While most books devoted to composite materials describe their behaviour after they have been manufactured, the present one is devoted to analysis of stress, strain and temperature fields just during their manufacturing process.
The distribution of temperature in a hardening matrix is considered for axisymmetrical bodies or bodies with polar symmetry. The constitutive equation is either elastic or viscoelastic, or quasielastic (i.e. the elastic properties are piecewise linear functions on temperature). The stress and strain fields in a composite material with polymeric matrix during “wet” or “dry” winding and heating is analysed; the mathematical problem is reduced to the solving of a nonhomogeneous and nonlinear system of partial differential equations.
The mechanism of formation of cracks and other flaws during polymerization and cooling in various stages is considered, including the loosing of structural stability and how to prevent the flaws. The problem of determination of stress and strain states, taking into account the residual stresses due to the manufacturing process, is further formulated and various particular cases (plane, antiplane, dynamic) are considered. For the solving of various problems, the theory of complex functions and the Cauchy integral are used. A theory of various kinds of cracks is made reducing the problem to the Riemann-Hilbert problem and using the Keldysh-Sedov formula. In the last chapters the propagation of longitudinal and transverse waves in a layered composite is studied, and further are considered also the Love and Rayleigh waves as well as the vibrational loading of a layered halfspace, cylinder or sphere.
The book contains a variety of problems concerning the theory of composite materials using a variety of mathematical methods, most of the results are due to the authors. The book can be recommended for those interested in the mechanics of composite materials and for the graduate students.