For homogeneous isotropic material with elastic properties E, G and v. We have derived the following form \varepsilon_{x}=\frac{1}{\mathbf{E}}\left[\sigma_{x}-v\left(\sigma_{y}+\sigma_{z}\right)\right] \varepsilon_{y}=\frac{1}{\mathbf{E}}\left[\sigma_{y}-v\left(\sigma_{x}+\sigma_{z}\right)\right] \varepsilon_{z}=\frac{1}{\mathbf{E}}\left[\sigma_{z}-v\left(\sigma_{x}+\sigma_{y}\right)\right] Derive (show) that the stress can be written in the

following form \sigma_{x}=2 G \varepsilon_{x}+\lambda\left[\varepsilon_{x}+\varepsilon_{y}+\varepsilon_{z}\right] \sigma_{y}=2 G \varepsilon_{y}+\lambda\left[\varepsilon_{x}+\varepsilon_{y}+\varepsilon_{z}\right] \sigma_{z}=2 G \varepsilon_{z}+\lambda\left[\varepsilon_{x}+\varepsilon_{y}+\varepsilon_{z}\right] \text { where } \lambda=\frac{v E}{(1+v)(1-2 v)} \text { and } G=\frac{E}{2(1+v)}