On the influence of pseudoelastic material behaviour in planar shape-memory tubular continuum structures

Abstract

For planar tubular continuum structures based on precurved shape memory alloy tubes a beam model with respect to the pseudoelastic material behaviour of NiTi is derived. Thereunto a constitutive material law respecting tension-compression asymmetry as well as hysteresis is used. The beam model is then employed to calculate equilibrium curvatures of concentric tube assemblies without clearance between the tubes. In a second step, the influence of clearance is approximated to account for non-concentric tube assemblies. These elastokinematic results are integrated into a purely kinematic model to describe the cannula path under the presence of material hysteresis and clearance. Finally a photogrammetric measurement system is used to track the path of an exemplary two-tube continuum structure to examine the accuracy of the proposed model. It is shown that material hysteresis leads to a hysteresis phenomena in the path of the tubular continuum structure.

Towards optimal control of concentric tube robots in stereotactic neurosurgery

“…The main focus of our future work will be to integrate extended mechanical models, as proposed in the literature. Here, the test rig presented in [18] will play an important role. The presented methods already show that there is a huge potential of optimization-based surgical instrument design and surgical planning, though.…”

“…In order to achieve high curvatures of the robot and thereby also high reversible strains in the material, the pseudoelastic effect of shape memory alloys such as NiTi is used [16]. With such materials elastic strains in the range of 4% to 6% (for polycrystals) are realizable [17] with the disadvantage of introducing a nonlinear and hysteretic stressstrain-behaviour into the mechanical system [18]. Together with necessary tube-to-tube clearances and contact-based friction forces between these tubes, this results in a hysteretic tip position path [19].…”

“…Then, also effects related to material induced hysteresis can be taken into account. If, in addition, the hysteresis of shape memory alloys is considered, as in [18], the curvature of the cannula depends on its history and, thus, not only on the current state x. Torsional instabilities as well as friction forces are known for similar effects on the tip position [19,20]. Whereas friction forces are still an active field of research, elastostatic instabilities are well described in the literature [15,24,25].…”

“…Both technical boundary conditions, such as parameter ranges, mechanical material characteristics (cf [18]. ), and medical aspects, such as intolerable lateral movements of the cannula or the structure of the brain, have to be taken into account as boundary conditions on tube trajectories.…”

Data augmentation for design of concentric tube continuum robots by generative adversarial networks

“…Therefore, the planning's overall accuracy heavily relies on the accuracy of the used physical model. While several publications focus on increasing model coverage [6,7], the downside is a further increased modeling effort with many phenomenological parameters to be measured or identified and a potential to overfit these models. Hence, learning-based approaches for modeling CTCRs are seen as promising [8].…”