The constitutive law in the linear theory of elasticity

Abstract

As repeatedly mentioned earlier, see Subsections 2.3.6 and 2.3.9, the tensors of finite strain can be replaced by a linear strain tensor $\hat \varepsilon$ provided that the components of the gradient of the displacement vector ∇u are small. The latter is equivalent to the components of tensor $\hat \varepsilon$ and the rotation vector ω being small

$$ \left| {\frac{{\partial u_s }} {{\partial u_k }}} \right| \ll 1,\left| {\varepsilon _{sk} } \right| \ll 1,\left| {\omega _s } \right| \ll 1. $$

((1.1.1))