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Traditional continuum mechanics regards the motion of material elementforming a continuum as the translational motion of rigid body, and the theoremof moment of momentum about an axis passing through the centroid of materialelement is added to describe the dynamics of the material elements of acontinuum. There are several questions in the theories of elasticity and fluiddynamics developed from above assumption: 1. The rigid body rotation termed ingeometric relationships conflicts with the assumption of translational motionof material elements; 2. The constraint of compatibility conditions ondisplacement field is different from the property of displacement field; 3. Thedecomposition of gradient of displacement and velocity is inconsistent with thedecomposition of vector fields which are often decomposed into divergence fieldand curl field; 4.The calculation of stress on an inclined plane is equivalentto denying the necessity of body force and inertial force in Cauchy's equationof motion; 5. Stokes hypothesis is required in the theory of fluid dynamics toguarantee that the pressure derived from the fluid's constitutive relationshipis equal to the thermodynamic pressure. The study re-establishes the theoriesof elasticity and fluid dynamics based on new dynamic hypotheses to replacecurrent imperfect theories. In the new theories, it is assumed that the theoremof momentum is the only dynamic law that a continuum obeys, which describes thetranslational motion of deformable media.

Theories of Elasticity and Fluid Dynamics Established from New Dynamic Hypotheses