Resonance meters for viscoelasticity measurement Department of Biophysics and Physical Chemistry, Faculty of Pharmacy, Heyrovskeho 1203, 500 05 Hradec Kralove, Czech Republic DELTER v.o.s. Lohenice 43, 535 01 Prelouc, Czech Republic

Introductory remarks Quantification of relations between strains and stresses in dynamic loading is one of the key tasks of biomechanics. In contrast to static loading, in dynamic loading energy losses play a relevant role. Viscoelasticity must thus be taken into account. Rheological viscoelastic models are currently applied on this field. Nevertheless, they do not ensure a satisfactory approximation. There are two main sources of discrepancy between the behavior of rheological models and the behavior of real viscoelastic structures. The first issue is the problematic disregard of the influence of inertial forces. The second lies in the fact that the current rheological models use lumped parameters which are incongruous with the distributed parameters in real bodies. Complex moduli or, more generally, complex stiffness's, provide adequate tools for satisfactory characterizing dynamic behavior of linear mechanical systems.

Principle of resonance apparatuses (RMA) RMA measure complex stiffness and complex moduli. RMA are based on the measurement of mechanical resonance of samples of biological materials. Resonance methods represent an alternative to direct measurements of frequency characteristics (DMA apparatuses). Crucial advantage of resonance meters consists in the high sensitivity of measurements and the elimination of errors resulting from the effect of the mass of the sample and the mass of the moving part of the meter on measurement results. Moreover, its design enables contactless sensing, which further improves the accuracy and precision. Application of this principle leads to a reduction of costs and elimination of some errors.

Inverse problem solutions inertial body sample F Fundamental equations: l0 Complex stiffness definition: Complex modulus definition: Complex stiffness of system sample-inertial body in periodic mode: Loss modulus of sample: Storage modulus of sample:

RMA – tensile measurements

RMA – measurements in bending loading

RMA – measurements of surface stiffness

Solutions of problems of mechanical compatibility Potential application of measurement of viscoelasticity in biomechanics Solutions of problems of mechanical compatibility   Origin of additional stresses in mechanically incompatible bodies. Tangent stresses in tensile loading.   Condition of mechanical compatibility is the same complex stiffness in all bodies in contact.

Solutions of problems of complex mechanical systems Potential application of measurement of viscoelasticity in biomechanics Solutions of problems of complex mechanical systems Knowledge of stiffness's of partial bodies enables calculation of stiffness of whole system F Serial systems body1 body2 body n body 3 L1 L2 L3 Parallel systems F 1 2 n F1 F2 F3 L