[SY-M2] VISCOELASTIC BEHAVIOUR OF HETEROGENEOUS MATERIALS STUDIED THANKS TO AN EXTENSION OF CRAFT SOFTWARE IN HARMONIC REGIME
Following the routes opened by the resort to spectral solvers applied on real composite microstructures to analyse the homogenization problem in elasticity, we extended a FFT approach implemented in the CRAFT solver [1] to viscoelastic materials. The idea is to propose a virtual Dynamical Mechanical Analysis experiment applied on heterogeneous microstructures. DMA performs a frequency analysis of the transfer function of the material by applying a sinusoidal harmonic steady-state regime. The transfer function (modulus, relaxation, compliance... quantities) is complex with classical storage and loss components (real and imaginary parts) [2]. It offers a full frequency characterization of the material constitutive law which can be applied afterwards in all cases of temporal excitations. CRAFT code and its central Lippmann-Schwinger equation are then solved in complex variables.
Examples will be given of various microstructures made of two individual viscoelastic constituents assumed to behave according to a standard 3-parameter Voigt rheological model (spring connected in series with a Voigt unit [2]). As already shown [3], the key resulting effect on the homogenized effective material is the appearance of an additional fading memory term i.e. of a transfer function with broadened spectrum of relaxation times. Following this fact and connections established with fractional rheological models, we will show that a very efficient effective model can describe the mesoscopic behaviour of a great variety of microstructures.
REFERENCES
[1] H. Moulinec, P. Suquet, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comput. Methods Appl. Mech. Engrg., 157, 69-94, 1998.
[2] N.W. Tschoegl, The Phenomenological Theory of Linear Viscoelastic Behavior, An Introduction, Springer Verlag, 1989.
[3] R. Brenner, P. Suquet, Overall response of viscoelastic composites and polycrystals: exact asymptotic relations and approximate estimates. Int. J. Sol. Struct., 50(10), 1824-1838, 2013.
[4] S. Andre, Y. Meshaka, C.Cunat, Rheological constitutive equation of solids: a link between models based on irreversible thermodynamics and on fractional order derivative
equations, Rheologica Acta, 42, 500-515.
Examples will be given of various microstructures made of two individual viscoelastic constituents assumed to behave according to a standard 3-parameter Voigt rheological model (spring connected in series with a Voigt unit [2]). As already shown [3], the key resulting effect on the homogenized effective material is the appearance of an additional fading memory term i.e. of a transfer function with broadened spectrum of relaxation times. Following this fact and connections established with fractional rheological models, we will show that a very efficient effective model can describe the mesoscopic behaviour of a great variety of microstructures.
REFERENCES
[1] H. Moulinec, P. Suquet, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comput. Methods Appl. Mech. Engrg., 157, 69-94, 1998.
[2] N.W. Tschoegl, The Phenomenological Theory of Linear Viscoelastic Behavior, An Introduction, Springer Verlag, 1989.
[3] R. Brenner, P. Suquet, Overall response of viscoelastic composites and polycrystals: exact asymptotic relations and approximate estimates. Int. J. Sol. Struct., 50(10), 1824-1838, 2013.
[4] S. Andre, Y. Meshaka, C.Cunat, Rheological constitutive equation of solids: a link between models based on irreversible thermodynamics and on fractional order derivative
equations, Rheologica Acta, 42, 500-515.