Thick fibrous composite reinforcements behave as special second-gradient materials: three-point bending of 3D interlocks

Madeo, Angela; Ferretti, Manuel; Dell’Isola, Francesco; Boisse, Philippe

doi:10.1007/s00033-015-0496-z

Cited by 56 publications

(42 citation statements)

References 57 publications

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“…However, in various papers dealing with woven composites, it is shown how the addition of energies related to the local stiffness of the yarns is useful, if not necessary, to describe the macroscopic deformation behavior of the interlocks (e.g. [6,15,26,36,35]).…”

Section: Second Gradient 3d Modeling Of the Deep Drawingmentioning

confidence: 99%

Modelling the deep drawing of a 3D woven fabric with a second gradient model

Barbagallo

Madeo

Morestin

et al. 2016

Mathematics and Mechanics of Solids

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Experimental testing on dry woven fabrics exhibits a complex set of evidences that are difficult to be completely described using classical continuum models. The aim of this paper is to show how the introduction of energy terms related to the micro-deformation mechanisms of the fabric, in particular to the bending stiffness of the yarns, helps in the modeling of the mechanical behavior of this kind of materials. To this aim, a second gradient, hyperelastic, initially orthotropic continuum theory is proposed to model fibrous composite interlocks at finite strains. In particular, the present work explores the relationship between the onset of wrinkling appearing during the simulation of the deep drawing of a woven fabric and the use of a second gradient model. It is shown that the introduction of second gradient terms accounting for the description of in-plane and out-of-plane bending rigidities, decreases the onset of wrinkles during the simulation of deep-drawing.In this work, a quadratic energy, roughly proportional to the square of the curvature of the fibers, is presented and implemented in the simulations. This simple constitutive assumption allows to clearly show the effects of the second gradient energy on both the wrinkling description and the numerical stability of the model. The results obtained in second gradient simulations are descriptive of the experimental evidence of deep drawing whose description is targeted in this work. The present paper provides additional evidence of the fact that first gradient continuum theories alone cannot be considered fully descriptive of the behavior of dry woven composite reinforcements. On the other hand, the proposed second gradient model for fibrous composite reinforcements opens the way both to the more accurate simulation of complex forming processes and to the possibility of controlling the onset of wrinkles.

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Section: Second Gradient 3d Modeling Of the Deep Drawingmentioning

confidence: 99%

Modelling the deep drawing of a 3D woven fabric with a second gradient model

Barbagallo

Madeo

Morestin

et al. 2016

Mathematics and Mechanics of Solids

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“…. , N z still transform like the components of a dyad with the modification that the sign changes for reflections61 ; their interpretation can be found therein, that 62 L n = L x cos nx + L y cos ny + L z cos nz (L, M, Z)…”

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confidence: 97%

Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”^** by E. Hellinger

Eugster

Dell’Isola

2016

Z Angew Math Mech

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The fundamental review article DIE ALLGEMEINEN ANSÄTZE DER MECHANIK DER KONTINUA in the Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Bd. IV‐4, Hft. 5 (1913) by Ernst Hellinger has not been translated into English so far. We believe that such a circumstance is really deprecative, as the insight reached by Hellinger in the mathematical structure of continuum mechanics seems, in some aspects, unsurpassed even nowadays. Hellinger's scientific manuscripts do not fill more than one and half boxes in library storage , but their impact on mathematics and mechanical sciences is profound. Indeed, the Hellinger‐Reissner variational principle is still a fundamental tool in theoretical and numerical mechanics. The intent of this paper is threefold: i) to allow to those who cannot understand German to enjoy the reading of a crystal‐clear and still topical article whose content has some enlightening parts, ii) to show that only one century ago the principle of virtual work (or virtual velocities) was regarded as the central principle in continuum mechanics and that Hellinger did forecast already then the main lines of its development, iii) to discuss some technical and conceptual aspects of the variational principles in continuum mechanics which some authors consider still controversial.

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“…Finally, we note that our model can be viewed as a part of a larger class of second-gradient-type theories, where the interfaces are modelled from a unified point of view as boundary-layer-type solutions, see for example recent works of dell'Isola and coworkers [10,24,30].…”

Section: Comparison With the Previous Workmentioning

confidence: 99%

Plasticity in multi-phase solids with incoherent interfaces and junctions

Basak

Gupta

2015

Continuum Mech. Thermodyn.

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Boundaries and junctions (both internal and external) can contribute significantly to the plastic deformation of metallic solids, especially when the average size of the grains (phases) is less than hundred nanometres or when the size of the solid itself is of the order of microns. The overall permanent deformation of the solid is a result of a coupling between bulk plasticity with moving interfaces/junctions/edges and intrinsic plasticity of internal and external surfaces. We use a novel continuum thermodynamic theory of plastic evolution, with incoherent interfaces and non-splitting junctions, to derive flow rules for bulk and surface plasticity in addition to kinetic relations for interface, edge, and junction motion, all coupled to each other. We assume rate-independent associative isotropic plastic response with bulk flow stress dependent on accumulated plastic strain and an appropriate measure of inhomogeneity. The resulting theory has two internal length scales: one given by the average grain size and another associated with the material inhomogeneity.

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Thick fibrous composite reinforcements behave as special second-gradient materials: three-point bending of 3D interlocks

Cited by 56 publications

References 57 publications

Modelling the deep drawing of a 3D woven fabric with a second gradient model

Modelling the deep drawing of a 3D woven fabric with a second gradient model

Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”^** by E. Hellinger

Plasticity in multi-phase solids with incoherent interfaces and junctions

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Thick fibrous composite reinforcements behave as special second-gradient materials: three-point bending of 3D interlocks

Cited by 56 publications

References 57 publications

Modelling the deep drawing of a 3D woven fabric with a second gradient model

Modelling the deep drawing of a 3D woven fabric with a second gradient model

Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”** by E. Hellinger

Plasticity in multi-phase solids with incoherent interfaces and junctions

Contact Info

Product

Resources

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Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”^** by E. Hellinger