## Appendix A Isotropic Fundamental Solution  
The 2D Laplace transform fundamental solutions for isotropic material are as follows [30]:  
\[\bar{U}_{ij}(\mathbf{x}^{{}^{\prime}},\mathbf{x},s)=\frac{1}{4\pi\mu}\big{(} \phi\delta_{ij}-\chi r_{i}r_{j}\big{)} \tag{10}\]  
and  
\[ \begin{split}\bar{T}_{ij}(\mathbf{x}^{{}^{\prime}},\mathbf{x},s )&=\frac{1}{4\pi}\Big{[}\Big{(}\phi_{r}-\frac{\chi}{r} \Big{)}\bigg{(}\frac{\partial r}{\partial n}\delta_{ij}+r_{j}n_{i}\bigg{)}\\ &-2\frac{\chi}{r}\bigg{(}n_{j}r_{i}-2r_{j}r_{i}r_{j}\frac{ \partial r}{\partial n}\bigg{)}\\ &-2\chi_{r}r_{i}r_{j}\frac{\partial r}{\partial n}+\bigg{(}\frac {c_{1}^{2}}{c_{2}^{2}}-2\bigg{)}\Big{(}\phi_{r}-\chi_{r}-2\frac{\chi}{r}\Big{)} r_{j}n_{j}\Big{]},\end{split}  \tag{11}\]  
while the solutions \(\bar{S}_{kij}(\mathbf{x}^{{}^{\prime}},\mathbf{x},s)\) and \(\bar{D}_{kij}(\mathbf{x}^{{}^{\prime}},\mathbf{x},s)\) can be expressed as follows:  
\[ \begin{split}\bar{D}_{kij}(\mathbf{x}^{{}^{\prime}},\mathbf{x},s )&=\frac{1}{4\pi}\Big{[}2\Big{(}\chi_{r}-2\frac{\chi}{r} \Big{)}r_{i}r_{j}r_{k}\\ &+2\frac{\chi}{r}\delta_{ij}r_{k}-\Big{(}\phi_{r}-\frac{\chi}{r} \Big{)}\Big{(}\delta_{ik}r_{j}+\delta_{jk}r_{i}\Big{)}\\ &-\frac{\lambda}{\mu}\Big{(}\phi_{r}-\chi_{r}-2\frac{\chi}{r} \Big{)}(\delta_{ij}r_{k})\Big{]}\end{split}  \tag{12}\]and  
\[ \begin{split}\bar{S}_{kij}(\mathbf{x}^{{}^{\prime}},\mathbf{x},s)= \frac{\mu}{4\pi}\left\{\frac{\partial r}{\partial n}\Big{[}4\Big{(}\chi_{rr}-5 \frac{\chi_{r}}{r}+8\frac{\chi}{r^{2}}\Big{)}r_{j}r_{j}r_{k}\right.\\ \left.-\left(\phi_{rr}-\frac{\phi_{r}}{r}-3\frac{\chi_{r}}{r}+6 \frac{\chi}{r^{2}}\right)\Big{(}\delta_{ik}r_{,j}+\delta_{jk}r_{j}\Big{)}\right. \\ \left.+2\Big{(}2\frac{\chi_{r}}{r}-4\frac{\chi}{r^{2}}+\frac{ \lambda}{\mu}\Big{(}\chi_{rr}+\frac{\chi_{r}}{r}-4\frac{\chi}{r^{2}}-\phi_{rr} -\frac{\phi_{r}}{r}\Big{)}\Big{)}\delta_{ij}r_{k}\right]\\ +2\Big{(}2\frac{\chi_{r}}{r}-4\frac{\chi}{r^{2}}+\frac{\lambda}{ \mu}\Big{(}\chi_{rr}+\frac{\chi_{r}}{r}-4\frac{\chi}{r^{2}}-\phi_{rr}-\frac{ \phi_{r}}{r}\Big{)}\Big{)}r_{i}r_{j}n_{,k}-\\ \left(\phi_{r}-\frac{\phi_{r}}{r}-3\frac{\chi_{r}}{r}+6\frac{ \chi}{r^{2}}\right)\big{(}r_{,j}n_{,j}+r_{,i}n_{,j}\big{)}r_{k}\\ +\left(4\frac{\chi}{r^{2}}+\frac{\lambda}{\mu}\Big{(}4\frac{\chi_ {r}}{r}+8\frac{\chi}{r^{2}}-4\frac{\phi_{r}}{r}\Big{)}\right.\\ \left.+\frac{\lambda^{2}}{\mu^{2}}\Big{(}\chi_{rr}+4\frac{\chi_{ r}}{r}+2\frac{\chi}{r^{2}}-\phi_{,rr}-2\frac{\phi_{r}}{r}\Big{)}\right) \delta_{ij}n_{k}\\ -2\Big{(}\frac{\phi_{r}}{r}-\frac{\chi}{r^{2}}\Big{)}\Big{(} \delta_{kj}n_{i}+\delta_{ki}n_{j}\Big{)}\Bigg{\}}\end{split}  \tag{10}\]  
For 2D problems, \(\phi\) and its derivatives are given by the following:  
\[\phi=\left[-\frac{c_{2}}{c_{1}}K_{1}(z_{1})+K_{1}(z_{2})\right]\frac{1}{z_{2} }+K_{0}(z_{2}), \tag{11}\]  
\[\phi_{r}=\left\{\frac{c_{2}}{c_{1}}[K_{0}(z_{1})z_{1}+2K_{1}(z_{1})]-[K_{0}(z _{2})z_{2}+2K_{1}(z_{2})]-K_{1}(z_{2})z_{2}^{2}\right\}\frac{1}{rz_{2}}, \tag{12}\]  
and  
\[ \begin{split}\phi_{,rr}=&\frac{1}{z_{2}r^{2}}\Bigg{\{} -\frac{c_{2}}{c_{1}}\Big{[}3K_{0}(z_{1})z_{1}+K_{1}(z_{1})(z_{1}^{2}+6)\Big{]} \\ &+\Big{[}3K_{0}(z_{2})z_{2}+K_{1}(z_{2})(z_{2}^{2}+6)\Big{]}+ \Big{[}K_{0}(z_{2})z_{2}+K_{1}(z_{2})\Big{]}z_{2}^{2}\Bigg{\}},\end{split}  \tag{13}\]  
while, for function \(\chi\) and its derivatives, we have the following:  
\[\chi=-\bigg{(}\frac{c_{2}}{c_{1}}\Big{)}^{2}\bigg{[}K_{0}(z_{1})+\frac{2}{z_{1 }}K_{1}(z_{1})\bigg{]}+K_{0}(z_{2})+\frac{2}{z_{2}}K_{1}(z_{2}), \tag{14}\]  
\[\chi_{,r}=\Bigg{\{}\bigg{(}\frac{c_{2}}{c_{1}}\Big{)}^{2}\bigg{[}K_{1}(z_{1})z_ {1}+2\bigg{[}K_{0}(z_{1})+\frac{2}{z_{1}}K_{1}(z_{1})\bigg{]}\bigg{]}-\bigg{[}K _{1}(z_{2})z_{2}+2\bigg{[}K_{0}(z_{2})+\frac{2}{z_{2}}K_{1}(z_{2})\bigg{]} \bigg{]}\Bigg{\}}\frac{1}{r}, \tag{15}\]  
and  
\[