We propose a simple model to describe spider orb webs. The model has a formal analytical solution when no thread elements are broken. When the radial threads are sufficiently strong compared to the spiral threads, the model is free of stress concentrations even when a few spiral threads are broken. This is in contrast with what occurs in common elastic materials. According to our model, spiders can increase the number of spiral threads to make a dense web (to catch small insects) or adjust the number of radial threads (to adapt to environmental conditions or reduce the cost of making the web) without reducing the damage tolerance of the web.

Blisters are commonly observed when an adhesive sheet is carelessly deposited on a plate. Although such blisters are usually not desired for practical applications, we show through model experiments on angular blisters how material properties can be deduced from height profile measurements. In particular the typical curvature of the crests is found proportional to an elasto-capillary length that compares the bending stiffness of the sheet with adhesion energy. In addition, the radius of the tip allows to estimate the product of this length with the thickness of the sheet. The relevance of these results to realistic random configurations is finally confirmed. arXiv:1207.2437v1 [cond-mat.soft]

We revisit the standard elastic-plastic fracture theory developed by Hutchinson, Rice, and Rosengren (HRR) and reproduce, by a simple scaling argument, the stress singularity around the crack tip derived by HRR. From the singular behavior thus reconfirmed, we propose a general scaling relation which guarantees an effect similar to the tip-blunting effect: the maximum stress at the crack tip in a structured material can be reduced by increasing the structure size. This proposed relation is explicitly confirmed by numerical calculations performed for a coarse-grained lattice model, and leads to general scaling relations for fracture surface energy and to a possible reinforcement of cellular solids due to the pores.

We investigate crack propagation in a simple two-dimensional visco-elastic model and find a scaling regime in the relation between the propagation velocity and energy release rate or fracture energy, together with lower and upper bounds of the scaling regime. On the basis of our result, the existence of the lower and upper bounds is expected to be universal or model-independent: the present simple simulation model provides generic insight into the physics of crack propagation, and the model will be a first step towards the development of a more refined coarse-grained model. Relatively abrupt changes of velocity are predicted near the lower and upper bounds for the scaling regime and the positions of the bounds could be good markers for the development of tough polymers, for which we provide simple views that could be useful as guiding principles for toughening polymer-based materials.

Nacre is a natural composite material which has been studied because of its remarkable structure and its strength. In this paper, we revisit a layered model of nacre proposed previously [K. Okumura and P. G. de Gennes, Eur. Phys. J. E 4, 121 (2001)] in order to understand the physical reasons for the toughening via numerical simulation. We construct a two-dimensional lattice model which reflects the layered structure and perform a numerical study. This grid model reproduces the essential features predicted by the analytical solutions to the previous model and the results elucidate the reasons why the tip-stress concentration is reduced and tip displacement is enhanced in the layered system.

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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