Showing papers on "Mixture theory published in 1988"

A Mixture Theory Approach to the Modeling of Fiber-Reinforced Composites Subject to Impulsive Loading

Abstract: An investigation of shock wave modeling in fiber-reinforced composites is conducted in this paper. This may be conveniently carried out by using an appropriate mixture theory in conjunction with an orthotropic constitutive model. The theory of mixtures permits the development of a methodology which is both complex enough to encompass the essential physics, and yet sufficiently simple for incorporation into existing wave propagation codes.

Transient Finite Element Analysis of Elastoplastic Fiber Reinforced Composites

Abstract: The mixture theory proposed by Murakami and Hegemier [1] is applied to the transient dynamic analysis of elastoplastic fiber reinforced composites. The model is based on the two scale-asymptotic expansions as described by Bensoussan, Lions and Papanicolaou [2], and Sanchez-Palencia [3]. Equations of motion are obtained from the principle of virtual work, while the appropriate incremental constitutive equations are deduced from Reissner’s [4] mixed variational principle. The finite element method is used for the spatial discretization. The resulting semi-discrete equations of motion are then integrated using the explicit method. The fibers are assumed elastic, while the matrix obeys a von Mises yield criterion with linear hardening. A semi-infinite fiber reinforced composite under a step pressure is considered. Stress profiles show the dispersive nature of the waves in the composite.

I~E SHORT-TERMACTION OF A HAPd4ONIC PULSE

Abstract: Fiber composites are evidently the most widespread type of structural composites. Therefore, not only have a whole series of theoretical models been developed for such structures in the mechanics of composites, but many experimental observations have also been undertaken. Despite the apparent independence of experiments in solving the problems which are under consideration, they are always based on some theoretical scheme. Consequently, the microstrucrural theory of mixtures, which operates with mean parameters of the matrix and the fibers in contrast to traditional theories dealing with mean parameters of the composite as a whole, cannot make adequate use of the previously accumulated experimental data. Mixture theory requires experimental observation of the motion of elements of the miorostructure, and hence new experiments based on the mixture model are needed. One of the few such investigations was described in [4], which reported the results of fairly complex experiments on massive samples of fiber composite under the short-term action of a harmonic pulse in the frequency range from 50 kHz to 1.5 MEz. It follows from the experimental dispersional relations that, in the experimental frequency range, the length of the waves excited in the samples falls within the whole of the permissible range permitted by continuum theory, i.e., from values which are 2-3 orders of magnitude greater than the characteristic dimension of the microstructure to values amounting to a few such distances. The experiments are based on measurement of the steady oscillations in the samples. The steady-wave amplitudes are measured separately in the fiber and in the matrix. In each component of the composite (fiber and matrix), two waves with different phase and group velocities are observed. The theoretical description adopted in [4] for the steady waves, using the shear theory of the mixture and the theory of effective rigidities, is in good agreement with experiment. However, the amplitude values differ considerably from the theoretical predictions. This discrepancy has subsequently been eliminated by complicating the model of the mixture so as to take additional account of the inertial mechanism of interaction between the mixture components [3]. Since the theoretical scheme of [3] also permits analysis of nonsteady phenomena occurring in a composite sample, and it is fairly difficult to separate steady waves completely in the experiment, it is expedient to calculate the nonsteady components in the theoretical solution with respect to this more complex model. In this case, first, the theoretical analysis becomes complete and final, and second there appears the possibility Of quantitatively estimating the degree to which nonsteady effects influence the overall pattern of oscillations in the fiber and matrix. In the present work, the basic results of theoretical analysis in the above formulation are described, The theoretical scheme adopted reduces to finding the solution of the following system of equations of iotion of linear mixture theory [3]