Fracture mechanical properties of hard cellular solids (porous materials) with the Young modulus E larger than 3000 MPa have been well understood; scaling relations between fracture mechanical quantities and porosity are established, which can be explained by a theory based on the geometrical parameters of a cellular solid. In this study, we obtain experimentally the fracture energy of a very soft polyethylene foam with E around 1 MPa. We find scaling laws different from those for hard foams, which can be understood by considerations independent of the structural parameters of foams.
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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