Erratum: Simple Model for the Mechanics of Spider Webs [Phys. Rev. Lett.<b>104</b>, 038102 (2010)]

Aoyanagi, Yuko; Okumura, Ko

doi:10.1103/physrevlett.115.039903

Cited by 7 publications

(6 citation statements)

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“…For example, a spider may vary the properties of a piece of thread depending on its placement in the web 8. While it has been shown that webs themselves are robust and flaw tolerant,4, 9 how precise must a spider construct the structures that attach a web to its environment? Uncertainty and variation in environmental conditions suggest a need for robust and adaptable anchorages, yet webs illustrate reproducible and deliberate geometric construction.…”

Section: Introductionmentioning

confidence: 99%

Synergetic Material and Structure Optimization Yields Robust Spider Web Anchorages

Pugno

Cranford

Buehler

2013

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Section: Introductionmentioning

confidence: 99%

Synergetic Material and Structure Optimization Yields Robust Spider Web Anchorages

Pugno

Cranford

Buehler

2013

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“…4 Cellular solids are generally lightweight smart materials like spider webs 5,6 and support our life, for example, daily by their insulating or shock-absorbing features. Active studies on foam solids to date have revealed, e.g., (1) simple fracture mechanical properties that are well-understood as a function of the volume fraction of solid ϕ 7−9 and (2) advantages of the porous structure for reinforcement.…”

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confidence: 99%

Fracture of Soft Foam Solids: Interplay of Visco- and Plasto-elasticity

Kashima

Okumura

2014

ACS Macro Lett.

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Fracture mechanical properties of a very soft solidified foam of polyethylene with Young's modulus about 1 MPa are studied by changing stretching velocity in a wide range, by using sheets of the material in order to suppress finite-size effects. Unexpectedly, we find that the fracture can be described well by linear elastic fracture mechanics for a given fracture rate in the wide range. This allows a direct determination of velocity-dependent fracture energy of the soft foam. As a result, we find that the fracture energy is composed of a static plastoelastic component and another dynamic viscoelastic component, elucidating a simple physical interpretation of each component and giving guiding principles useful for practical applications to reinforce industrial polymer materials. Furthermore, we introduce a finite stress criterion for fracture that is similar in spirit to the cohesive zone model and, using our data, demonstrate that this stress criterion is consistent with the Griffith's energy balance. I n nature and in daily life, there is a variety of cellular structures or foam solids, ranging from familiar ones, such as cork, balsa, bread, coral, and apples, 1 to exotic remarkable ones, such as the stereom of echinoderms, 2 the skeleton of a certain sponge, 3 and the frustules of diatoms. 4 Cellular solids are generally lightweight smart materials like spider webs 5,6 and support our life, for example, daily by their insulating or shock-absorbing features. Active studies on foam solids to date have revealed, e.g., (1) simple fracture mechanical properties that are well-understood as a function of the volume fraction of solid ϕ 7−9 and (2) advantages of the porous structure for reinforcement. 10,11 However, experimental studies are limited to hard cellular solids with Young's modulus E larger than 3000 MPa, such as poly(methyl acrylate) (PMA), rigid polyurethane (PU), and cellular glass. In addition, any velocity dependences of fracture properties of foam solids have never been discussed in a systematic way, while such an issue has received considerable attention for adhesive interface, 12−14 flexible laminates, 15 viscoelastic solids, 16,17 and weakly cross-linked gels. 18,19 Recently, a very soft polyethylene foam with E around 1 MPa has been studied, and scaling laws different from those for hard porous materials were established. 20 Here, we study the fracture energy of similar soft foams with changing fracture rate in a wide range to surprisingly find that linear elastic fracture mechanics 21,22 works well for a fixed velocity in the wide range. The velocity-dependent fracture energy is shown to be composed of a static plastoelastic component and another dynamic viscoelastic component, with the latter scaling linearly with the rate. The velocity dependence originates from that of a yield stress that is introduced through the opening distance at crack tips ( Figure 1). Furthermore, we demonstrate that the Griffith criterion can be regarded as a stress criterion: we find with our data that the Griffith's ene...

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“…[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.…”

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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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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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Erratum: Simple Model for the Mechanics of Spider Webs [Phys. Rev. Lett.104, 038102 (2010)]

Cited by 7 publications

References 0 publications

Synergetic Material and Structure Optimization Yields Robust Spider Web Anchorages

Synergetic Material and Structure Optimization Yields Robust Spider Web Anchorages

Fracture of Soft Foam Solids: Interplay of Visco- and Plasto-elasticity

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

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