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The paper presents a
comprehensive formulation for the analysis of the stiffness and strength of
fiber-reinforced composites with the matrix enhanced by adding elastic or shape
memory alloy (SMA) spheroidal particles. The micromechanical model used to
evaluate the stiffness tensor of the matrix with embedded particles is based on the
Benveniste version of the Mori–Tanaka theory. In the case of a superelastic shape
memory alloy particulate matrix, the stiffness of the particles depends on the
martensitic fraction that is in turn affected by the state of stress within the particle.
In this case an exact solution for the stiffness tensor of the composite material with
elastic fibers and matrix and embedded SMA particles is developed combining
the recent macromechanical solution for multi-phase composites with the
inverse method of the analysis of SMA. In the particular case, this solution
results in explicit formulae for the homogeneous material constants of a
SMA particulate material subjected to axial loading. Upon the completion of
the stiffness analysis the strengths of a fiber-reinforced material with the
matrix containing elastic or SMA particles can be analyzed using the Eshelby
solution for the stresses. As follows from numerical examples, elastic spherical
particles added to the matrix of a fiber-reinforced composite significantly
improve the transverse strength and stiffness of the material, even if the
volume fraction of such particles is relatively small. The effect of elastic
particles on the longitudinal strength and stiffness is less pronounced. It is
also illustrated that the stress-induced transformation of superelastic SMA
particles results in significant changes of the properties of SMA particulate
composites.
