1. Transmission coefficients for P and S waves in HardBego stones The point where the incident ray reaching the S critique angle hits the interface The point where the incident ray reaching the P critique angle hits the interface Transmitted P ray Transmitted S ray Reflected S ray from P ray Reflected S ray from S ray Reflected P ray from P ray Part 1 transmitted S wave Part 2 transmitted S wave Ip: Normal component of the energy flux density vector of the transmitted P wave Is: Normal component of the energy flux density vector of the transmitted S wave I i: Normal component of the energy flux density vector of the incident P wave

2. Ray tracing plots in HardBego Stone Transmitted P wave wavefront Transmitted S wave wavefront Reflected P wave wavefront Reflected S wave wavefront Transmitted P tensile tail wavefront All ray/wave front plots only include transmitted P/S rays which are reflected once at the boundary before advancing to the axis, reflected P and S rays induced by transmitted P rays hitting the boundary. FEM simulations show these rays primarily contribute to tensile stress built in. Transmitted P wave Reflected P-S wave Transmitted S wave Reflected P wave Reflected S wave Reflected P-S wave Reflected P wave Transmitted tensile tail

3. Tensile Stress Pressure in fluids Tensile stress Reflected P waves focus

4. Pressure in Fluids Tensile stress Reflected P-S waves focus Reflected S waves focus

5. One sensor is placed at (0, 3) mm where the reflected P and S waves focus to detect tensile stress The other sensor is placed at (0, 2.4) mm where the reflected P-S waves focus to detect tensile stress c Reflected P waves focus Reflected S waves focus Reflected P-S waves focus

6. Curl displacement Pressure In Fluids Curl Displacement

7. Pressure In Fluids Curl Displacement

8. Div displacement Pressure in Fluids Div Displacement

9. Pressure in Fluids Div Displacement

10. Max shear stress Pressure in Fluids Max Shear stress

11. Pressure in Fluids Max Shear stress

12. Contribution from various types of waves P and part 1 S wavesPart 2 S wavesP and S wavesHead and surface waves Max tensile stress 24.76 MPa Max tensile stress 33.64 MPa Max tensile Stress 58.30 MPa Max tensile stress 32.3142 MPa (different locations)

13. Maximum tensile stress in different sizes stones

14. Wavefronts when the maximum tensile stress occurs 2 mm4 mm6 mm8 mm

15. 10 mm12 mm