Time domain finite element estimates of dynamic stiffness of viscoelastic composites with stiff spherical inclusions

Abstract

a b s t r a c tA weighted residual time domain unstructured mesh finite element approach was used to obtain numerical estimates for the dynamic stiffness of medium and high stiffness contrast composites consisting of viscoelastic epoxy matrix filled with stiff spherical inclusions. Both random and regular microstructure composites were studied. It was shown that over the broad temperature and inclusion fraction ranges studied, the generalized self-consistent model ( Christensen and Lo, 1979 ) provided accurate predictions for the effective dynamic stiffness of random composites obeying classical Percus-Yevick hard sphere statistics. Assuming sphere flocculation, we have studied the role of microstructural effects and found that upon increasing stiffness contrast, they become progressively more important for both the effective storage and loss moduli. As a consequence, for the reliable predictions of effective stiffness of high contrast composites with rubber like matrices, one should necessarily use homogenization models accounting not only for the inclusion concentration but also for the finer microstructural details. However, it was also found that for such high stiffness contrast viscoelastic composites, the ratio of their effective storage and loss shear moduli (the damping factor) remains essentially unchanged as compared to that of pure unfilled matrix so it is the invariability of the damping factor that can be viewed as a special signature of underlying micromechanical mechanism of reinforcement.

Homogenization estimates for the effective response of fractional viscoelastic particulate composites

“…The material parameters are given in Table 1 the GSC scheme provides accurate estimates. These results are consistent with the ones obtained in [25] by using finite-element computations with a time-integration approach. It can be also noted that the SC scheme, which presents a percolation threshold for an infinite mechanical contrast, leads to an unrealistic quasi-elastic effective response at volume fraction c = 0.5.…”

“…with q k = 1 + 2(ωτ k ) α cos πα 2 + (ωτ k ) 2α . From the approximation (33) and the conditions on time integrals of the effective relaxation spectrum (25), it follows that…”

“…. The elastic moduli, used in[25], correspond to silica particles and a typical epoxy resin matrix. It is noted that the elastic shear moduli contrast vary from 30, in the glassy state (ω → +∞), to 3000, in the relaxed state (ω → 0).…”

Comparison of full field and single pore approaches to homogenization of linearly elastic materials with pores of regular and irregular shapes

“…The functions are in good agreement with the limits postulated before, so we can claim homogeneity of the RVEs containing parallel pores. Note that the isotropy of a structure can also be evaluated when the effective properties are known, see for example, and Gusev (2016b) .…”

Optimizing the damping properties of unidirectional composites by incorporating carbon fibers with a thin viscoelastic coating

“…Recently, Gusev presented time-domain finite element simulation for composites with different microstructures, including composites with viscoelastic coated spherical inclusions. It was found that the n-layered model [8] is remarkably accurate even in the case of high stiffness contrast and thin coating layers [12][13][14]. Unwin et al further highlighted the progress in damping techniques by the use of polymer composites with viscoelastic coated spherical inclusions [15,16].…”