi

2015

Computer Methods in Applied Mechanics and Engineering

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In this work, a two-scale approach to degradation and failure in polycrystalline materials is proposed. The formulation involves the engineering component level (macro-scale) and the material grain level (micro-scale). The macro-continuum is modelled using a three-dimensional boundary element formulation in which the presence of damage is taken into account employing an initial stress approach for modelling the local softening in the neighborhood of points experiencing degradation at the micro-scale. The microscopic degradation is explicitly modelled by associating Representative Volume Elements (RVEs) to relevant points of the macro continuum, for representing the polycrystalline microstructure in the neighborhood of the selected points. A three-dimensional grain-boundary formulation is used to simulate intergranular degradation and failure in the microstructure, whose morphology is generated using Voronoi tessellations. Intergranular degradation and failure are modelled through cohesive and frictional contact laws. To couple the two scales, macro-strains are transferred to the RVE as periodic boundary conditions, while overall macro-stresses are obtained as volume averages of the micro-stress field. The comparison between effective macro-stresses for the damaged and undamaged RVE allows to define a macroscopic measure of material degradation. To avoid pathological damage localization at the macro-scale, integral non-local counterparts of the strains are employed. The multiscale processing algorithm is described. Some multiscale simulations are performed to investigate the capability of the method.

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Multiscale Continuous and Discontinuous Modeling of Heterogeneous Materials: A Review on Recent Developments

Cited by 153 publications

References 143 publications

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Multiscale modeling of polycrystalline materials: A boundary element approach to material degradation and fracture

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