Theory of Elasticity pp 127-150 | Cite as
The constitutive law in the linear theory of elasticity
Chapter
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)
Keywords
Stress Tensor Bulk Modulus Linear Theory Strain Tensor Adiabatic Process
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© Springer-Verlag Berlin Heidelberg 2005