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In the theory of linear elasticity the Cauchy stress tensor is a linear function of the small strain tensor $\boldsymbol{\varepsilon}$ : $$\begin{equation} \boldsymbol{\sigma}=\boldsymbol{\mathcal{C}}:\boldsymbol{\varepsilon}\,.\label{eq402} \end{equation}$$ Here, $\boldsymbol{\mathcal{C}}$ is the fourth-order elasticity tensor that contains the material properties. In the most general case this tensor has 21 independent parameters. However, in the presence of material symmetry the number of independent parameters is greatly reduced. For example, in the case of isotropic linear elasticity only two independent parameters remain. In this case, the elasticity tensor is given by $\boldsymbol{\mathcal{C}}=\lambda\mathbf{I}\otimes\mathbf{I}+2\mu\mathbf{I}\,\overline{\underline{\otimes}}\,\mathbf{I}$ , or equivalently, $$\begin{equation} \mathcal{C}_{ijkl}=\lambda\delta_{ij}\delta_{kl}+\mu\left(\delta_{ik}\delta_{jl}+\delta_{il}\delta_{jk}\right)\,.\label{eq403} \end{equation}$$ The material coefficients $\lambda$ and $\mu$ are known as the Lamé parameters. Using this equation, the stress-strain relationship can be written as $$\begin{equation} \sigma_{ij}=\lambda\varepsilon_{kk}\delta_{ij}+2\mu\varepsilon_{ij}\,.\label{eq404} \end{equation}$$ If the stress and strain are represented inVoigt notation, the constitutive equation can be rewritten in matrix form as $$\begin{equation} \left[\begin{array}{c} \sigma_{11}\\ \sigma_{22}\\ \sigma_{33}\\ \sigma_{12}\\ \sigma_{23}\\ \sigma_{13} \end{array}\right]=\left[\begin{array}{cccccc} \lambda+2\mu & \lambda & \lambda & 0 & 0 & 0\\ \lambda & \lambda+2\mu & \lambda & 0 & 0 & 0\\ \lambda & \lambda & \lambda+2\mu & 0 & 0 & 0\\ 0 & 0 & 0 & \mu & 0 & 0\\ 0 & 0 & 0 & 0 & \mu & 0\\ 0 & 0 & 0 & 0 & 0 & \mu \end{array}\right]\left[\begin{array}{c} \varepsilon_{11}\\ \varepsilon_{22}\\ \varepsilon_{33}\\ \gamma_{12}\\ \gamma_{23}\\ \gamma_{13} \end{array}\right]\,.\label{eq405} \end{equation}$$ The shear strain measures $\gamma_{ij}=2\varepsilon_{ij}$ are called the engineering strains.