Computational Rod Model With User-Defined Nonlinear Constitutive Laws

Fatehiboroujeni, Soheil; Palanthandalam-Madapusi, Harish J.; Goyal, Sachin

doi:10.1115/1.4041028

Cited by 7 publications

(7 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While in the analysis presented here, the constitutive equations as embodied in Eqs. ( 5) and ( 6) are linear and local, the method can be adapted to analyze problems where the constitutive relationships are nonlinear and nonlocal [33].…”

Section: Numerical Schemementioning

confidence: 99%

Nonlinear Oscillations Induced by Follower Forces in Prestressed Clamped Rods Subjected to Drag

Fatehiboroujeni

Gopinath

Goyal

2018

Journal of Computational and Nonlinear Dynamics

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Numerical Schemementioning

confidence: 99%

Nonlinear Oscillations Induced by Follower Forces in Prestressed Clamped Rods Subjected to Drag

Fatehiboroujeni

Gopinath

Goyal

2018

Journal of Computational and Nonlinear Dynamics

Self Cite

View full text Add to dashboard Cite

show abstract

“…stress and strain, of RNA nanotubes. We approach the modeling strategy of RNA nanotubes based on the ideas similar to the modeling of carbon nanotubes and several other nanorods (Cheng et al 2009b;Tserpes and Papanikos 2005;Odijk 1986;Kohji et al 1978;Tashiro et al 1978;Badu and Melnik 2017b;Fatehiboroujeni et al 2018;Fang et al 2013;Gupta and Kumar 2018;Fatehiboroujeni et al 2018;Maghsoodi and Perkins 2018;Kumar et al 2016;Schmidt et al 2015;Gupta and Kumar 2017;Venkataiah et al 2018;Badu and Melnik 2017a).…”

Section: Introductionmentioning

confidence: 99%

Atomistic to continuum model for studying mechanical properties of RNA nanotubes

Badu

Prabhakar

Melnik

et al. 2020

Computer Methods in Biomechanics and Biomedical Engineering

View full text Add to dashboard Cite

With rapid advancements in the emerging field of RNA nanotechnology, its current and potential applications, new important problems arise in our quest to better understand properties of RNA nanocomplexes. In this paper, our focus is on the modeling of RNA nanotubes which are important for many biological processes. These RNA complexes are also important for human beings, with their theurapeutical and biomedical applications discussed vigorously in the literature over the recent years. Here, we develop a continuum model of RNA nanotubes, originally obtained from self assembly of RNA building blocks in the molecular dynamics simulation. Based on the finite element method, we calculate the elastic properties of these nanostructures and provide a relationship between stress and strain induced in the RNA nanotube. We also analyze the variations in the displacement vector along the assembly axis for RNA nanotubes of different sizes. In particular, we show that oscillations in the amplitudes of strains and displacements significantly differ for such RNA nanotubes. These findings are discussed in the context of atomistic simulations and experimental results in this field.

show abstract

“…The Generalized-α method is adopted to compute the numerical solution of this system, subjected to necessary and sufficient initial and boundary conditions. A detailed description of this numerical scheme applied to the rod formulation is given in [69] and references therein. Our computational model has been validated by comparing the critical value of the follower force in the planar cantilever scenario with analytical results of Beck's column [66].…”

Section: A Solution Methodology Accuracy and Convergencementioning

confidence: 99%

“…A. Governing equations following the Kirchhoff approach The continuum rod model that we use follows Kirchhoff's approach [68] assuming each cross-section of the rod to be rigid and is described in detail elsewhere [69].…”

Section: Computational Scheme: Animated Continuum Rod Modelmentioning

confidence: 99%

Flapping, swirling and flipping: Non-linear dynamics of pre-stressed active filaments

Fatehiboroujeni¹,

Gopinath

Goyal

2020

Preprint

Self Cite

View full text Add to dashboard Cite

Initially straight slender elastic filaments and rods with geometrically constrained ends buckle and form stable two-dimensional shapes when compressed by bringing the ends together. It is known that beyond a critical value of this pre-stress, clamped rods transition to bent, twisted three-dimensional equilibrium shapes. Here, we analyze the three-dimensional instabilities and dynamics of such pre-stressed, initially twisted filaments subject to active follower forces and dissipative fluid drag. We find that degree of boundary constraint and the directionality of active forces determines if oscillatory instabilities can arise. When filaments are clamped at one end and pinned at the other with follower forces directed towards the clamped end, stable planar flapping oscillations result; reversing the directionality of the active forces quenches the instability. When both ends are clamped however, computations reveal a novel secondary instability wherein planar oscillations are destabilized by off-planar perturbations resulting in three-dimensional swirling patterns with periodic flips. These swirl-flip transitions are characterized by two distinct and time-scales. The first corresponds to unidirectional swirling rotation around the end-to-end axis. The second captures the time between flipping events when the direction of swirling reverses. We find that this spatiotemporal dance resembles relaxation oscillations with each cycle initiated by a sudden jump in torsional deformation and then followed by a period of gradual decrease in net torsion until the next cycle of variations. Our work reveals the rich tapestry of spatiotemporal patterns when weakly inertial strongly damped rods are deformed by non-conservative active forces. Practically, our results suggest avenues by which pre-stress, elasticity and activity may be used to design synthetic fluidic elements to pump or mix fluid at macroscopic length scales.

show abstract

Computational Rod Model With User-Defined Nonlinear Constitutive Laws

Cited by 7 publications

References 41 publications

Nonlinear Oscillations Induced by Follower Forces in Prestressed Clamped Rods Subjected to Drag

Nonlinear Oscillations Induced by Follower Forces in Prestressed Clamped Rods Subjected to Drag

Atomistic to continuum model for studying mechanical properties of RNA nanotubes

Flapping, swirling and flipping: Non-linear dynamics of pre-stressed active filaments

Contact Info

Product

Resources

About