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Any substance that has mass and volume, i.e. it occupies spaces, is matter. Matter is made up of discrete particles and can be categorised into three common states: solid, liquid and gas, based on the characteristics of its particles.

Solid is a state of matter with highest rigidity. A strong force of attraction between solid particles and the low molecular energy that restrains the particles’ movement endow solids the ability to hold on to their own shape. Inversely, a gas particle possesses high energy, while the attraction force between the particles is too weak to hold them in place.

Regardless of the strength of the force of attraction, particles can never fit perfectly with one another. Gaps and discontinuities are present between particles, and, as a result, the properties of a substance vary at different locations on it at the microscopic level due to different arrangements of particles, as shown in Fig. 1.1.

For engineering purposes, however, the microscopic discontinuities and resultant variations are neglected by considering the substance as a continuum. A continuum is an idealised matter the particles of which are continuously distributed and fill the entire space it occupies. Thus, in such an idealised matter, discontinuities are completely removed. This matter can be divided into infinitesimal elements, and all of them can

exhibit the same properties. Under this condition, the properties of the matter are expressed as a continuous function of space and time. This is demonstrated in Fig. 1.2.

A matter can be categorised into fluid or solid. A fluid is a substance that will deform continually when shear stress is applied on it. In other words, a fluid does not have shear resistance. By this definition, liquid and gas are both categorised as fluids. By contrast, solids can resist shear with their attraction force and hence do not deform continually when subjected to shear stress.

The study of a solid’s behaviour, e.g. deformation and stress distribution in both linear and non-linear manner under external forces, is known as solid mechanics, and such a study for fluids is known as fluid mechanics. Both studies are grouped as continuum mechanics, since the subject of study, i.e. the substance, is always considered a continuum.

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