The mechanical properties of cellular solids

Complementary patterns of stiffness in stem and leaf sheaths of Triticale : Measurements of ultrasound velocity

The variation in the stiffness of stem and leaf sheaths along the shoot axis of Triticale (Triticosecale W., cv. Jago) was examined, using an ultrasonic method, at two stages of development, (i) at the stage of high stem mechanical instability when upper internodes are forming (heading), and (ii) at milk maturity when development of strengthening tissues is completed (three weeks after anthesis). The squared velocity of low-frequency longitudinal pulse waves was used as a measure of the specific modulus of elasticity, averaged over the whole cross section of the structures and related to the unit density of the material. Structural material of varying effective stiffness was found to be utilized along leaf sheaths with a pattern complementary to that in growing stems. The stiffness increased basipetally along leaf sheaths in the direction of increasing flexibility of internodes. Maximum values of the specific modulus of elasticity in particular leaf sheaths were enhanced acropetally, ensuring the stronger mechanical protection of those meristematic zones which were actively elongating and were located at the upper internodes. The stiffest material present in leaf sheaths covered only those stem sections which could be the most critical for plant safety during stem elongation. This characteristic and very regular pattern of stiffness alteration along the shoot axis was structurally determined as it remained similar after air drying the specimens. It is concluded that adaptation of cereals to withstand environmental loads is realized not only on morphological and anatomical levels but is also reflected in a specific heterogeneity in the material properties of the cell walls which support the plant.

Mechanical properties of trabecular bone. Dependency on strain rate

The effect of strain rate (epsilon) and apparent density (rho) on stiffness (E), strength (sigma u), and ultimate strain (epsilon u) was studied in 60 human trabecular bone specimens from the proximal tibia. Testing was performed by uniaxial compression to 5% specimen strain. Six different strain rates were used: 0.0001, 0.001, 0.01, 0.1, 1, and 10 s-1. Apparent density ranged between 0.23 and 0.59 g cm-3. Linear and non-linear regression analyses using strength, stiffness and ultimate strain as dependent variables (Y) and strain rate and apparent density as independent variables were performed using the following models: Y = a rho b epsilon c, Y = rho b(a + c epsilon; Y = (a + b rho)epsilon c, Y = a rho 2 epsilon c, E = a rho 3 epsilon c. The variations of strength and stiffness were explained equally well by the linear and the power function relationship to strain rate. The exponent was 0.07 in the power function relationship between strength and strain rate and 0.05 between stiffness and strain rate. The variation of ultimate strain was explained best using a power function relationship to strain rate (exponent = 0.03). The variation of strength and stiffness was explained equally well by the linear, power function and quadratic relationship to apparent density. The cubic relationship between stiffness and apparent density showed a less good fit. Ultimate strain varied independently of apparent density.

Measurement of the density of trabecular bone

Methods of assessing real and apparent trabecular bone density are discussed. A method of defatting trabecular bone using trichlorethylene in an ultrasound bath for 4 h followed by rehydration in distilled water under vacuum is described, and its effectiveness discussed.

Compressive axial strain distributions in cancellous bone specimens

The compressive axial strain distribution in cylindrical trabecular bone specimens was studied using digitized images of the specimen surface. Specimens were tested with strain rate 0.00015 s-1. Images were taken at 0, 1, 2, 3, 4, 6, 8 and 10% strain. Using an optical illusion of movement by rapidly changing succeeding images, failures were classified as transverse (33%) or oblique collapses (67%). The location of failure was not determined by the specimen density gradient. Local axial strain in the distal, intermediate and proximal third was measured throughout the compression in the transversely failing specimens, whereas local strain in the obliquely failing specimens was measured in the pre-failure phase only. Axial strain inhomogeneity was observed in the pre-failure as well as in the post-failure phase. In the pre-failure phase the intermediate third was strained significantly less than the thirds near the ends. In the post-failure phase specimen strain occurred solely in the collapsed part. Ultimate strain of the transversely failing specimens was 2.5% and ultimate strain of the failing third was 3.7%. At failure less than 1% strain was observed in the intermediate third and at 10% specimen strain 1.5% local strain was found in the intermediate third. The results indicate unreliability of conventional stiffness and strain measurements in trabecular bone specimens probably due to lack of trabecular constraint at the end surfaces. Conventional measurements tend to underestimate stiffness and, by giving an average value of strain in spite of considerable strain inhomogeneity, to underestimate failure strain.

Foam Structures with a Negative Poisson's Ratio

A novel foam structure is presented, which exhibits a negative Poisson's ratio. Such a material expands laterally when stretched, in contrast to ordinary materials.

The mechanical behaviour of cancellous bone

Cancellous bone has a cellular structure: it is made up of a connected network of rods and plates. Because of this, its mechanical behaviour is similar to that of other cellular materials such as polymeric foams. A recent study on the mechanisms of deformation in such materials has led to an understanding of how their mechanical properties depend on their relative density, cell wall properties and cell geometry. In this paper, the results of this previous study are applied to cancellous bone in an attempt to further understand its mechanical behaviour. The results of the analysis agree reasonably well with experimental data available in the literature.