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3.1 Weak formulation for Solid Materials
Generally, the finite element formulation is established in terms of a weak form of the differential equations under consideration. In the context of solid mechanics this implies the use of the virtual work equation: Here, is a virtual velocity and is the virtual rate of deformation tensor. This equation is known as the spatial virtual work equation since it is formulated using spatial quantities only. We can also define the material virtual work equation by expressing the principle of virtual work using only material quantities. Here, is the body force per unit undeformed volume and is the traction vector per unit initial area.