ABSTRACT of the Doctoral Thesis

Mechanical Properties and Finite Element Simulation of Spider Tactile Hairs

by Hans-Erich Dechant (2001)

Striving towards an in depth understanding of stimulus transformation in arthropod tactile hairs, the mechanical events associated with tactile stimulation were studied. Two components of the hair contribute to these mechanical events: The hair's articulation with its specific stiffness characteristics and the hair shaft which is predominantly bent. An experimental device was developed to investigate the mechanical properties - namely the forces occurring at the joint and the stiffness characteristics of the joint - of the hair experimentally. These force measurements are based on the deflection of a calibrated glass fibre which introduces the load to the investigated structures. Applying this method forces in the range of micro-Newtons can be measured.

To describe the properties of the articulation a mathematical model of the directional characteristics was developed. The mechanical directionality of the joints of tactile hairs of the wandering spider Cupiennius salei was determined by measuring the torsional stiffness associated with the deflection of the hair in different directions. Data on insect filiform hairs and spider trichobothria in the literature confirm the applicability of the model developed in the present work to a wide range of cuticular hairs. Despite obvious structural differences the directional characteristics of all these joints can be described quantitatively by only three parameters (sometimes even two suffice):
(i) the torsional stiffness in the preferred direction of deflection,
(ii) the torsional stiffness in the direction transversal to the preferred one, and
(iii) in some cases the torsional stiffness associated with deflection away from the preferred direction.
An equation describing the deflection angles for constant load in different directions is derived.

Further attention was given to the properties of the hair shaft. Considering hair diameter, wall thickness, and curvature, the hair is subdivided into six regions with its specific mechanical properties. Each of these regions is related to different mechanical functions. A Finite Element Model was developed to investigate the interactions between hair shaft bending and joint deflection and its influence to stimulus transformation.

A tarsal tactile hair of the spider Cupiennius salei was taken as an example to apply the model to a real hair. An iterative method was applied to obtain material data for the investigated hair shaft. This method takes advantage of the force data received from the deflection method with glass fibres mentioned above. When the hair is touched by a plane parallel to the tarsus surface the point of stimulus contact moves towards the hair base with increasing load and hair deflection. Thereby the effective lever arm is reduced protecting the hair against breaking near its base. The mechanical working range of the hair at the same time increases implying higher mechanical sensitivity for small deflections than for large deflections. The major stresses within the hair shaft are axial stresses due to bending. The position of stress maxima moves along the shaft with the movement of the stimulus contact point. Remarkably, the amplitude of this maximum hardly changes with increasing loading force due to the way the hair shaft is deflected by the stimulus. Maximum stresses change with different material properties, at the same time the dependence of the maximum stresses on the hair shaft's Young's modulus corresponds remarkably to the dependence of the strength values found in the literature on cuticle's Young's modulus.

Furthermore the 3-dimensional sensitivity characteristic of the entire structure was simulated. The 3-dimensional simulations show, that each single hair has a "blind spot" in its sensitivity distribution which is situated near a zone with extreme high sensitivity.

revised 011107 (hjb)