![]() ![]() It is the context where sensitivity analysis should come into play to determine which input and output data are essential with respect to the goal of computation. This embedding makes the uncertainty of inputs more troublesome. Input data are often fully or partially obtained as solutions to inverse problems, i.e., the inputs of a state problem are the outputs of an inverse problem, which itself needs some input data. The goal is to infer lower and upper bounds of composite material parameters ( Torquato, 2002). Take assumptions on the character of composite materials made of handbook constituents, for example. The fact is that we frequently combine the available handbook data with micromechanical arguments. Although these sources cover various material parameters, not all useful data are available there and only extensive handbooks contain at least selected basic statistical features of the data ( ASM, 1992). What are the mines of material data? In mechanical engineering and structural mechanics, design engineers use material handbooks to find input data. In problems where the yield strength is important, the uncertainty in its value has a more explicit impact. This lack of knowledge will probably be harmless in common linear elasticity problems because the variation of the modulus of elasticity is not significant, especially if compared with the uncertainty in loading. On top of that, the nature of material response is three-dimensional nevertheless, sample parameters are measured in one-dimensional arrangements as a rule. Also, material properties are sensitive to various other factors too, e.g., instantaneous temperature, temperature history, load history, and fatigue. Does the analyst of a structure always know whether this or that piece of alloy comes from a plate, sheet, or different source? Moreover, parameter values respecting the origin of samples are rarely available even in the crisp form of Table 2.2, which does not statistically reflect the diversity of individual measurements.
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