Particles or fibres are added as a means of reinforcement and provide strength and stiffness to the composite.
The matrix phase is added to bond the fibres together, protect the fibres from damage, and distribute the load from one fibre to another.
There are many common examples of composite materials used around us. Boats and surfboards are made from fibreglass, which is a combination of glass fibres in a polymer matrix. Concrete is a composite of cement and aggregate. Wood and bone are both natural composites.
If we consider fibreglass, for example, we can see the benefits that can be derived from combining materials. We know that polymers have a low stiffness but are highly ductile. We also know that ceramics and glasses are very stiff and strong but are prone to catastrophic failure as a result of flaws made though processing. By combining the two materials we can achieve a strong and stiff material without the risk of catastrophic failure. If a single fibre breaks then the load is simply transferred to other surrounding fibres through the polymer matrix.
The properties of the composite are determined by the properties of the fibres, their length, diameter, orientation, and amount, as well as the properties of the matrix, and the bonding between the matrix and the fibres.
The mechanical properties of a composite are primarily determined by the mechanical properties of the constituent materials.
The fibres act to resist tension, the matrix acts to resist shear, and both act together to resist compression.