Non-aging materials

We now consider the most important special case of (1.2.2), namely where the mechanical properties of the material do not vary with time, at least over the timescale of interest. This means that G tJ ) must be unchanged under any overall time change, giving for any /q 

We will sometimes describe this property by saying that the material properties are time-homogeneous. Equations (1.2.4), (1.2.5) become 

In the latter form, the term G(oo)c(-oo) will often be zero since e(-oo) generally vanishes. 

Finally, the compact notation (1.2.22), involving a singular kernel, becomes 

Note that the relations (1.2.32) are convolution integrals, as given by (A3.1.17), since y t) obey the Causality condition  

---

The decomposition of hereditary integrals described in Sect. 2.4 for non-aging materials and the general techniques based on that decomposition may be extended to the case of aging viscoelastic bodies. A form of this decomposition has been used by Graham (1980) to develop solutions for frictional contact problems that involve varying contact area. 

Extensions of the correspondence principle, given in Sect. 2.6 for non-aging materials, may also be proved for aging viscoelastic materials and used to solve problems [see Graham and Williams (1972), Graham (1978 b) and Graham and Golden (1987)]. 

Non-Metallic Materials Numerous engineering thermoplastics have been commercialised including materials such as polyetherether ketone (PEEK) and polyether sulphate (PES) with much improved thermal/chemical resistance. The usage of FRP equipment has increased, and fluoropolymer lining technology/applications have come of age. Of particular interest is the development of stoved, fluoropolymer coating systems for process industry equipment. 

Human exposure to PFCs is likely to occur via a number of vectors and routes, for example food, drinking water, the ingestion of non-food materials, dermal contact and inhalation. Circumstantial factors such as place of residence, age, nature of PFCs vector, may also influence exposure. For example, according to Tittlemier et al. [27], food seems to represent the major intake pathway of PFAS in adult Canadians however, house dust, solution-treated carpeting and treated apparel might contribute a non-negligible 40% to the overall exposure. 

We observed that for freshly contaminated soil, the compound readily desorbed into the aqueous phase and was available for microbial consumption whereas for soils containing mostly the non-labile material, the contaminant availability was limited by the mass transfer into the aqueous phase. The fraction of contaminant, which is irreversibly bound to soil is typically present in micropores or chemically bound to soil humic matter and thus is not accessible for microbial utilization. These observations are in agreement with those reported for other chemicals in the literature. It is believed that the longer the contaminant age within the soil the lower the fraction of the contaminant that will be bioavailable. The observations have significant implications to the current remedy and the possibility of natural attenuation at the site. 

Linear Viscoelasticity Theory. FTMA is based on linear viscoelasticity theory. A one dimensional form of constitutive equation for linear viscoelastic materials which are isotropic, homogeneous, and hereditary (non-aging) is given by (21) ... 

The chemostat is the best laboratory idealization of nature for population studies. It is a dynamic system with continuous material inputs and outputs, thus modeling the open system character and temporal continuity of nature. The input and removal of nutrient analogs the continuous turnover of nutrients in nature. The washout of organisms is equivalent to non-age specific death, predation or emigration which always occurs in nature. [Wi]... 

Ageing plays a key role in the non-linear viscoelastic behaviour of polymers. When left at rest and at constant temperature, there is continuous stiffening. However, when the aged material is slightly heated or mechanically deformed, it is deaged and softened (Struik, 1978, 1983). 

A comprehensive analytical model for predicting long term durability of resins and of fibre reinforced plastics (FRP) taking into account viscoelastic/viscoplastic creep, hygrothermal effects and the effects of physical and chemical aging on polymer response has been presented. An analytical tool consisting of a specialized test-bed finite element code, NOVA-3D, was used for the solution of complex stress analysis problems, including interactions between non-linear material constitutive behavior and environmental effects. 

Fisher, Reeves, E. A. et al. Comparison of the wear of aged and non-aged ultrahigh molecular weight polyethylene sterilized by gamma irradiation and by gas plasma. Journal of Materials Science Materials in Medicine, 8 (1997), p. 375-378... 

Henceforth, it will be assumed, unless otherwise specified, that the material under consideration is non-aging. 

II. One-dimensional Constitutive Equations, (a) One-dimensional stress-strain relations for a non-aging linear viscoelastic material take the form... 

Sternberg (1964) extended this representation to non-isothermal conditions while Efimov (1966 b) and Graham and Williams (1972) generalized it to the case of an aging material. 

Solution of Problems Involving Aging Materials or Non-isothermal Conditions 87... 

Our discussion so far has been largely confined to materials that are non-aging and whose viscoelastic functions are independent of position. As noted however in Sect. 1.7, both of these properties may be lost under non-isothermal conditions. Also there are of course materials that are aging under isothermal conditions. We therefore briefly indicate methods of solution applicable to such materials. 

---