Closed-cell elastic properties

Another model was presented by Gibson and Ashby [1], based on a cubic cell model for a closed-cell foam, which takes into account the enclosed gas. As shown in Figure 1, the thickness of the edges and the faces of PP foam cell are approximately equal, which means there is no accumulation of material in the corners. Therefore, the main deformation mechanisms are the stretching of the cell walls and the compression of the enclosed gas. As a result, the elastic properties of the closed-cell foam are described by ... 

The above analytical model will give a reasonable approximation when designing a syntactic foam material. There are examples of more complicated numerical models available throughout literature if more detailed analysis is desired. We refer the reader to Gibson and Ashby (15) for analytical relationships for elastic properties for both open- and closed-celled foam that are based on the properties of the unfoamed material and relative density of the foam. 

The ratio (p/G) has the units of time and is known as the elastic time constant, te, of the material. Little information exists in the published literature on the rheomechanical parameters, p, and G for biomaterials. An exception is red blood cells for which the shear modulus of elasticity and viscosity have been measured by using micro-pipette techniques 166,68,70,72]. The shear modulus of elasticity data is usually given in units of N m and is sometimes compared with the interfacial tension of liquids. However, these properties are not the same. Interfacial tension originates from an imbalance of surface forces whereas the shear modulus of elasticity is an interaction force closely related to the slope of the force-distance plot (Fig. 3). Typical reported values of the shear modulus of elasticity and viscosity of red blood cells are 6 x 10 N m and 10 Pa s respectively 1701. Red blood cells typically have a mean length scale of the order of 7 pm, thus G is of the order of 10 N m and the elastic time constant (p/G) is of the order of 10 s. 

On the other hand, the mechanical properties of monolithic carbon gels are of importance when they are to be used as adsorbents and catalyst supports in fixed-bed reactors, since they must resist the weight of the bed and the stress produced by its vibrations or movements. A few smdies have been published on the mechanical properties of resorcinol-formaldehyde carbon gels under compression [7,36,37]. The compressive stress-strain curves of carbon aerogels are typical of brittle materials. The elastic modulus and compressive strength depend largely on the network connectivity and therefore on the bulk density, which in turn depends on the porosity, mainly the meso- and macroporosity. These mechanical properties show a power-law density dependence with an exponent close to 2, which is typical of open-cell foams. 

Scaffolds made of PCL and HAp were a topic of investigations of Causa and coworkers [164]. They found that the mechanical properties of the composites are close to those of human bone only after the addition of 20 vol% of HAp. In particular, the elastic modulus is within the range of values for human cortical bone. Moreover, with the use of primary human osteoblasts, a high proUferation rate and a moderate increase of alkaline phosphatase activity were found, mainly on the surface of PCL-based composites with 13 and 20 vol% of HAp, though at the last time point (4 weeks) all the HAp-added polymers were covered by confluent layers of cells. It was concluded that the structure of a scaffold along with its surface physicochemical characteristics affect cell behaviour, but, on the other hand, mechanical properties are also crucial for implant performance. 

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