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Open Access Publications from the University of California

Scholarly Works (7 results)

  • Thesis
  • Peer Reviewed
UC Merced Electronic Theses and Dissertations (2018)

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.

    Cover page: Inverse Approaches for Identification of Constitutive Laws of Slender Structures Motivated by Application to Biological FilamentsCreative Commons 'BY-NC-SA' version 4.0 license
    • Article
    • Peer Reviewed
    UC Merced Previously Published Works (2020)
    The deformations of several slender structures at nano-scale are conceivably sensitive to their non-homogenous elasticity. Owing to their small scale, it is not feasible to discern their elasticity parameter fields accurately using observations from physical experiments. Molecular dynamics simulations can provide an alternative or additional source of data. However, the challenges still lie in developing computationally efficient and robust methods to solve inverse problems to infer the elasticity parameter field from the deformations. In this paper, we formulate an inverse problem governed by a linear elastic model in a Bayesian inference framework. To make the problem tractable, we use a Gaussian approximation of the posterior probability distribution that results from the Bayesian solution of the inverse problem of inferring Young's modulus parameter fields from available data. The performance of the computational framework is demonstrated using two representative loading scenarios, one involving cantilever bending and the other involving stretching of a helical rod (an intrinsically curved structure). The results show that smoothly varying parameter fields can be reconstructed satisfactorily from noisy data. We also quantify the uncertainty in the inferred parameters and discuss the effect of the quality of the data on the reconstructions.
      Cover page: Linearized Bayesian inference for Youngs modulus parameter field in an elastic model of slender structures
      • Article
      • Peer Reviewed
      UC Merced Previously Published Works (2019)
      Elastically driven filaments subjected to animating compressive follower forces provide a synthetic way to mimic the oscillatory beating of active biological filaments such as eukaryotic cilia. The dynamics of such active filaments can, under favorable conditions, exhibit stable time-periodic responses that result due to the interplay of elastic buckling instabilities, geometric constraints, boundary conditions, and dissipation due to fluid drag. In this paper, we use a continuum elastic rod model to estimate the critical follower force required for the onset of the stable time-periodic flapping oscillations in pre-stressed rods subjected to fluid drag. The pre-stress is generated by imposing either clamped-clamped or clamped-pinned boundary constraints and the results are compared with those of clamped-free case, which is without pre-stress. We find that the critical value increases with the initial slack--that quantifies the pre-stress, and strongly depends on the type of the constraints at the boundaries. The frequency of oscillations far from the onset, however, depends primarily on the magnitude of the follower force, not on the boundary constraints. Interestingly, oscillations for the clamped-pinned case are observed only when the follower forces are directed towards the clamped end. This finding can be exploited to design a mechanical switch to initiate or quench the oscillations by reversing the direction of the follower force or altering the boundary conditions.
        Cover page: Effect of Boundary Constraints on the Nonlinear Flapping of Filaments Animated by Follower Forces
        • Article
        • Peer Reviewed
        UC Merced Previously Published Works (2018)
        Flagella and cilia are examples of actively oscillating, whiplike biological filaments that are crucial to processes as diverse as locomotion, mucus clearance, embryogenesis and cell motility. Elastic driven rod-like filaments subjected to compressive follower forces provide a way to mimic oscillatory beating in synthetic settings. In the continuum limit, this spatiotemporal response is an emergent phenomenon resulting from the interplay between the structural elastic instability of the slender rods subjected to the non-conservative follower forces, geometric constraints that control the onset of this instability, and viscous dissipation due to fluid drag by ambient media. In this paper, we use an elastic rod model to characterize beating frequencies, the critical follower forces and the non-linear rod shapes, for prestressed, clamped rods subject to two types of fluid drag forces, namely, linear Stokes drag and non-linear Morrison drag. We find that the critical follower force depends strongly on the initial slack and weakly on the nature of the drag force. The emergent frequencies however, depend strongly on both the extent of pre-stress as well as the nature of the fluid drag.
          Cover page: FOLLOWER FORCES IN PRE-STRESSED FIXED-FIXED RODS TO MIMIC OSCILLATORY BEATING OF ACTIVE FILAMENTS
          • Article
          • Peer Reviewed
          UC Merced Previously Published Works (2018)
          Elastic-driven slender filaments subjected to compressive follower forces provide a synthetic way to mimic the oscillatory beating of biological flagella and cilia. Here, we use a continuum model to study the dynamical, nonlinear buckling instabilities that arise due to the action of nonconservative follower forces on a prestressed slender rod clamped at both ends and allowed to move in a fluid. Stable oscillatory responses are observed as a result of the interplay between the structural elastic instability of the inextensible slender rod, geometric constraints that control the onset of instability, energy pumped into the system by the active follower forces, and motion-driven fluid dissipation. Initial buckling instabilities are initiated by the effect of the follower forces and inertia; fluid drag subsequently allows for the active energy pumped into the system to be dissipated away and results in self-limiting amplitudes. By integrating the equations of equilibrium and compatibility conditions with linear constitutive laws, we compute the critical follower forces for the onset of oscillations, emergent frequencies of these solutions, and the postcritical nonlinear rod shapes for two forms of the drag force, namely linear Stokes drag and quadratic Morrison drag. For a rod with fixed inertia and drag parameters, the minimum (critical) force required to initiate stable oscillations depends on the initial slack and weakly on the nature of the drag force. Emergent frequencies and the amplitudes postonset are determined by the extent of prestress as well as the nature of the fluid drag. Far from onset, for large follower forces, the frequency of the oscillations can be predicted by evoking a power balance between the energy input by the active forces and the dissipation due to fluid drag.
            Cover page: NONLINEAR OSCILLATIONS INDUCED BY FOLLOWER FORCES IN PRE-STRESSED CLAMPED RODS SUBJECTED TO DRAG
            • Article
            • Peer Reviewed
            UC Merced Previously Published Works (2021)
            Initially straight slender elastic filaments or rods with constrained ends buckle and form stable two-dimensional shapes when prestressed by bringing the ends together. Beyond a critical value of this prestress, rods can also deform off plane and form twisted three-dimensional equilibrium shapes. Here, we analyze the three-dimensional instabilities and dynamics of such deformed filaments subject to nonconservative active follower forces and fluid drag. We find that softly constrained filaments that are clamped at one end and pinned at the other exhibit stable two-dimensional planar flapping oscillations when active forces are directed toward the clamped end. Reversing the directionality of the forces quenches the instability. For strongly constrained filaments with both ends clamped, computations reveal an instability arising from the twist-bend-activity coupling. Planar oscillations are destabilized by off-planar perturbations resulting in twisted three-dimensional swirling patterns interspersed with periodic flipping or reversal of the swirling direction. These striking swirl-flip transitions are characterized by two distinct timescales: the time period for a swirl (rotation) and the time between flipping events. We interpret these reversals as relaxation oscillation events driven by accumulation of torsional energy. Each cycle is initiated by a fast jump in torsional deformation with a subsequent slow decrease in net torsion until the next cycle. Our work reveals the rich tapestry of spatiotemporal patterns when weakly inertial strongly damped rods are deformed by nonconservative active forces. Taken together, our results suggest avenues by which prestress, elasticity, and activity may be used to design synthetic macroscale pumps or mixers.
              Cover page: Three-dimensional nonlinear dynamics of prestressed active filaments: Flapping, swirling, and flipping
              • Article
              • Peer Reviewed
              UC Merced Previously Published Works (2018)
              Computational rod models have emerged as efficient tools to simulate the bending and twisting deformations of a variety of slender structures in engineering and biological applications. The dynamics of such deformations, however, strongly depends on the constitutive law in bending and torsion that, in general, may be nonlinear, and vary from material to material. Jacobian-based computational rod models require users to change the Jacobian if the functional form of the constitutive law is changed, and hence are not user-friendly. This paper presents a scheme that automatically modifies the Jacobian based on any user-defined constitutive law without requiring symbolic differentiation. The scheme is then used to simulate force-extension behavior of a coiled spring with a softening constitutive law.
                Cover page: COMPUTATIONAL ROD MODEL WITH USER-DEFINED NONLINEAR CONSTITUTIVE LAWS
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