A microstructural model for homogenisation and cracking of piezoelectric polycrystals

Benedetti, Ivano; Gulizzi, Vincenzo; Milazzo, Alberto

doi:10.1016/j.cma.2019.112595

Cited by 24 publications

(18 citation statements)

References 78 publications

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“…The form of Equations (1)-(4) suggests the introduction of generalized quantities (see, e.g., [32][33][34]). More specifically, for the sake of the present formulation, it is convenient to define the generalized displacement vector u , the generalized strain vector and the generalized stress vector τ as…”

Section: Generalized Formulation For Piezoelectricitymentioning

confidence: 99%

Layer-Wise Discontinuous Galerkin Methods for Piezoelectric Laminates

2020

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In this work, a novel high-order formulation for multilayered piezoelectric plates based on the combination of variable-order interior penalty discontinuous Galerkin methods and general layer-wise plate theories is presented, implemented and tested. The key feature of the formulation is the possibility to tune the order of the basis functions in both the in-plane approximation and the through-the-thickness expansion of the primary variables, namely displacements and electric potential. The results obtained from the application to the considered test cases show accuracy and robustness, thus confirming the developed technique as a supplementary computational tool for the analysis and design of smart laminated devices.

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Section: Generalized Formulation For Piezoelectricitymentioning

confidence: 99%

Layer-Wise Discontinuous Galerkin Methods for Piezoelectric Laminates

2020

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“…The methodology allows to study the microstructural evolution capturing the transition of individual interfaces from a pristine to a damaged and eventually cracked status. It has been successfully employed to model quasi-static micro-cracking [28,29,30], small-strains crystal plasticity [31], hydrogen embrittlement [32], high-cycle fatigue [33], micro-cracking of piezoelectric aggregates [34] and multi-scale modelling of polycrystalline components [35].…”

Section: Intergranular Fracture Propagationmentioning

confidence: 99%

Elucidating the Effect of Bimodal Grain Size Distribution on Plasticity and Fracture Behavior of Polycrystalline Materials

Barbe

Benedetti

Gulizzi

et al. 2020

J. Multiscale Modelling

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The refinement of grains in a polycrystalline material leads to an increase in strength but as a counterpart to a decrease in elongation to fracture. Different routes are proposed in the literature to try to overpass this strength-ductility dilemma, based on the combination of grains with highly contrasted sizes. In the simplest concept, coarse grains are used to provide relaxation locations for the highly stressed fine grains. In this work, a model bimodal polycrystalline system with a single coarse grain embedded in a matrix of fine grains is considered. Numerical full-field micro-mechanical analyses are performed to characterize the impact of this coarse grain on the stress-strain constitutive behavior of the polycrystal: the effect on plasticity is assessed by means of crystal plasticity finite element modeling [B. Flipon, C. Keller, L. Garcia de la Cruz, E. Hug and F. Barbe, Tensile properties of spark plasma sintered AISI 316L stainless steel with unimodal and bimodal grain size distributions, Mater. Sci. Eng. A 729 (2018) 248–256] while the effect on intergranular fracture behavior is studied by using boundary element modeling [I. Benedetti and V. Gulizzi, A grain-scale model for high-cycle fatigue degradation in polycrystalline materials, Int. J. Fract. 116 (2018) 90–105]. The analysis of the computational results, compared to the experimentally characterized tensile properties of a bimodal 316L stainless steel, suggests that the elasto-plastic interactions taking place prior to micro-cracking may play an important role in the mechanics of fracture of this steel.

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“…BEM 8,9 is a numerical technique widely employed for the solution of several classes of problems in solids and materials mechanics, including computational homogenization of materials with complex morphology or constitutive behavior 10,11,12,13,14,15,16,17 . The technique, based on a boundary integral reformulation of the considered problem, allows reducing the analysis dimensionality, e.g.…”

Section: Introductionmentioning

confidence: 99%

Coupling BEM and VEM for the Analysis of Composite Materials with Damage

Cascio

Benedetti

2021

J. Multiscale Modelling

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Numerical tools which are able to predict and explain the initiation and propagation of damage at the microscopic level in heterogeneous materials are of high interest for the analysis and design of modern materials. In this contribution, we report the application of a recently developed numerical scheme based on the coupling between the Virtual Element Method (VEM) and the Boundary Element Method (BEM) within the framework of continuum damage mechanics (CDM) to analyze the progressive loss of material integrity in heterogeneous materials with complex microstructures. VEM is a novel numerical technique that, allowing the use of general polygonal mesh elements, assures conspicuous simplification in the data preparation stage of the analysis, notably for computational micro-mechanics problems, whose analysis domain often features elaborate geometries. BEM is a widely adopted and efficient numerical technique that, due to its underlying formulation, allows reducing the problem dimensionality, resulting in substantial simplification of the pre-processing stage and in the decrease of the computational effort without affecting the solution accuracy. The implemented technique has been applied to an artificial microstructure, consisting of the transverse section of a circular shaped stiff inclusion embedded in a softer matrix. BEM is used to model the inclusion that is supposed to behave within the linear elastic range, while VEM is used to model the surrounding matrix material, developing more complex nonlinear behaviors. Numerical results are reported and discussed to validate the proposed method.

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A microstructural model for homogenisation and cracking of piezoelectric polycrystals

Cited by 24 publications

References 78 publications

Layer-Wise Discontinuous Galerkin Methods for Piezoelectric Laminates

Layer-Wise Discontinuous Galerkin Methods for Piezoelectric Laminates

Elucidating the Effect of Bimodal Grain Size Distribution on Plasticity and Fracture Behavior of Polycrystalline Materials

Coupling BEM and VEM for the Analysis of Composite Materials with Damage

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