Scaling views on strength of soft/hard composites

We frequently find composite structures, especially comprised of soft and hard elements, in many strong materials in nature: timber, teeth etc. For example, in

nacre

, found inside of certain seashells,

hard and brittle

aragonaite plates are glued together by

soft and thin

protein layers. Toughness of nacre is about 3000 times as high as that of pure aragonite, although the volume fraction of the soft protein is only 1/100! This lecture concerns, on a macroscopic level of continuum models, fracture properties of nacre and similar layered structures. We show that one of the important mechanisms of the enhancement of strength is

a weakened stress concentration around the tip due to the structure

[

1

]–[

4

]. Our approach may be quite unusual in the light of computational solid and structural mechanics; we work with the vision of impressionists: ignoring many details to capture simple views from complex systems; in many cases, discussing only on the level of scaling laws (i.e., power laws), which is one of the standard strategies of

soft matter physics

. The mechanism of the above less effective stress concentration works in the regime of linear elasticity. With the above-mentioned strategy, we also discuss how viscoelastic effects can play a vital role. This predicts an unusual crack shape, different from the conventional parabolic one in the linear elastic fracture mechanics: the shape is like that of a trumpet! [

5

] In addition, we may discuss some of the following topics: (1) Possible views on an isotropic composite [

6

]: doublenetwork gel consisting of two independently cross-liked networks, composites especially promising for artificial joints that are synthesized recently [

7

]. (2) Elastic particle-reinforced composites [

6

]. We propose a continuum elastic model to extract the controlling parameters of toughness of the composites. (3) Strength of perforated paper [

8

], related to freezing effects of apples and potatoes in food science [

9

]. (4) a direct experimental confirmation of Griffith’s scaling law in linear-elastic polymer foam [

10

].