Pure cross-anisotropy for geotechnical elastic potentials

The pure cross-anisotropy is understood as a special scaling of strain (or stress). The scaled tensor is used as an argument in the elastic stiffness (or compliance). Such anisotropy can be overlaid on the top of any elastic stiffness, in particular on one obtained from an elastic potential with its own stress-induced anisotropy. This superposition does not violate the Second Law. The method can be also applied to other functions like plastic potentials or yield surfaces, wherever some cross-anisotropy is desired. The pure cross-anisotropy is described by the sedimentation vector and at most two constants. Scaling with more than two purely anisotropic constants is shown impossible. The formulation was compared with experiments and alternative approaches. Static and dynamic calibration of the pure anisotropy is also discussed. Graphic representation of stiffness with the popular response envelopes requires some enhancement for anisotropy. Several examples are presented. All derivations and examples were accomplished using the algebra program Mathematica.

Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane Formulations

Coaptation characteristics are crucial in an assessment of the competence of reconstructed aortic valves. Shell or membrane formulations can be used to model the valve cusps coaptation. In this paper we compare both formulations in terms of their coaptation characteristics for the first time. Our numerical thin shell model is based on a combination of the hyperelastic nodal forces method and the rotation-free finite elements. The shell model is verified on several popular benchmarks for thin-shell analysis. The relative error with respect to reference solutions does not exceed 1–2%. We apply our numerical shell and membrane formulations to model the closure of an idealized aortic valve varying hyperelasticity models and their shear moduli. The coaptation characteristics become almost insensitive to elastic potentials and sensitive to bending stiffness, which reduces the coaptation zone.

Nonholonomic Systems With Redundant Degrees of Freedom Can Exploit Nonlinear Frequency Response to Improve Speed and Efficiency of Locomotion

Rigid body nonholonomic systems serve as models for locomotion of several terrestrial animals such as snakes as well as for fish-like swimming motion. Several well known nonholonomic systems have also found applications in the field of mobile robotics in everything from wheeled vehicles to articulated snake like robots. However, one aspect of their dynamics has remained unexplored. This is to do with the effects of increasing the degrees of freedom by adding additional ‘segments’ such as in a chain, with the joints between segments having a nonzero torsional stiffness. Such nonholonomic systems when subjected to periodic actuation or inputs have additional modes of oscillation. The interplay of the nonholonomic constraints, linear elastic potentials and additional degrees of freedom can produce rich frequency-amplitude response in the dynamics of the system and can lead to significantly higher speed and efficiency. In this paper we explore such dynamics with the example of a well known nonholonomic system, the Chaplygin sleigh and a variant of it with an additional degree of freedom. Such models can be expected to better match the dynamics of biological swimmers and have widespread applications for soft and under-actuated robots.