Hierarchical Load Sharing

SNIC 2017/7-136


SNAC Small

Principal Investigator:

Otte Marthin


Uppsala universitet

Start Date:


End Date:


Primary Classification:

20301: Applied Mechanics




Today’s manmade composites usually consist of a matrix with some stiff inclusion, such as carbon fibers. The result is a stiff, lightweight material with a high strength. They also become quite brittle, however, abruptly failing when a sufficiently high force is applied, in contrast to ductile materials who first dissipates energy through plastic deformation before breaking. This allows manmade composites to be used in vehicles, decreasing the fuel consumption, but less useful in buildings, where brittle materials may be dangerous. The historical building material wood, do not have this problem however, even though being a fiber composite. After a stiff response at small strains, wood starts to plastically deform after its yield strength, even more so in living trees. This is not a unique property to wood, but also occurs in other biological composites, such as tendon and bone. What these biomaterials have in common is a hierarchical structure, where the stiff inclusions themselves are composites. This hierarchical structure continues for several levels, stretching from the length scale of nanometers (cellulose) to that of millimeters (annual rings). Only some of the failure mechanisms occurring in these biological composites have been discovered, and more research is needed. Assume a case where a large number of fibers are glued together to a fiber composite, and a tensile load is applied in the direction of the fibers. If a fiber inside the composite breaks, the macroscopic stiffness of the composite barely changes. Therefore, the mean stress inside the composite remains almost unchanged. The force previously carried by the broken fiber has to be redistributed among the remaining fibers, in the plane of the crack. Depending on the stiffness and strength of the glue (matrix), the force is redistributed among a few fibers close to the crack, or over a large number of fibers. The former case results in a very stiff composite, which abruptly breaks when a critical amount of fibers have broken within a short distance from each other, a so called critical cluster. That is, the composite becomes strong and brittle. The latter case instead results in a composite which quickly loses stiffness, but instead allows the composite to be extended a much large distance before breaking, consuming a lot of energy. Manmade composites of today, are of the type where the load are redistributed within a small area. Our hypothesis is that biomaterials uses different types of load redistribution at different structural length scales. In this way, biomaterials may start off as a stiff composite for small strains, whilst still providing the toughness of a softer one. Early results has proven that one may combine the described types of load redistribution by using multiple structural levels. However, to prove that this combination results in a good combination of high strength and toughness, multiple tensile tests has to be simulated. A larger number of fibers (1000+) must also be used than in the early simulations (<730).