Stress and displacement around a crack in layered network systems mimicking nacre

Aoyanagi, Yuko; Okumura, Ko

doi:10.1103/physreve.79.066108

Cited by 10 publications

(7 citation statements)

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“…One such example is a simplified two-dimensional spring-bead model. [21] This model has revealed qualitative features but does not allow quantitative discussions.In this study, we construct a more realistic numerical model of nacre that explicitly includes the layered structure in the calculation by finite element method (FEM) in the presence of a crack (c.f. ref.…”

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Realistic Numerical Analysis of a Bioinspired Layered Composite with a Crack: Robust Scaling Laws and Crack Arrest

Hamamoto

Okumura

2013

Adv Eng Mater

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Nacre is a prototype of natural strong and tough materials and has been studied extensively. However, no numerical models have been developed that faithfully reflect the layered structure made of alternately stacked soft and hard layers, in order to study the fracture toughness in the presence of a macroscopic crack. In this study, we construct a realistic numerical model by finite element method (FEM) that explicitly takes the layered structure into account and study the stress and deformation fields around a crack. Although we reflect a realistic layered structure, we remarkably find simple scaling laws for the elastic fields, which predict considerable reduction of the stress concentration around the crack tips in exchange for enhancement of the deformation. We also find that the divergence at the crack tips in the scaling law for the stress field is cut-off at the scale of layers, which significantly restrains the maximum stress appearing at the tips. We further find that a crack tip is necessarily stopped at a soft layer and this crack arrest guarantees strong effects of the reduction of the stress concentration and cut-off of the stress singularity. In addition, these toughening mechanisms lead to the prediction of the correct order of the fracture energy experimentally reported in a seminal paper. These mechanisms and the FEM model developed here will be useful for the development of artificial tough advanced materials.Tough and strong materials in nature quite often exhibit magnificent hierarchical structures. Nacre is probably the most well studied material as such; it is a shining layered composite found inside certain sea shells or on the surface of pearl. This material is remarkable in that only a small amount of the soft component between the layers of the hard component makes the fracture energy a few thousand times as high as that of the monolithic material made of the hard component. [1,2] Accordingly various toughening mechanism of nacre have been proposed, [3][4][5][6][7][8] and nacre has bioinspired a number of remarkable materials. [9][10][11][12][13] Here, in particular, we focus on a simple model of nacre [14] that provides simple understandings of the type recently revealed for spider webs, [15][16][17] (although it does not include recently found complex structures beyond the layered structure [18,19] ). This is because simple scaling laws were obtained for the model to predict the correct order of the fracture energy of nacre, on the basis of analytical solutions for two crack problems. [14,20] However, in this model the layered structure is coarsegrained or homogenized: the continuum model is valid on scales larger than the layer period and thus can predict nothing on smaller scales. In particular, this model is insensitive to the position of crack tips, i.e. whether the tips are located in soft or hard layers. To study such issues, we need to construct appropriate numerical models that allow us to seek what happens at scales inaccessible by the coarsegrained continuum model. One such ex...

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“…One such example is a simplified two-dimensional spring-bead model. [21] This model has revealed qualitative features but does not allow quantitative discussions.…”

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confidence: 99%

Realistic Numerical Analysis of a Bioinspired Layered Composite with a Crack: Robust Scaling Laws and Crack Arrest

Hamamoto

Okumura

2013

Adv Eng Mater

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“…in previous numerical calculations [39,40].) In summary, when the stress concentration is high, its reduction due to nonlinearity becomes greater.…”

Section: Eq (4) (This Significantly Enhanced Deformation In Soft Lamentioning

confidence: 62%

“…Using a simple linear model of nacre, and deriving an analytical expression of the stress and strain fields near a crack tip, we have shown that there is a significant reduction in stress near crack tips in nacre [25,38]. This reduction in stress concentration was numerically confirmed using a simple network model [39], as well as finite-element calculations [40]. These numerical studies elucidated a physical picture for the mitigation of stress concentration, where enhanced elongation of soft layers effectively suppresses the deformation of the hard layer component, leading to a reduction in stress concentration.…”

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Toughening in a nacre-like soft-hard layered structure due to weak nonlinearity in the soft layer

Aoyanagi

Okumura

2019

Phys. Rev. Materials

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Recently, it has been found experimentally that hydrated nacre exhibits a nonlinear mechanical response. While mechanical nonlinearity has been shown to be important in other biological structures, such as spider webs, the implications of mechanical nonlinearity in nacre have not been explored. Here, we show that the nonlinear mechanical response of nacre can be reproduced by an analytical model, which reflects a nacre-like layered structure, consisting of linear-elastic hard sheets glued together by weakly nonlinear-elastic soft sheets. We develop scaling analysis on this analytical model, and perform numerical simulations using a lattice model, which is a discrete counterpart of the analytical model. Unexpectedly, we find the weak nonlinearity in the soft component significantly contributes to enhancing toughness by redistributing the stress at a crack tip over a wider area. Beyond demonstrating a mechanism that explains the unusual properties of biological nacre, this study points to a general design principle for constructing tough composites using weak nonlinearity, and is useful as a guiding principle to develop artificial layered structures mimicking nacre. I. INTRODUCTIONNatural materials often exhibit remarkable hierarchical structures leading to outstanding mechanical characteristics [1-5], as observed in bone, spider silk [6], and the exoskeletons of crustaceans [7,8]. Nacre, which is found in many seashells and protects shellfish from their environment, is composed of soft and hard layers, and has been studied as a prototype material for several decades [9][10][11]. Researchers have been inspired by nacre's remarkable structure to develop new materials that demonstrate excellent mechanical performance. [12][13][14][15][16][17][18].There have been many studies discussing the mechanisms responsible for the toughness of nacre. Toughening mechanisms have been proposed based on a variety of experimental observations, such as (1) step-wise elongation [19], (2) micro-cracking and crack bridging [20], (3) thin compressive layers [21], (4) rough layer interfaces [22], (5) mineral bridges [23], and (6) wavy surface of the plates [24]. On the theoretical side, various approaches have been explored, including (1) elastic models [21] based on analytical solutions [25, 26] and on scaling arguments [27, 28], (2) viscoelastic

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“…This was done by applying the displacement boundary conditions very slowly, such that the results did not change upon decreasing the loading rate . Note that this is a general approach in which the computing time does not depend on the non-linearity in the cohesive law, and has been used by other authors for complicated non-linear problems ( Aoyanagi and Okumura, 2009 ).…”

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Conditions controlling kink crack nucleation out of, and delamination along, a mixed-mode interface crack

Pro

Sehr

Lim

et al. 2018

Journal of the Mechanics and Physics of Solids

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This paper analyzes the competition between kink nucleation and interface fracture for an interface crack (without a putative kink flaw) subject to mixed-mode loading. The simulations utilize a distributed cohesive zone approach that embeds cohesive elements throughout the entire mesh; dynamic crack path evolution occurs through a loss of cohesive traction associated with a critical separation between elements. The simulations identify mesh densities that lead to mesh-independent results for randomly oriented triangular meshes, and provide clear guidelines regarding parameters that recover toughness-controlled cracking (i.e. linear elastic fracture mechanics). The results demonstrate that, when the when the normalized bulk toughness is far from the transition between kinking and delamination, crack direction and critical loads are identical to those predicted by He and Hutchinson, who analyzed cracking from a putative flaw associated with the maximum energy release rate. Near the transition between fracture modes, kink nucleation depends on the relative size of the interface and bulk process zones, such that additional criteria are needed (beyond those postulated by He and Hutchinson). Regime maps are presented which indicate regions of kink nucleation versus delamination as a function of controlling cohesive parameters.

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Stress and displacement around a crack in layered network systems mimicking nacre

Cited by 10 publications

References 31 publications

Realistic Numerical Analysis of a Bioinspired Layered Composite with a Crack: Robust Scaling Laws and Crack Arrest

Realistic Numerical Analysis of a Bioinspired Layered Composite with a Crack: Robust Scaling Laws and Crack Arrest

Toughening in a nacre-like soft-hard layered structure due to weak nonlinearity in the soft layer

Conditions controlling kink crack nucleation out of, and delamination along, a mixed-mode interface crack

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