Improvement of structural efficiency in metals by the control of topological arrangements in ultrafine and coarse grains

Improvement of structural efficiency in various materials is critically important for sustainable society development and the efficient use of natural resources. Recently, a lot of attention in science and engineering has been attracted to heterogeneous-structure materials because of high structural efficiency. However, strategies for the efficient design of heterogenous structures are still in their infancy therefore demanding extensive exploration. In this work, two-dimensional finite-element models for pure nickel with bimodal distributions of grain sizes having ‘harmonic’ and ‘random’ spatial topological arrangements of coarse and ultrafine-grain areas are developed. The bimodal random-structure material shows heterogeneities in stress–strain distributions at all scale levels developing immediately upon loading, which leads to developing concentrations of strain and premature global plastic instability. The bimodal harmonic-structure material demonstrates strength and ductility significantly exceeding those in the bimodal random-structure as well as expectations from a rule of mixtures. The strain hardening rates also significantly exceed those in homogeneous materials while being primarily controlled by coarse-grain phase at the early, by ultrafine-grain at the later and by their compatible straining at the intermediate stages of loading. The study emphasises the importance of topological ultrafine-/coarse-grain distributions, and the continuity of the ultrafine-grain skeleton in particular.

A two-dimensional model for stress driven diffusion in bone tissue

The growth and resorption of bone are governed by interaction between several cells such as bone-forming osteoblasts, osteocytes, lining cells and bone-resorbing osteoclasts. The cells considered in this study reside in the periosteum. Furthermore, they are believed to be activated by certain substances to initiate bone growth. This study focuses on the role that stress driven diffusion plays in the transport of these substances from the medullary cavity to the periosteum. Calculations of stress driven diffusion are performed under steady state conditions using a finite element method with the concentration of nutrients in the cambium layer of the periosteum obtained for different choices of load frequencies. The results are compared with experimental findings, suggesting that increased bone growth occurs in the neighbourhood of relatively high nutrient concentration.

Strain driven transport for bone modeling at the periosteal surface

Bone modeling and remodeling has been the subject of extensive experimental studies. There have been several mathematical models proposed to explain the observed behavior, as well. A different approach is taken here in which the bone is treated from a macroscopic view point. In this investigation, a one-dimensional analytical model is used to shed light on the factors which play the greatest role in modeling or growth of cortical bone at the periosteal surface. It is presumed that bone growth is promoted when increased amounts of bone nutrients, such as nitric oxide synthase (NOS) or messenger molecules, such as prostaglandin E2 (PGE2), seep out to the periosteal surface of cortical bone and are absorbed by osteoblasts. The transport of the bone nutrients is assumed to be a strain controlled process. Equations for the flux of these nutrients are written for a one-dimensional model of a long bone. The obtained partial differential equation is linearized and solved analytically. Based upon the seepage of nutrients out of the bone, the effect of loading frequency, number of cycles and strain level is examined for several experiments that were found in the literature. It is seen that bone nutrient seepage is greatest on the tensile side of the bone; this location coincides with the greatest amount of bone modeling.