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The monograph formulates and solves selected issues of the theory of linear elasticity and rheology of thermosetting polymers and unidirectional monotropic fibre-reinforced thermoset matrix (UFRT) composites. The analytical modelling includes: the quasi-exact homogenization theory of UFRT composites; the inverse problem in the homogenization theory of UFRT composites; the elastic and rheological constitutive modelling of thermosetting polymers and UFRT composites (standard and inverse, uncoupled and coupled constitutive equations); experimental validation of a new rheological model for thermosets, based on the Mittag-Leffler fractional exponential generic function; and numerical validation of a new rheological model for UFRT composites, based on a single Mittag-Leffler fractional exponential generic function. Both the thermosetting polymers and UFRT composites are described by the minimum numbers of the viscoelastic constants. The monograph also presents testing, identification, validation and cognitive studies, including: experimental identification of the elastic and viscoelastic constants of representative resins; numerical identification of the elastic and viscoelastic constants of representative UFRT composites, based on the homogenization theory, the uncoupled rheological constitutive equations, and the elastic-viscoelastic correspondence principle; and simulations of selected rheological processes in the representative resin and representative UFRT composites. The formulations, analytical solutions and numerical analyses are original and unique worldwide.

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