Cosserat Theories: Shells, Rods and Points

Rubin, M. B.

doi:10.1007/978-94-015-9379-3

Cited by 281 publications

(180 citation statements)

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“…By substituting kinematic relations (10) into generalized Hooke 's law (11) and the obtained result into the equations of motion (8) the differential equations of motion in form of displacements and rotation can be obtained. In vector form they can be represented as the following…”

Section: -D Micropolar Elasticity In Orthogonal Coordinatesmentioning

confidence: 99%

“…The mechanics of generalized continua has long history of development. Since the publication of landmark book of Cosserat brothers [6] in the literature there are various known generalizations of the classical or Cauchy continuum which are summarized in many books [7][8][9][10][11][12] and papers [13][14][15][16][17]. Especially we have to mention remarkable books of Eringen [18] and Nowaski [19,20] and fundamental treatise of Truesdell and Toupin [21].…”

Section: Introductionmentioning

confidence: 99%

“…The model of micropolar beams based on the classical Euler-Bernoulli hypothesis has been considered in [27,28] and on Timoshenko's hypothesis in [29][30][31][32]. Various models of micropolar cured rods have been considered in [3,11,25,[33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

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Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Zozulya

2017

Curved and Layered Structures

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New models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress and strain tensors, vectors of displacements and rotation and body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then in the same way as in the theory of elasticity, system of differential equations in term of displacements and boundary conditions for Fourier coefficients have been obtained. The Timoshenko's and EulerBernoulli theories are based on the classical hypothesis and 2-D equations of linear micropolar elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scale when taking into account micropolar couple stress and rotation effects.

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Section: -D Micropolar Elasticity In Orthogonal Coordinatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Zozulya

2017

Curved and Layered Structures

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“…The cluster of markers was characterized with Triangular Cosserat Point Elements (TCPEs) defined by all combinations of three markers and the kinematics of each TCPE was analysed using the nonlinear continuum mechanics theory of a Cosserat point with homogeneous deformations 30 . The main idea of the TCPE method is to use physical deformation parameters to identify instantaneous subsets of TCPEs which predict the best possible bone pose in the presence of STA.…”

Section: Introductionmentioning

confidence: 99%

Bone Pose Estimation in the Presence of Soft Tissue Artifact Using Triangular Cosserat Point Elements

Solav¹,

Rubin²,

Cereatti³

et al. 2017

Preprint

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Accurate estimation of the position and orientation (pose) of a bone from a cluster of skin markers is limited mostly by the relative motion between the bone and the markers, which is known as the Soft Tissue Artifact (STA). This work presents a method, based on continuum mechanics, to describe the kinematics of a cluster affected by STA. The cluster is characterized by Triangular Cosserat Point Elements (TCPEs) defined by all combinations of three markers.The effects of the STA on the TCPEs are quantified using three parameters describing the strain in each TCPE and the relative rotation and translation between TCPEs. The method was evaluated using previously collected ex-vivo kinematic data. Femur pose was estimated from 12 skin markers on the thigh, while its reference pose was measured using bone pins. Analysis revealed that instantaneous subsets of TCPEs exist which estimate bone position and orientation more accurately than the Procrustes Superimposition applied to the cluster of all markers. It has been shown that some of these parameters correlate well with femur pose errors, which suggests that they can be used to select, at each instant, subsets of TCPEs leading an improved estimation of the underlying bone pose.2

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“…In fact, many solutions for loop formation have been described by Love (2013) as early as 1924 based on a graphical argument. A more contemporary account was provided by Antman (1995) and Rubin (2013) in a numerical context. Pai (2002) appears to have been the first to advocate and implement the Cosserat rod theory for surgical simulation.…”

Section: Physical Based Simulationsmentioning

confidence: 99%

Real time simulation of inextensible surgical thread using a Kirchhoff rod model with force output for haptic feedback applications

Wang

Fratarcangeli

Ruimi

et al. 2017

International Journal of Solids and Structures

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International Journal of Solids and Structures (ISSN: 0020-7683)Citation for the published paper: Wang, Z. ; Fratarcangeli, M. ; Ruimi, A. et al. (2017) "Real time simulation of inextensible surgical thread using a Kirchhoff rod model with force output for haptic feedback applications". International Journal of Solids and Structures, http://dx.doi.org/10.1016/j.ijsolstr.2017.02.017Downloaded from: http://publications.lib.chalmers.se/publication/248860 Notice: Changes introduced as a result of publishing processes such as copy-editing and formatting may not be reflected in this document. For a definitive version of this work, please refer to the published source. Please note that access to the published version might require a subscription.Chalmers Publication Library (CPL) offers the possibility of retrieving research publications produced at Chalmers University of Technology. It covers all types of publications: articles, dissertations, licentiate theses, masters theses, conference papers, reports etc. Since 2006 it is the official tool for Chalmers official publication statistics. To ensure that Chalmers research results are disseminated as widely as possible, an Open Access Policy has been adopted. The CPL service is administrated and maintained by Chalmers Library.(article starts on next page)International Journal of Solids and Structures 113-114 (2017) 192-208 Contents lists available at ScienceDirect a b s t r a c tWe discuss the dynamics of an inextensible thin Kirchhoff rod used in the modeling of surgical threads, and demonstrate a very efficient scheme to not only simulate the motion of the thread in real-time (up to 1 ms per frame) but also obtain the constraint axial forces which can be fed back to a haptic system. The numerical scheme is based on a family of schemes called geometric or discrete variational integrators guaranteeing that the momentum and energy are exactly conserved over long periods of time for conservative systems. Besides, we report on an efficient numerical procedure to handle the inextensibility of the thread through physically based Lagrange multipliers, as well as the internal dissipation of the thread. We have performed simulations to verify the capabilities of our model to conserve momentum and energy, accurately calculate the axial constraint forces along the thread for haptic feedback, and capture bending-torsion coupling leading to the formation of plectonemes. While many of the ideas are well known in the computer graphics community (especially in hair modeling), we have implemented several improvements for the specific purpose of speeding up the computations for developing physically based haptic interfaces for knot tying and suturing.

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Cosserat Theories: Shells, Rods and Points

Cited by 281 publications

References 0 publications

Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Bone Pose Estimation in the Presence of Soft Tissue Artifact Using Triangular Cosserat Point Elements

Real time simulation of inextensible surgical thread using a Kirchhoff rod model with force output for haptic feedback applications

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