The linear, isotropic, elastic solid

A model substance that represents closely the deformation behaviour for small strains of a wide range of materials is the linear isotropic, elastic solid. As the name impUes, the substance is isotropic, satisfies Hooke s law for aU strains and shows perfect elasticity. 

Consider a cube of such a material with its edges parallel, respectively to the coordinate axes Ox, Oy, Oz and let balanced forces be applied that produce stresses Oy and simultaneously. The total effect of these stresses can be determined by means of the principle of superposition the effect of each stress acting separately is determined and the total effect of the stresses acting simultaneously is obtained by adding together the separate effects. 

When alone acts, a linear strain is produced in the x direction 

If the unstrained edge length of the cube of material is Lq, the unstrained volume is Ll- When the cube is subjected to the balanced external forces its volume is (L LyL ), where  

These expressions follow from the definition of linear strains. When the linear strains are small, as is normally the case in 

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