Mechanical Properties of Long Leaves: Experiment and Theory

The static properties of leaves with parallel venation from terrestrial orchids of the genus Epipactis were modelled as coupled elastic rods using the geometrically exact Cosserat theory and the resulting boundary-value problem was solved numerically using a method from Shampine, Muir and Xu. The response of the leaf structure to the applied force was obtained from preliminary measurements. These measurements allowed the Young’s modulus of the Epipactis leaves to be determined. The appearance of wrinkles and undulation characteristics for some leaves has been attributed to the small torsional stiffness of the leaf edges.

An Integrated Multi-Sensor Network for Adaptive Grasping of Fragile Fruits: Design and Feasibility Tests

Secure grasping of fragile fruits and other agricultural products without potential slip and damage is still a challenge due to the size and shape varying, bruise susceptible, as well as hardness changing during fruit and vegetable maturation. In the robotic grasping process, the mechanical damage mainly depends upon the aggressiveness of the gripper and the sensitivity of the product to the damage. In this study, a flexible gripper integrated with multi-sensor network is designed and tested. The network proposed includes three kinds of sensors that enable the gripper to grasp various products with the sense of touch and visual perception. Particular attention has been attached to the sensors applied between the fingers, and this makes sensing and grasping capabilities improved. To create an accurate grasping system, a grasping algorithm and the force control model are proposed for any bending state based on Cosserat theory. The boundary detection is included in the grasping algorithm, detecting the shape edge by some certain point calculation. The created grasping system guarantees mechanical compliance by evaluating and adjusting the finger status including force, angle, and direction. Multi-group tests have been done on grasping several objects of different sizes and materials in daily life. The relationship between force, bending, and surface material is also analyzed and compared under different conditions. The numerical comparisons related to the measurement error are analyzed based on their standard deviations. Experimental results indicate that this flexible manipulator with proposed system and strategy has better grasping ability for fragile fruits with its good flexibility and dexterity.

A Cosserat Model of Elastic Solids Reinforced by a Family of Curved and Twisted Fibers

A Cosserat theory for fiber-reinforced elastic solids developed in Steigmann (2012) is generalized to accommodate initial curvature and twist of the fibers. The basic variables of the theory are a conventional deformation field and a rotation field that describes the local fiber orientation. Constraints on these fields are introduced to model the materiality of the fibers with respect to the underlying matrix deformation. A variational argument delivers the relevant equilibrium equations and boundary conditions and furnishes the interpretation of the Lagrange multipliers associated with the constraints as shear tractions acting on the fiber cross sections. Finally, the theory of material symmetry for such solids is developed and applied to the classification of some explicit constitutive functions.

Anisotropic Constitutive Model of Intermittent Columnar Jointed Rock Masses Based on the Cosserat Theory

In this work, an anisotropic constitutive model of hexagonal columnar jointed rock masses is established to describe the distribution law of deformation and the failure of columnar joint caverns under anisotropic conditions, and is implemented to study the columnar jointed rock mass at the dam site of the Baihetan Hydropower Station on the Jinsha River. The model is based on the Cosserat theory and considers the mesoscopic bending effect on the macroscopic mean. The influences of joint plane inclination on equivalent anisotropic elastic parameters are discussed via the introduction of an off-axis transformation matrix and the analysis of an example. It is also pointed out that the six-prism columnar jointed rock mass changes from transverse isotropy to anisotropy under the influence of the angle. A numerical calculation program of the Cosserat constitutive model is developed and is applied to the simulation calculation of a Baihetan diversion tunnel to compare and analyze the respective plastic zones and stress distributions after tunnel excavation under both isotropic and anisotropic conditions. The results reveal that, compared with the isotropic model, the proposed Cosserat anisotropic model better reflects the state of stress and asymmetric distribution of the plastic zone after tunnel excavation, and the actual deformation of the surrounding rock of the tunnel is greater than that calculated by the isotropic method. The results aid in a better understanding of the mechanical properties of rock masses.

On duality between Cosserat elasticity and fractons

We present a dual formulation of the Cosserat theory of elasticity. In this theory a local element of an elastic body is described in terms of local displacement and local orientation. Upon the duality transformation these degrees of freedom map onto a coupled theory of a U(1) vector-valued one-form gauge field and an ordinary U(1) gauge field. We discuss the degrees of freedom in the corresponding gauge theories, relation to symmetric tensor gauge theories, the defect matter and coupling to the curved space.

Material Symmetries in Homogenized Hexagonal-Shaped Composites as Cosserat Continua

In this work, material symmetries in homogenized composites are analyzed. Composite materials are described as materials made of rigid particles and elastic interfaces. Rigid particles of arbitrary hexagonal shape are considered and their geometry described by a limited set of parameters. The purpose of this study is to analyze different geometrical configurations of the assemblies corresponding to various material symmetries such as orthotetragonal, auxetic and chiral. The problem is investigated through a homogenization technique which is able to carry out constitutive parameters using a principle of energetic equivalence. The constitutive law of the homogenized continuum has been derived within the framework of Cosserat elasticity, wherein the continuum has additional degrees of freedom with respect to classical elasticity. A panel composed of material with various symmetries, corresponding to some particular hexagonal geometries defined, is analyzed under the effect of localized loads. The results obtained show the difference of the micropolar response for the considered material symmetries, which depends on the non-symmetries of the strain and stress tensor as well as on the additional kinematical and work-conjugated statical descriptors. This work underlines the importance of resorting to the Cosserat theory when analyzing anisotropic materials.