JAIC 1994, Volume 33, Number 2, Article 7 (pp. 153 to 170)
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Journal of the American Institute for Conservation
JAIC 1994, Volume 33, Number 2, Article 7 (pp. 153 to 170)




As stated, the numerical model is composed of assembled element stiffness matrices. These matrices are computed from the geometry of the actual object and the mechanical properties of the materials used to construct the object. It is essential to have this information as accurate as possible. The geometric relationships are taken directly from measurements of the object to be modeled. Determining the mechanical properties of the materials used to construct the object presents other problems altogether. For elastic structural analysis, there is no permanent deformation to the materials as a result of some applied force (Higdon et al. 1967). Many cold-temperature and low RH analyses can be treated as elastic systems, since there is little plastic deformation in such environments. Under these conditions, the mechanical properties needed for an analysis are the strength, stiffness, and coefficient of expansion for the individual materials. The strength is the maximum stress the material can sustain before breaking. The stiffness is commonly known as the modulus of a material. The modulus is the ratio of stress to strain in the elastic region of a material and relates the deformation of a material to the applied forces. In mathematical terms it is

Fig. .
where E is the modulus of elasticity, σ is the stress in the material, ∊ is the strain in the material. This relationship is critical to the correct analysis of any structure, since it is necessary to have the model structure deform correctly under the applied forces.

The mechanical properties of the organic materials found in cultural objects are significantly affected by environmental parameters. For example, artists' paints—whether traditional oils, alkyds, or acrylics—get stiffer and stronger with cooling and desiccation. Oil paints also get stiffer and stronger with drying time. All paints become glassy and tend to fracture prematurely below certain temperatures, and they also start to lose strength significantly (Mecklenburg and Tumosa 1991b). These characteristics are also found in hide glues used in paintings and furniture and in gelatins used in the emulsion and anticurl layers of photographic materials. Cultural materials also demonstrate different mechanical properties depending on the rate at which the forces are applied (Mecklenburg and Tumosa 1991b). It takes time for materials to equilibrate to changes in temperature and relative humidity, so the mechanical properties needed to properly calculate the effects of temperature and humidity are those that reflect the long-term equilibrium conditions. Whereas an analysis of a structure subjected to external forces such as those encountered in shock or vibration can employ constant material properties if in a constant environment, the analyses of structures subjected to changes in environment must take into account the fact that the mechanical properties may vary as a function of the environmental parameters. It is also necessary to keep in mind that in addition to the environmentally induced changes in strength and stiffness, nearly all of the materials want to shrink with cooling and desiccation or swell with heating and humidification. Thus, the analysis also requires an accurate knowledge of humidity and/or temperature coefficients of expansion. An expansion coefficient is often expressed as a simple constant over a wide temperature or humidity range, but an accurate numerical solution sometimes requires a more refined mathematical function relating how the expansion coefficient varies over the environmental range of interest.

Copyright 1994 American Institute for Conservation of Historic and Artistic Works