Abstract
FFT-based solvers are increasingly used by many researcher groups interested in modelling the mechanical behavior associated to a heterogeneous microstructure. A development is reported here that concerns the viscoelastic behavior of composite structures generally studied experimentally through Dynamic Mechanical Analysis (DMA). A parallelized computation code developed with complex-valued quantities provides virtual DMA experiments directly in the frequency domain on a heterogeneous system described by a voxel grid of mechanical properties. The achieved precision and computation times are very good. An effort has been made to illustrate the application of such a virtual DMA tool through two examples from the literature: the modelling of glassy/amorphous systems at a small scale and the modelling of experimental data obtained in temperature sweeping mode by DMA on a particulate composite made of glass beads and a polystyrene matrix, at a larger scale. Both examples show how virtual DMA can contribute to question, analyze, and understand relaxation phenomena on either theoretical or experimental points of view.
Highlights
Dynamic Mechanical Analysis (DMA) is known to be a privileged tool to study materials whose rheological behavior is viscoelastic by nature, i.e. introduces irreversible dissipation of mechanical energy into heat
It is in that direction that very recent computations of virtual DMA kind have been performed with FFT solvers
The effective mechanical behavior resulting from various models considered for the multiscale morphological microstructure description has FFT solver for virtual Dynamic Mechanical Analysis experiments been successfully computed in 3D with an FFT solver in space and harmonic complex treatment of the dynamic part
Summary
Dynamic Mechanical Analysis (DMA) is known to be a privileged tool to study materials (especially polymers and rubbers) whose rheological behavior is viscoelastic by nature, i.e. introduces irreversible dissipation of mechanical energy into heat. The technique measures a conservative (storage) or dissipative (loss) modulus or compliance, which are the real and imaginary parts of their complex nature M∗(ω) = M ′(ω) + jM ′′(ω) for instance for the modulus It relies on harmonic steady-state excitations in strain, applied at pulsation ω on a material specimen and on the recording of the corresponding output stress signal. Complex algebra gives eventually access to M ′(ω) and M ′′(ω) with a sweep in frequency allowing for full dynamical characterization of the material. Such a spectroscopic probing of the material exists in many different fields of physics like in thermal science to produce thermal conductivity/diffusivity measurements (Cahill 1990) but the main corpus of publications probably resorts to dielectric properties measurements (Nielsen and Landel 1994). Experimental data on the susceptibility of physical processes as function of frequency is, in general, a central tool to develop physical model of relaxation processes (Havriliak Jr. and Havriliak 1995; Jonscher 1996)
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