A scheme for identification of time-variable shear and bulk modulus of plant viscoelastic materials
Anna Stankiewicz
Akademia Rolnicza w LublinieKrzysztof Gołacki
Akademia Rolnicza w LublinieAbstract
The aim of the paper is to investigate a computer identification algorithm for determining the time-varying shear and bulk modulus of linear viscoelastic materials based on experimentally obtained stress and strain uniaxial relaxation functions of an cylindrical specimens of the tested material is proposed. On the first stage of the identification procedure the models of the uniaxial relaxation functions are determined and next, on the second stage, the shear and bulk modulus are computed. It is proved that if four parameter Maxwell models are used to approximate the uniaxial relaxation functions, then the shear and bulk modulus can be given as a linear combination of exponential functions and multiple convolution integrals of original and modified Bessel functions. For least squares identification of uniaxial relaxation functions by positive sums of exponentials the Prony's method is applied. Applying the scheme proposed the time-dependent shear and bulk modulus of the beet sugar root samples are computed using discrete time-measurements of the force relaxation of an unconfined and of a laterally constrained cylindrical specimens of the material obtained in double independent stress relaxation tests.
Keywords:
viscoelasticity, stress relaxation test, shear and bulk modulus, identification algorithm, Bessel functionsReferences
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Akademia Rolnicza w Lublinie
Akademia Rolnicza w Lublinie
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