iMechanica - Cosserat rod
https://imechanica.org/taxonomy/term/6455
enModeling ribbons/strips as a Cosserat rod
https://imechanica.org/node/26903
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/6463">helical ribbons</a></div><div class="field-item odd"><a href="/taxonomy/term/6455">Cosserat rod</a></div><div class="field-item even"><a href="/taxonomy/term/12690">elastic strips</a></div><div class="field-item odd"><a href="/taxonomy/term/13890">Cosserat Plates</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>This study presents a computational approach to obtain nonlinearly elastic constitutive relations of strip/ribbon-like structures modeled as a special Cosserat rod. Starting with the description of strips as a general Cosserat plate, the strip is first subjected to a strain field which is uniform along its length. The Helical Cauchy-Born rule is used to impose this uniform strain field which deforms the strip into a six-parameter family of helical configurations-the six parameters here correspond to the six strain measures of rod theory. Two vector variables are introduced to model the position of the deformed centerline of the strip's cross-section and to model orientation of thickness lines along the strip's width. The minimization of the strip's plate energy together with the aforementioned uniformity in strain field reduces the partial differential equations of plate theory from the entire mid-plane of the strip to just a system of nonlinear ordinary differential equations along the strip's width line for the above mentioned two vector variables. A nonlinear finite element formulation is further presented to solve the above mentioned set of ordinary differential equations. This, in turn, yields the strip's stored energy per unit length as well as the induced internal force, moment and stiffnesses of the strip for every prescribed set of six strain measures of rod theory. The proposed scheme is used to study uniform bending, twisting and shearing of a strip. For the case of uniform twisting and shearing, the strip is also seen to buckle along its width into a more complex configuration which are accurately captured by the presented scheme. We demonstrate that the presented scheme is more general and accurate than the existing schemes available in the literature.</p>
<p>The article will soon appear in CMAME and the same can be accessed at the following link: <a href="https://www.researchgate.net/publication/374752915_A_computational_approach_to_obtain_nonlinearly_elastic_constitutive_relations_of_strips_modeled_as_a_special_Cosserat_rod">https://www.researchgate.net/publication/374752915_A_computational_appro...</a></p>
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</div></div></div>Tue, 17 Oct 2023 05:26:50 +0000Ajeet Kumar26903 at https://imechanica.orghttps://imechanica.org/node/26903#commentshttps://imechanica.org/crss/node/26903Geometrically exact elastoplastic rods -determination of yield surface in terms of stress resultants
https://imechanica.org/node/24774
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/6383">Elastoplastic deformation</a></div><div class="field-item odd"><a href="/taxonomy/term/6455">Cosserat rod</a></div><div class="field-item even"><a href="/taxonomy/term/1257">yield surface</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>This work addresses the determination of yield surfaces for geometrically exact elastoplastic rods. Use is made of a formulation where the rod is subjected to an uniform strain field along its arc length, thereby reducing the elastoplastic problem of the full rod to just its cross-section. By integrating the plastic work and the stresses over the rod's cross-section, one then obtains discrete points of the yield surface in terms of stress resultants. Eventually, Lamé curves in their most general form are fitted to the discrete points by an appropriate optimisation method. The resulting continuous yield surfaces are examined for their scalability with respect to cross-section dimensions and also compared with existing analytical forms of yield surfaces.</span></p>
<p><span>The article will soon appear in <em>Computational Mechanics</em> which can also be accessed at the following link: </span><span><span><a href="https://www.researchgate.net/publication/346484659_Geometrically_exact_elastoplastic_rods_-determination_of_yield_surface_in_terms_of_stress_resultants">https://www.researchgate.net/publication/346484659_Geometrically_exact_e...</a></span></span></p>
</div></div></div>Wed, 02 Dec 2020 02:18:17 +0000Ajeet Kumar24774 at https://imechanica.orghttps://imechanica.org/node/24774#commentshttps://imechanica.org/crss/node/24774A finite element formuation for a direct approach to elastoplasticity in special Cosserat rods
https://imechanica.org/node/24673
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/6383">Elastoplastic deformation</a></div><div class="field-item odd"><a href="/taxonomy/term/6455">Cosserat rod</a></div><div class="field-item even"><a href="/taxonomy/term/447">Finite Element Method</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>A finite element formulation is presented for a direct approach to model elastoplastic deformation in slender bodies using the special Cosserat rod theory. The direct theory has additional plastic strain and hardening variables, which are functions of just the rod's arc-length, to account for plastic deformation of the rod. Furthermore, the theory assumes the existence of an effective yield function in terms of stress resultants, i.e., force and moment in the cross-section and cross-section averaged hardening parameters. Accordingly, one does not have to resort to the three-dimensional theory of elastoplasticity during any step of the finite element formulation. A return map algorithm is presented in order to update the plastic variables, stress resultants and also to obtain the consistent elastoplastic moduli of the rod. The presented FE formulation is used to study snap-through buckling in a semi-circular arch subjected to an in-plane transverse load at its mid-section. The effect of various elastoplastic parameters as well as pre-twisting of the arch on its load-displacement curve are presented.</span> </p>
<p><span>The article will soon appear in IJNME and the same can be accessed at the following link: </span><span><span><a href="https://www.researchgate.net/publication/344344096_A_finite_element_formulation_for_a_direct_approach_to_elastoplasticity_in_special_Cosserat_rods">https://www.researchgate.net/publication/344344096_A_finite_element_form...</a></span></span></p>
</div></div></div>Sun, 25 Oct 2020 03:01:46 +0000Ajeet Kumar24673 at https://imechanica.orghttps://imechanica.org/node/24673#commentshttps://imechanica.org/crss/node/24673Phonons in chiral nanorods and nanotubes: a Cosserat rod based continuum approach
https://imechanica.org/node/23320
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/3514">phonon</a></div><div class="field-item odd"><a href="/taxonomy/term/6455">Cosserat rod</a></div><div class="field-item even"><a href="/taxonomy/term/139">Carbon nanotube</a></div><div class="field-item odd"><a href="/taxonomy/term/6462">chirality</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>A Cosserat rod based continuum approach is presented to obtain phonon dispersion curves of flexural, torsional, longitudinal, shearing and radial breathing modes in chiral nanorods and nanotubes. Upon substituting the continuum wave form in the linearized dynamic equations of stretched and twisted Cosserat rods, we obtain analytical expression of a coefficient matrix (in terms of the rod's stiffnesses, induced axial force and twisting moment) whose eigenvalues and eigenvectors give us frequencies and mode shapes, respectively, for each of the above phonon modes. We show that, unlike the case of achiral tubes, these phonon modes are intricately coupled in chiral tubes due to extension-torsion-inflation and bending-shear couplings inherent in them. This coupling renders the conventional approach of obtaining stiffnesses from the long wavelength limit slope of dispersion curves redundant. However, upon substituting the frequencies and mode shapes (obtained independently from phonon dispersion molecular data) in the eigenvalue-eigenvector equation of the above mentioned coefficient matrix, we are able to obtain all the stiffnesses (bending, twisting, stretching, shearing and all coupling stiffnesses corresponding to extension-torsion, extension-inflation, torsion-inflation and bending-shear couplings) of chiral nanotubes. Finally, we show unusual effects of the single-walled carbon nanotube's chirality as well as stretching and twisting of the nanotube on its phonon dispersion curves obtained from the molecular approach. These unusual effects are accurately reproduced in our continuum formulation.</p>
<p>The article will soon appear in Mathematics and Mechanics of Solids and it can also be accessed at the following link: <a href="https://www.researchgate.net/publication/333237562_Phonons_in_chiral_nanorods_and_nanotubes_a_Cosserat_rod_based_continuum_approach">https://www.researchgate.net/publication/333237562_Phonons_in_chiral_nan...</a></p>
</div></div></div>Fri, 24 May 2019 01:52:20 +0000Ajeet Kumar23320 at https://imechanica.orghttps://imechanica.org/node/23320#commentshttps://imechanica.org/crss/node/23320An asymptotic numerical method for continuation of spatial equilibria of special Cosserat rods
https://imechanica.org/node/22085
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/6455">Cosserat rod</a></div><div class="field-item odd"><a href="/taxonomy/term/11926">asymptotic numerical method</a></div><div class="field-item even"><a href="/taxonomy/term/5325">numerical continuation</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>We present an efficient numerical scheme based on asymptotic numerical method for continuation of spatial equilibria of special Cosserat rods. Using quaternions to represent rotation, the equations of static equilibria of special Cosserat rods are posed as a system of thirteen first order ordinary differential equations having cubic nonlinearity. The derivatives in these equations are further discretized to yield a system of cubic polynomial equations. As asymptotic-numerical methods are typically applied to polynomial systems having quadratic nonlinearity, a modified version of this method is presented in order to apply it directly to our cubic nonlinear system. We then use our method for continuation of equilibria of the follower load problem and demonstrate our method to be highly efficient when compared to conventional solvers based on the finite element method. Finally, we demonstrate how our method can be used for computing the buckling load as well as for continuation of postbuckled equilibria of hemitropic rods.</span></p>
<p>The article will soon appear in <em>Computer Methods in Applied Mechanics and Engineering</em>. It can also be accessed at the following link: <a href="https://www.researchgate.net/publication/322750460_An_asymptotic_numerical_method_for_continuation_of_spatial_equilibria_of_special_Cosserat_rods">https://www.researchgate.net/publication/322750460_An_asymptotic_numeric...</a></p>
</div></div></div>Sun, 28 Jan 2018 05:13:13 +0000Ajeet Kumar22085 at https://imechanica.orghttps://imechanica.org/node/22085#commentshttps://imechanica.org/crss/node/22085A thermo-elasto-plastic theory for special Cosserat rods
https://imechanica.org/node/21990
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/6455">Cosserat rod</a></div><div class="field-item odd"><a href="/taxonomy/term/10072">elasto-plasticity</a></div><div class="field-item even"><a href="/taxonomy/term/2903">thermoelasticity</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>A general framework is presented to model coupled thermo-elasto-plastic deformations in the theory of special Cosserat rods. The use of the one-dimensional form of the energy balance in conjunction with the one-dimensional entropy balance allows us to obtain an additional equation for the evolution of a temperature-like one-dimensional field variable together with constitutive relations for this theory. Reduction to the case of thermoelasticity leads us to the well known nonlinear theory of thermoelasticity for special Cosserat rods. Later on, additive decomposition is used to separate the thermoelastic part of the strain measures of the rod from their plastic counterparts. We then present the most general quadratic form of the Helmholtz energy per unit rod's undeformed length for both hemitropic and transversely isotropic rods. We also propose a prototype yield criterion in terms of forces, moments and hardening stress resultants as well as the associative flow rules for the evolution of plastic strain measures and hardening variables.</span></p>
<p><span>The article will soon appear in <em>Mathematics and Mechanics of solids</em> and can also be accessed at the following link: </span><span><span><a href="https://www.researchgate.net/publication/322113320_A_thermo-elasto-plastic_theory_for_special_Cosserat_rods">https://www.researchgate.net/publication/322113320_A_thermo-elasto-plast...</a></span></span></p>
</div></div></div>Tue, 02 Jan 2018 23:47:28 +0000Ajeet Kumar21990 at https://imechanica.orghttps://imechanica.org/node/21990#commentshttps://imechanica.org/crss/node/21990A one-dimensional Rod Model for Carbon Nanotubes
https://imechanica.org/node/10599
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/139">Carbon nanotube</a></div><div class="field-item odd"><a href="/taxonomy/term/6455">Cosserat rod</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>We recently published a paper in International Journal of Solids and Structures titled "A rod model for three dimensional deformations of single walled carbon nanotubes".(paper attached)</p>
<p><a href="http://www.sciencedirect.com/science/article/pii/S0020768311002149">http://www.sciencedirect.com/science/article/pii/S0020768311002149</a></p>
<p>There are several research papers dealing with continuum modeling of a nanotube using shell theory. Longer nanotubes, however, appear more as a one dimensional rod but there is almost no work towards modeling of a nanotube using rod theory. The objective of this paper is to model a nanotube using rod theory. It also highlights challenges and associated future research plans. Not to mention, a one dimensional rod model is advantageous both from theoretical and computational viewpoint.</p>
<p>Comments and feedback most welcome!</p>
</div></div></div>Tue, 19 Jul 2011 23:11:47 +0000Ajeet Kumar10599 at https://imechanica.orghttps://imechanica.org/node/10599#commentshttps://imechanica.org/crss/node/10599Error | iMechanica