Load-absorption by a filament in a fiber-reinforced material

Zusammenfassung Die Arbeit befasst sich mit der statischen Lastübertragung auf eine halbunendliche elastische Faser, die in einer unendlich ausgedehnten elastischen Matrix mit bestimmten mechanischen Eigenschaften eingebettet ist. Im Unendlichen wird für die Matrix ein einachsiger Spannungszustand parallel zur Faser angenommen. Mit Hilfe eines angereicherten Vorgehens lässt sich die gesuchte Faserkraft durch eine Fredholmsche Integralgleichung zweiter Art charakterisieren. Zur Erleichterung der numerischen Lösung der Integralgleichung wird das asymptotische Verhalten der von der Faser aufgenommenen Kraft herangezogen. Eine Reihe quantitativer Resultate zeigt die Vertiefung der Faserkraft und ihre Abhängigkeit von den physikalischen Parametern; ferner wird die Singularität am Faserende diskutiert.

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Dedicated to Professor Ziegler on his sixtieth birthday

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The results communicated in this paper were obtained in the course of an investigation conducted under Contract Nonr-220(58) with the Office of Naval Research in Washington, D.C.     

Damping by dry friction of dynamic loads in a fiber-reinforced composite

Conclusions The accurate analytical solutions of a number of nonlinear problems of impacts on semiinfinite and finite fibers, interacting with the matrix in accordance with the dry friction law, were obtained. We examined the cases of both unidirectional motions and reversed motions caused by unloading, and also oscillatory motions. The results can be used to calculate the energy dissipated in the separating sections of the composite in shock effects. It was shown that the amount of energy dissipated in the dynamic effect is considerably greater than in the quasistatic effect. Thus, dissipation in the system with friction depends strongly on the nature of load application with time.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 28–37, January–February, 1986.     

Dynamic response of fiber-reinforced composite plates

The dynamic stability of orthotropic thick plates subjected to a periodic uniaxial stress and a bending stress is investigated. Both the rotary inertia and the transverse stress are considered in the investigation. The governing equations of motion of Mathieu type are established by applying the Galerkin method with reduced eigenfunction transforms. Based on Bolotin’s method, the dynamic instability regions of graphite- and glass-fiber-reinforced plates are evaluated by solving eigenvalue problems. A dynamic instability index is defined and used as an instability measure to study the influence of various parameters. The effects of material properties and load parameters on the instability region and on the index of dynamic instability of orthotropic plates are discussed.     

On the stressed state in a fiber-reinforced composite material with twisted filaments

Using the model of a piecewise-homogeneous body in the framework of the linear theory of elasticity we study the distribution of internal stresses in a fiber-reinforced composite material with twisted filaments under loading at infinity by uniformly distributed normal strains in the direction of the filaments. It is assumed that the concentration of filaments is rather sparse and their interaction is not taken into account.Translated fromMatematicheskie Melody i Fiziko-Mekhanicheskie Polya, Issue 31, 1990, pp. 74–79.     

Study of microbuckling of fiber-reinforced composite materials

On the basis of the theory of microbuckling of lamina-reinforced composites and formula predicting the critical composite stress for microbuckling in the shear mode _cs published in the literature, a FORTRAN program for study of the behavior of microbuckling of fiber reinforced composites has been developed. Some types of composite materials (reinforcement of different fibers and epoxy matrix) have been studied. Graphics and curves, accounting for the dependences of the compressive stress at failure _cs from the reinforcement volume k, specimen length L, and shear modulus of resin G_r have been obtained. The comparison of the theoretical diagrams presented here and experimental and theoretical results, published in the literature shows good agreement. The basic conclusion of the work presented here is that the study could be used for other fiber reinforced composites (with different mechanical properties of matrices and fibers).Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 531–538, July–August, 1996.     

Yield condition for circular cylindrical shells made of a fiber-reinforced composite

A yield condition is obtained for circular cylindrical shells made of a definite class of fiber-reinforced composite material whose components possess plastic properties. It is shown that, in the plane of generalized stresses — the axial bending moment and the circumferential force (when the axial force is absent) — the yield curve consists of two linear and four curvilinear sections. By approximating the curvilinear sections, we get a piecewise linear yield condition described by a hexagon in the plane indicated. The nonlinear equations and the corresponding piecewise linear equations of the yield condition for particular cases are given in the form of tables. In solving specific boundary-value problems, we consider a circular cylindrical shell simply supported at its ends and loaded with a uniform internal pressure, for which the load-carrying capacity is determined in relation to the mechanical properties of composite components and some characteristic geometrical parameters. The results of numerical calculations are represented in the form of graphs. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 655–666, September–October, 2006.     

Optimization of cyclindrical shells of fiber-reinforced composite materials

Problems of optimizing nonelastic circular shells are considered. The material of the shells is assumed to be a fiber-reinforced composite with fibers unidirectionally embedded in a relatively less stiff but ductile metallic matrix so that the material has the yield surface suggested by Lance and Robinson. The shell is subjected to an impulsive loading of short-time periods generating initial kinetic energy. During plastic deformation of the shell the initial kinetic energy is transformed into the plastic strain energy. The shell thickness is assumed to be piecewise constant. Various thicknesses and coordinates of the rings, where the thickness has jumps, are preliminarily unspecified. We look for a shell design for which the maximum residual deflection has a minimum value for the total weight given. The alternative problem of minimizing the shell weight for the maximum deflection given is also studied.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, Octobe, 1995.Tartu University, Estonia. Published in Mekhanika Kompozitnykh Materialov, No. 1, pp. 65–71, January–February, 1996.     

Markov model for analyzing the residual static strength of a fiber-reinforced composite

The possibility of using a unified mathematical model, based on the theory of Markov chains, to describe the distribution of the conditional fatigue limit at a fixed number of loading cycles and the residual strength of a specimen after cyclic loading is demonstrated. Numerical examples are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 559–568, July–August, 2008.     

Computer modeling of dynamics of damage cumulation in the ductile matrix of a fiber-reinforced composite

Conclusions On the basis of the present results together with other previously obtained data [12, 14, 15, 18, 19] it can be assumed that the problem of deformation and failure [20, 21], which is often reduced to explaining the problem of whether failure is the result of deformation or its cause, has resulted from attempts to transfer the macroconsiderations of continuum to the atomic discrete level where the strain (shear accumulation) and failure (cumulation of ruptures) are interrelated to such an extent that their contraposition is of artificial nature. For example, the fluctuation rupture of the bond on the free boundary of the crystal causes formation of a dislocation and shearing [15], and shearing in the form of twinning leads to rupture of bonds and formation of a crack nucleus (see Fig. 1c). For analysis of failure, it is at present insufficient to use only dislocation [22] or only kinetic [21] considerations. As mentioned in [20], in the physics of failure it is necessary to examine all the objects examined in the physics of plasticity and, in addition to this, even more complicated objects. Attempts to simplify the problem proved to be unsuccessful and, consequently, the correct method of solving the problems of the physics of strength should be based on developing the methods of physics of strength up to analysis of atomic mechanisms of damage cumulation [20]. Molecular dynamics represents such a method of examining failure which makes it possible to change to the atomic level [10].Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 973–976, November–December, 1987.     

hp–Adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains

In this article, we develop the a posteriori error estimation of hp–version discontinuous Galerkin composite finite element methods for the discretization of second‐order elliptic partial differential equations. This class of methods allows for the approximation of problems posed on computational domains which may contain a huge number of local geometrical features, or microstructures. Although standard numerical methods can be devised for such problems, the computational effort may be extremely high, as the minimal number of elements needed to represent the underlying domain can be very large. In contrast, the minimal dimension of the underlying composite finite element space is independent of the number of geometric features. Computable bounds on the error measured in terms of a natural (mesh‐dependent) energy norm are derived. Numerical experiments highlighting the practical application of the proposed estimators within an automatic hp–adaptive refinement procedure will be presented. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1342–1367, 2014     

A discontinuous Galerkin method on refined meshes for the two-dimensional time-harmonic Maxwell equations in composite materials

In this paper, a discontinuous Galerkin method for the two-dimensional time-harmonic Maxwell equations in composite materials is presented. The divergence constraint is taken into account by a regularized variational formulation and the tangential and normal jumps of the discrete solution at the element interfaces are penalized. Due to an appropriate mesh refinement near exterior and interior corners, the singular behaviour of the electromagnetic field is taken into account. Optimal error estimates in a discrete energy norm and in the L²$L^2$-norm are proved in the case where the exact solution is singular.     

Standing waves in a counter-rotating vortex filament pair

The distance among two counter-rotating vortex filaments satisfies a beam-type of equation according to the model derived in [15]. This equation has an explicit solution where two straight filaments travel with constant speed at a constant distance. The boundary condition of the filaments is 2π-periodic. Using the distance of the filaments as bifurcating parameter, an infinite number of branches of periodic standing waves bifurcate from this initial configuration with constant rational frequency along each branch.     

Motion of a vortex filament in the half-space

A model equation for the motion of a vortex filament immersed in three-dimensional, incompressible and inviscid fluid is investigated as a preliminary attempt to model the motion of a tornado. We solve an initial–boundary value problem in the half-space, where we impose a boundary condition in which the vortex filament is allowed to move on the boundary.     

Cutting of aramide fiber-reinforced plastics by Co2 laser

Comparative characteristics of aramide fiber reinforced plastics (AFRP) made by laser cutting or machining are presented. It is found that the strength of the specimens cut out by laser is 4–25% higher, while the moisture absorption is at least 2 times lower as compared to those cut out by machining. The deviation of the cutting edge size for AFRP 2 mm thick does not exceed 0.4 mm. Calculated and experimental data are given. The possibilities and conditions of cutting the AFRP up to 6 mm thick are determined.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 375–384, May–June, 1999.