Pseudomomentum: origins and consequences

Singh, Harkishan; Hanna, James

doi:10.1007/s00033-021-01507-9

Cited by 7 publications

(4 citation statements)

References 79 publications

(218 reference statements)

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“…Kinematic models for BT catheters in curved channels that have been introduced were based on models for steerable needles. [9][10][11] The modeling of deformations and associated forces and moments of slender elastic rods inside rigid (circular) channels or environment has been the topic of several studies for different applications: (i) drill string buckling, [24][25][26][27] (ii) serpentine locomotion, [28][29][30] (iii) concentric tube instruments, [31][32][33] and (iv) (steerable) catheter and guidewire insertion, [34][35][36][37][38][39][40][41][42][43][44] among others. Due to geometric, material, and physical nonlinearities in the problem formulation, most work resorts to numerical approaches.…”

Section: Related Workmentioning

confidence: 99%

Multibody dynamic modeling of the behavior of flexible instruments used in cervical cancer brachytherapy

Straathof,

Meijaard,

van Vliet‐Pérez

et al. 2024

Medical Physics

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BackgroundThe steep radiation dose gradients in cervical cancer brachytherapy (BT) necessitate a thorough understanding of the behavior of afterloader source cables or needles in the curved channels of (patient‐tailored) applicators.PurposeThe purpose of this study is to develop and validate computer models to simulate: (1) BT source positions, and (2) insertion forces of needles in curved applicator channels. The methodology presented can be used to improve the knowledge of instrument behavior in current applicators and aid the development of novel (3D‐printed) BT applicators.MethodsFor the computer models, BT instruments were discretized in finite elements. Simulations were performed in SPACAR by formulating nodal contact force and motion input models and specifying the instruments’ kinematic and dynamic properties. To evaluate the source cable model, simulated source paths in ring applicators were compared with manufacturer‐measured source paths. The impact of discrepancies on the dosimetry was estimated for standard plans. To validate needle models, simulated needle insertion forces in curved channels with varying curvature, torsion, and clearance, were compared with force measurements in dedicated 3D‐printed templates.ResultsComparison of simulated with manufacturer‐measured source positions showed 0.5–1.2 mm median and <2.0 mm maximum differences, in all but one applicator geometry. The resulting maximum relative dose differences at the lateral surface and at 5 mm depth were 5.5% and 4.7%, respectively. Simulated insertion forces for BT needles in curved channels accurately resembled the forces experimentally obtained by including experimental uncertainties in the simulation.ConclusionThe models developed can accurately predict source positions and insertion forces in BT applicators. Insights from these models can aid novel applicator design with improved motion and force transmission of BT instruments, and contribute to the estimation of overall treatment precision. The methodology presented can be extended to study other applicator geometries, flexible instruments, and afterloading systems.

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Section: Related Workmentioning

confidence: 99%

Multibody dynamic modeling of the behavior of flexible instruments used in cervical cancer brachytherapy

Straathof,

Meijaard,

van Vliet‐Pérez

et al. 2024

Medical Physics

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“…This question would be better explored in the context of shells rather than plates. The retention of the divergence form of the equations after tangential projection, a structure made clear in early work on bulk elasticity [4] and in recent approaches to solid surfaces [87], likely reflects a connection between the statements of conservation of momentum and pseudomomentum [116].…”

Section: Additional Discussionmentioning

confidence: 95%

Some observations on variational elasticity and its application to plates and membranes

Hanna

2019

Z. Angew. Math. Phys.

Self Cite

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Energies and equilibrium equations for thin elastic plates are discussed, with emphasis on several issues pertinent to recent approaches in soft condensed matter. Consequences of choice of basis, choice of invariant strain measures, and of approximating material energies as purely geometric in nature, are detailed. Ambiguities in the definitions of energies based on small-strain expansions, and in a typical informal process of dimensional reduction, are noted. A simple example serves to demonstrate that a commonly used bending energy has undesirable features, and it is suggested that a new theory based on Biot strains be developed. A compact form of the variation of a plate energy is presented. Throughout, the divergence form of equations is emphasized. An appendix relates the naive approach adopted in the main text with standard quantities in continuum mechanics. * hannaj@vt.edu 1 Here invariance will be understood to mean that under general coordinate transformations, rather than the more restricted Cartesian sense found in some continuum mechanics texts. 2 I claim to be neither physicist nor mechanician but merely, to borrow Truesdell's usage, an idiot [1].

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“…But herein, we focus on a continuum body, where space is defined as attached to and co‐moving with the matter. Therefore, we may call it a “configurational” space, see [59] for the history of this distinction. We obtain the so‐called Rund–Trautman identity in this configurational space. …”

Section: Introductionmentioning

confidence: 99%

Energy based methods applied in mechanics by using the extended Noether's formalism

Abali

2023

Z Angew Math Mech

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Physical systems are modeled by field equations; these are coupled, partial differential equations in space and time. Field equations are often given by balance equations and constitutive equations, where the former are axiomatically given and the latter are thermodynamically derived. This approach is useful in thermomechanics and electromagnetism, yet challenges arise once we apply it in damage mechanics for generalized continua. For deriving governing equations, an alternative method is based on a variational framework known as the extended Noether's formalism. Its formal introduction relies on mathematical concepts limiting its use in applied mechanics as a field theory. In this work, we demonstrate the power of extended Noether's formalism by using tensor algebra and usual continuum mechanics nomenclature. We demonstrate derivation of field equations in damage mechanics for generalized continua, specifically in the case of strain gradient elasticity.

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Pseudomomentum: origins and consequences

Cited by 7 publications

References 79 publications

Multibody dynamic modeling of the behavior of flexible instruments used in cervical cancer brachytherapy

Multibody dynamic modeling of the behavior of flexible instruments used in cervical cancer brachytherapy

Some observations on variational elasticity and its application to plates and membranes

Energy based methods applied in mechanics by using the extended Noether's formalism

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