Equilibrium for perturbations of multifunctions by convex processes

We present a general equilibrium theorem for the sum of an upper hemicontinuous convex-valued multifunction and a closed convex process defined on a noncompact subset of a normed space. The lack of compactness is compensated by inwardness conditions related to the existence of viable solutions of some differential inclusion.     

Equilibrium cracks in composites reinforced with unidirectional fibres

A discrete-continuum approach, proposed by Novozhilov for analysing the equilibrium states of a brittle of crack in an isotropic body, is applied to a penny-shaped crack situated in a fibre-reinforced composite perpendicular to the fibres. The structural non-uniformity of the material is taken into account by the presence of unbroken fibres in the narrow part of the crack, adjoining the edge, and the different effect of the strength properties of the fibre and matrix on the limit state of the crack. Using this model, the range of dimensions of equilibrium cracks is established and an estimate is given of the critical size of the bridged part of the crack, corresponding to the onset of catastrophic fracture. It is shown that this dimension has the same value for a penny-shaped crack and for a crack under plane strain, does not depend on the form of the load and, under the condition of its smallness, is a brittle fracture characteristic of a fibre-reinforced material. The possibility of using this fracture model for two types of ceramics is analysed on the basis of experimental data.     

Semi-Markov failure rates processes

Usually, a reliability function is defined by a failure rate which is a real function taking the non-negative real values. In this paper the failure rate is assumed to be a stochastic process with non-negative and right continuous trajectories. The reliability function is defined as an expectation of a function of that random process. Particularly, the failure rate defined by the semi-Markov processes is considered here. The theorems dealing with the renewal equations for the conditional reliability functions with a semi-Markov process as a failure rate are presented in this paper. A system of that kind of equations for the discrete state space semi-Markov process is applied for calculating the reliability function for the 3-states semi-Markov random walk. Using the introduced system of renewal equations for the countable state space, the reliability function for the Furry-Yule failure rate process is obtained.     

Nonlinear failure mechanisms of laminated composites

Two distinct analytical models are described representing geometrically nonlinear instabilities in layered composites under in-plane compression — kink-banding and delamination buckling. The utilized technique is based on of energy minimization principles in order to examine the underlying mechanics of the systems. It is demonstrated that using this approach enables investigations to be undertaken far into the postbuckling range whilst changing system parameters. Thereby a greater phenomenological understanding of the mechanics of the systems is achieved. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of the rheological properties of granular composites by using a structural approach

Composites with an elastomeric matrix containing rigid particles of diameter 10–1000 μm are studied. One of possible mechanisms of the rheological behavior of such filled systems, related to the origination and growth of vacuoles near the rigid inclusions in a viscous matrix, is considered. For simulating the mechanism of formation of rheological properties of the filled elastomers, we use a structural cell in the form of an elastomeric cylinder, whose height and diameter are equal in magnitude, with a rigid spherical inclusion at its center. Deformation of the cells is examined with the observance of boundary conditions providing the preservation of their close packing. The inclusion is assumed to be rigid, and the matrix properties are described by equations of the linear hereditary viscoelasticity theory. The formation of vacuoles is described by using the approach suggesting that an initial debonding begins to propagate when the energy accumulated in the extended matrix reaches a value sufficient to create a new interface. The heterogeneity of the composite is simulated by taking into account the variability of the local filler concentration. Creep curves obtained for composite cells with different content of the solid phase are presented. Comparisons between the numerical and experimental results show a satisfactory agreement. Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 895–906, November–December, 2008.     

Investigation of the mechanical behavior of two-component granular composites in terms of structural models

A structural model is suggested for elastomers filled with particles of two fractions — with diameters exceeding 10 μm and submicronic ones. In each fraction, the particle diameter varies randomly, but between the fractions, the average particle diameter differs by several orders of magnitude. It is assumed that the small particles, together with the matrix, behave as a homogeneous medium relative to the large ones. By using this model, the mechanical behavior of composites based on elastomers filled with different volume contents of solid particles is investigated. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 191–200, March–April, 2007.     

A physically based failure criterion for laminated composites

The stress and strain fields in laminated composites can be described realistically with the help of a refined theory of elasticity for anisotropic materials. In contrast, the respective failure characteristics cannot be predicted satisfactorily based on the commonly used failure criteria. The main disadvantage of these generalized failure criteria, such as the quadratic failure criteria of Sakharov, Azzi/Tsai, Tsai/Wu, etc., is that they combine fundamentally different fracture mechanisms of the homogenized UD layer in one approximation by an interpolation polynomial. A completely different method for the formulation of realistic failure criteria, taking into account the heterogeneous anisotropic material structure relevant to the fracture, is based on the Mohr hypothesis for brittle materials that in fact only the stresses in the fracture plane induce failure. This physically based failure criterion not only considers the decisive eifference between the fiber fracture and the interfiber fracture, but also characterizes further fracture types in the plane parallel to the fibers.Institut für Leichtbau und Kunststoffetechnik (ILK) Technische Universität Dresden, D-01062 Dresden, Germany. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 413–422, July–August, 1999.