Mechanics of Uncertainty: Managing Uncertainty in Mechanics

Uncertainty is ubiquitous in the natural, engineered, and social environments. Devising rationales for explaining it, strategies for its integration into scientific determinism and mitigating its consequences has been an active arena of rational endeavor where many scientific concepts have taken turn at fame and infamy. Far from being a static concept, uncertainty is the complement of knowledge, and as thus, continually adapts itself to knowledge, feeding on its evolution to redefine its claim over science. Mechanics is a framework for applying deductive and mathematical reasoning to enhance our understanding of the physical world. Thus, far from being accidental, the interaction of mechanics and uncertainty is rather by design, as they both mold the physical world in a complementary fashion. The substance of this interaction is attested to by the simultaneous evolution of mechanics and rational models of uncertainty as embodied, for example, in the contributions of Gauss, Euler, Legendre, Laplace, Einstein, Feynman, and vonMises. Two driving forces behind a significant portion of current scientific research can be associated with technological developments in the areas of computing and sensing. Indeed, it has only recently become possible to resolve, numerically, very complex models of physical phenomena, as well as to probe these phenomena over length-scales that span orders of magnitude. This facility for doing science significantly changes the realm over which uncertainty can claim a hold, and merits a reconsideration of the scientific questions enabled through uncertainty modeling. The paper focuses on a particular class of recent developments related to the quantification, propagation, and management of uncertainty, using a probabilistic framework. An attempt is made at presenting a formalism that facilitates the adaptive quantification of uncertainty and of its effect on mechanics-based predictions. In addition to the more traditional quest for estimating the probability of extreme events such as failure, attention is given to estimating the confidence in model predictions and to adaptive schemes for improving this confidence through model refinement (mechanistic and numerical) as well as data refinement. The possibility of performing such an adaptation can play a significant role in shaping performance-based design practice in science and engineering by quantifying the information, and its associated worth, required to