Material Axes Research Articles

Advancing the deer calcaneus model for bone adaptation studies: exvivo strains obtained after transecting the tension members suggest an unrecognized important role for shear strains.

Sheep and deer calcanei are finding increased use as models for studies of bone adaptation, including advancing understanding of how the strain (deformation) environment influences the ontogenetic emergence of biomechanically relevant structural and material variations in cortical and trabecular bone. These artiodactyl calcanei seem ideal for these analyses because they function like simply loaded short-cantilevered beams with net compression and tension strains on the dorsal and plantar cortices, respectively. However, this habitual strain distribution requires more rigorous validation because it has been shown by limited invivo and exvivo strain measurements obtained during controlled ambulation (typically walking and trotting). The conception that these calcanei are relatively simply and habitually loaded 'tension/compression bones' could be invalid if infrequent, though biologically relevant, loads substantially change the location of the neutral axis (NA) that separates 'compression' and 'tension' regions. The effect on calcaneus strains of the tension members (plantar ligament and flexor tendon) is also not well understood and measuring strains after transecting them could reveal that they significantly modulate the strain distribution. We tested the hypothesis that the NA location previously described during simulated on-axis loads of deer calcanei would exhibit limited variations even when load perturbations are unusual (e.g. off-axis loads) or extreme (e.g. after transection of the tension members). We also examined regional differences in the predominance of the three strain modes (tension, compression, and shear) in these various load conditions in dorsal, plantar, medial, and lateral cortices. In addition to considering principal strains (tension and compression) and maximum shear strains, we also considered material-axis (M-A) shear strains. M-A shear strains are those that are aligned along the long axis of the bone and are considered to have greater biomechanical relevance than maximum shear strains because failure theories of composite materials and bone are often based on stresses or strains in the principal material directions. We used the same load apparatus from our prior study of mule deer calcanei. Results showed that although the NA rotated up to 8° medially and 15° laterally during these off-axis loads, it did not shift dramatically until after transection of all tension members. When comparing results based on maximum shear strain data vs. M-A shear strain data, the dominant strain mode changed only in the plantar cortex - as expected (in accordance with our a priori view) it was tension when M-A shear strains were considered (shear:tension=0.2) but changed to dominant shear when maximum shear strain data were considered (shear:tension=1.3). This difference leads to different conclusions and speculations regarding which specific strain modes and magnitudes most strongly influence the emergence of the marked mineralization and histomorphological differences in the dorsal vs. plantar cortices. Consequently, our prior simplification of the deer calcaneus model as a simply loaded 'tension/compression bone' (i.e. plantar/dorsal) might be incorrect. In vivo and in finite element analyses are needed to determine whether describing it as a 'shear-tension/compression' bone is more accurate. Addressing this question will help to advance the artiodactyl calcaneus as an experimental model for bone adaptation studies.

THERMAL BUCKLING FOR LOCAL DELAMINATION NEAR THE SURFACE OF LAMINATED CYLINDRICAL SHELLS AND DELAMINATED GROWTH

An investigation is carried out to understand the thermal buckling behavior of local delamination near the surface of fiber-reinforced laminated cylindrical shells and the delaminated growth. The shape of the delaminated region considered is elliptic and triangular. The direction of the fiber material's axis is arbitrary. The relationships between the critical thermal load and the geometrical and physical parameters of base laminated shells and sublaminated shells are described and some valuable conclusions are obtained. Finally, the possible expanding direction of the elliptic and triangular delaminated shape under thermal load is discussed.

Optimum Design of Laminated Plates Under Shear

This paper is concerned with the optimum design of plates with ortho tropic layers under shear. The plates considered are the laminates of N orthotropic layers whose principal material axes coincide with the plate axes. Each layer is assumed to have the same thickness and an equal number of fibers in the direction of +α i and —α i with respect to the plate axis. The fiber directions which give the highest shear buckling stress are found by utilizing a mathematical optimization technique.