The analysis of localized effects in composites with periodic microstructure

Aboudi, Jacob; Ryvkin, Michael

doi:10.1098/rsta.2012.0373

Cited by 6 publications

(6 citation statements)

References 16 publications

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“…The post peak response depends on both the fiber arrangement and the discretization. [31][32][33] In any case, periodicity is destroyed in the softening regime as displayed in Figure 5 and Figure 6, which visualize the distribution of the plastic deformation cumulated in the matrix, as obtained by the adoption of very fine meshes. In the case of large diameters and uneven reinforcement distribution, Figure 6(c), strain localization lines interfere with the fiber positions and break into differently oriented segments.…”

Section: Preliminary Analysesmentioning

confidence: 95%

“…Representative volume elements (RVEs) of the considered material samples are subjected to uniaxial tensile test in the plane transversal to the fiber axes, 27,33,40,70 where the overall mechanical response is mainly influenced by the metal characteristics, while the stiffness and strength of the ceramic prevail in the main reinforcement direction.…”

Section: The Problemmentioning

confidence: 99%

“…25 An alternative damaging scenario of metal-matrix composites assumes that plastic strains localize in the matrix, usually near the stiff reinforcement made of ceramic fibers or particles, which facilitate stress concentration. 9,14,[28][29][30] As a main consequence, the overall ductility is reduced, 10,[31][32][33] e.g. by the growth of micro-voids in the metal phase.…”

Section: Introductionmentioning

confidence: 99%

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Surrogate analytical models of damage localization in metal matrix composites

Bolzon

Pitchai

Talassi

2023

Journal of Composite Materials

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Several parameters entering the constitutive laws of metal matrix composites are not amenable to direct measurement. Their determination is therefore demanded to indirect identification procedures, based on the comparison between the output of some experimental works and the results of the iterative simulation of the performed tests. Largely repetitive numerical analyses can also support the optimized design of composite microstructures, the understanding of the actual stress-transfer mechanisms, and virtual testing. Surrogate analytical models can replace effectively non-linear finite element (FE) computations in parametric studies and identification procedures, reducing execution times and costs without compromising the accuracy of the results. In this context, a frequently used approach consists of the interpolation, by means of radial basis functions (RBFs), of data filtered by proper orthogonal decomposition (POD). This methodology is often used to reproduce the smooth output of different mechanical systems. This work is rather focused on the homogenized response of damaging metal matrix composites subjected to strain localization phenomena, and explores the accuracy achievable in these situations by the POD-RBF approximation of more traditional FE analyses. In all considered cases, the POD-RBF results are accurate, and able to distinguish between apparently similar situations. The approach is flexible, and the performance of the surrogate models can be tailored to the requirements of each application. In particular, various analytical approximations can be introduced to support the design of new microstructures and material couplings, and to understand the role of any material and/or geometry imperfections resulting from the production processes.

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Section: Preliminary Analysesmentioning

confidence: 95%

Section: The Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Surrogate analytical models of damage localization in metal matrix composites

Bolzon

Pitchai

Talassi

2023

Journal of Composite Materials

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“…In a series of investigations, [7], [22], [8], [2] and [12], localized damage, in the form of stiff and soft inclusions, cavities, finite, semi-infinite and interfacial cracks in composite materials, has been studied. In these investigations, a multiscale analysis approach has been developed, aimed to establish the behavior of composites with localized damage.…”

Section: Introductionmentioning

confidence: 99%

Micromechanical analysis of hyperelastic composites with localized damage using a new low-memory Broyden-step-based algorithm

Perchikov

Aboudi

2019

Arch Appl Mech

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A multiscale (micro-to-macro) analysis is proposed for the prediction of the finite strain behavior of composites with hyperelastic constituents and embedded localized damage. The composites are assumed to possess periodic microstructure and be subjected to a remote field. At the microscale, finite-strain micromechanical analysis based on the homogenization technique for the (intact) composite is employed for the prediction of the effective deformation. At the macroscale, a procedure, based on the representative cell method and the associated higher-order theory, is developed for the determination of the elastic field in the damaged composite. The periodic composite is discretized into identical cells and then reduced to the problem of a single cell by application of the discrete Fourier transform. The resulting governing equations, interfacial and boundary conditions in the Fourier transform domain, are solved by employing the higher-order theory in conjunction with an iterative procedure to treat the effects of damage and material nonlinearity. The initial conditions for the iterative solution are obtained using the weaklynonlinear material limit and a natural fixed-point iteration. A locally-convergent low-memory Quasi-Newton solver is then employed. A new algorithm for the implementation of the solver is proposed, which allows storing in the memory directly the vector-function history-sequence, which may be advantageous for convergence-control based on specific components of the objective vector-function. The strong-form Fourier transform-based approach employed here, in conjunction with the new solver, enables to extend the application of the method to nonlinear materials and may have computational efficiency comparable or possibly advantageous to that of standard approaches.

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“…In the section titled Micromechanics, the paper by Aboudi & Ryvkin [71] presents several methods of analysis of composite materials with periodic microstructures subjected to localized effects, such as concentrated loads, cracking or stationary/progressive damage. The study by Melcher et al [72] is devoted to mechanical systems subjected to repeated impacts.…”

Section: Description Of the Issuementioning

confidence: 99%

A celebration of mechanics: from nano to macro. The J. Michael T. Thompson Festschrift issue

Elishakoff

2013

Phil. Trans. R. Soc. A.

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This Theme Issue is dedicated to the topic ‘Mechanics: from nano to macro’ and marks the 75th birthday of Dr J. Michael T. Thompson, Fellow of the Royal Society, whose current affiliations are as follows: (i) Honorary Fellow, Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge; (ii) Emeritus Professor of Nonlinear Dynamics, Department of Civil, Environmental and Geomatic Engineering, University College London; and (iii) Professor of Theoretical and Applied Dynamics (Distinguished Sixth Century Chair, part-time), University of Aberdeen. He also serves as Chairman of the Board of Directors at ES-Consult (consulting engineers) in Copenhagen, Denmark. The pertinent question that arises from the very start is: should we first salute Michael and then describe the Theme Issue, or vice versa? Indeed, according to Blaise Pascal (1623–1662), the last thing one discovers in composing a work is what to put first. I would like to take the liberty of deviating from the tradition of the Philosophical Transactions and start with the tribute to Michael; after all he is the prime cause of this Theme Issue.

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The analysis of localized effects in composites with periodic microstructure

Cited by 6 publications

References 16 publications

Surrogate analytical models of damage localization in metal matrix composites

Surrogate analytical models of damage localization in metal matrix composites

Micromechanical analysis of hyperelastic composites with localized damage using a new low-memory Broyden-step-based algorithm

A celebration of mechanics: from nano to macro. The J. Michael T. Thompson Festschrift issue

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