531 research outputs found
Modelling Rod-like Flexible Biological Tissues for Medical Training
This paper outlines a framework for the modelling of slender rod-like biological tissue structures in both global and local scales. Volumetric discretization of a rod-like structure is expensive in computation and therefore
is not ideal for applications where real-time performance is essential. In our approach, the Cosserat rod model is introduced to capture the global shape changes, which models the structure as a one-dimensional entity, while the
local deformation is handled separately. In this way a good balance in accuracy and efficiency is achieved. These advantages make our method appropriate for
the modelling of soft tissues for medical training applications
Finite volume approach for the instationary Cosserat rod model describing the spinning of viscous jets
The spinning of slender viscous jets can be described asymptotically by
one-dimensional models that consist of systems of partial and ordinary
differential equations. Whereas the well-established string models possess only
solutions for certain choices of parameters and set-ups, the more sophisticated
rod model that can be considered as -regularized string is generally
applicable. But containing the slenderness ratio explicitely in the
equations complicates the numerical treatment. In this paper we present the
first instationary simulations of a rod in a rotational spinning process for
arbitrary parameter ranges with free and fixed jet end, for which the hitherto
investigations longed. So we close an existing gap in literature. The numerics
is based on a finite volume approach with mixed central, up- and down-winded
differences, the time integration is performed by stiff accurate Radau methods
Modelling methodology of MEMS structures based on Cosserat theory
Modelling MEMS involves a variety of software tools that deal with the
analysis of complex geometrical structures and the assessment of various
interactions among different energy domains and components. Moreover, the MEMS
market is growing very fast, but surprisingly, there is a paucity of modelling
and simulation methodology for precise performance verification of MEMS
products in the nonlinear regime. For that reason, an efficient and rapid
modelling approach is proposed that meets the linear and nonlinear dynamic
behaviour of MEMS systems.Comment: Submitted on behalf of EDA Publishing Association
(http://irevues.inist.fr/handle/2042/16838
A class of nonholonomic kinematic constraints in elasticity
We propose a first example of a simple classical field theory with
nonholonomic constraints. Our model is a straightforward modification of a
Cosserat rod. Based on a mechanical analogy, we argue that the constraint
forces should be modeled in a special way, and we show how such a procedure can
be naturally implemented in the framework of geometric field theory. Finally,
we derive the equations of motion and we propose a geometric integration scheme
for the dynamics of a simplified model.Comment: 28 pages, 7 figures, uses IOPP LaTeX style (included) (v3: section 2
entirely rewritten
Energy minimizers of the coupling of a Cosserat rod to an elastic continuum
We formulate the static mechanical coupling of a geometrically exact Cosserat rod to an elastic continuum. The coupling conditions accommodate for the diïŹerence in dimension between the two models. Also, the Cosserat rod model incorporates director variables, which are not present in the elastic continuum model. Two alternative coupling conditions are proposed, which correspond to two diïŹerent conïŹguration trace spaces. For both we show existence of solutions of the coupled problems. We also derive the corresponding conditions for the dual variables and interpret them in mechanical terms
Lie Symmetry Analysis for Cosserat Rods
We consider a subsystem of the Special Cosserat Theory of Rods and construct
an explicit form of its solution that depends on three arbitrary functions in
(s,t) and three arbitrary functions in t. Assuming analyticity of the arbitrary
functions in a domain under consideration, we prove that the obtained solution
is analytic and general. The Special Cosserat Theory of Rods describes the
dynamic equilibrium of 1-dimensional continua, i.e. slender structures like
fibers, by means of a system of partial differential equations.Comment: 12 Pages, 1 Figur
Importance and effectiveness of representing the shapes of Cosserat rods and framed curves as paths in the special Euclidean algebra
We discuss how the shape of a special Cosserat rod can be represented as a
path in the special Euclidean algebra. By shape we mean all those geometric
features that are invariant under isometries of the three-dimensional ambient
space. The representation of the shape as a path in the special Euclidean
algebra is intrinsic to the description of the mechanical properties of a rod,
since it is given directly in terms of the strain fields that stimulate the
elastic response of special Cosserat rods. Moreover, such a representation
leads naturally to discretization schemes that avoid the need for the expensive
reconstruction of the strains from the discretized placement and for
interpolation procedures which introduce some arbitrariness in popular
numerical schemes. Given the shape of a rod and the positioning of one of its
cross sections, the full placement in the ambient space can be uniquely
reconstructed and described by means of a base curve endowed with a material
frame. By viewing a geometric curve as a rod with degenerate point-like cross
sections, we highlight the essential difference between rods and framed curves,
and clarify why the family of relatively parallel adapted frames is not
suitable for describing the mechanics of rods but is the appropriate tool for
dealing with the geometry of curves.Comment: Revised version; 25 pages; 7 figure
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