Slender structures--bodies with large length to thickness ratio--occur not only in structural engineering applications, but also in several biological and nano-scale applications. Some of the recently emerging examples of interest include nanoscale biological filaments (e.g. DNA molecules, microtubules, cilia and flagella), carbon nano-tubes and silver nano-wires. Several of these slender structures undergo very large twisting and bending deformations. For example, biological filaments such as DNA perform their biological functions via well-regulated structural deformations that involve large twisting and bending.

Continuum mechanics based models of slender structures are effective in simulating the mechanics of nano-scale filaments. However, the accuracy of these simulations strictly depends on the knowledge of the constitutive laws that may in general be nonlinear and non-homogeneous. It necessitates an inverse problem framework that can leverage the data provided by physical experiments and molecular dynamics simulations to estimate the unknown parameters in the constitutive law.

The primary purpose of this research is to show the possibility of developing inverse methods for identification of constitutive laws of slender structures modeled as continuum rods. The overarching goal of this research was originally motivated by the query into structure-function relationship of biological filaments; how these two features of the constitutive law (nonlinearity and non-homogeneity) influence structural deformations of biological filaments that in turn govern their biological activity or functions. However, little is known even from the perspective of structural engineering that could serve this overarching goal. Therefore, I defined mechanics problems that address and focus on some engineering and mathematical challenges as a stepping stone towards the overarching goal. This research in a broad outlook makes a bipartite contribution. The first contribution is the development of a computational rod model that captures large dynamic bending and torsion of slender filaments with user-defined nonlinear constitutive laws. The second contribution is the development of both deterministic and statistical inverse methods to identify the uncertain parameters of the constitutive law of slender structures.

Finally, the forward rod model developed here offers a platform to study a variety of interesting engineering problems. Therefore, as an additional contribution of this dissertation, I studied the beating oscillations of buckled rods subjected to nonconservative follower loads. This is motivated by the beating dynamics of active filaments and paves the way towards designing biomimetic applications of active filaments.