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

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

Tensile Stress Pressure in fluids Tensile stress Reflected P waves focus

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

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

Curl displacement Pressure In Fluids Curl Displacement

Pressure In Fluids Curl Displacement

Div displacement Pressure in Fluids Div Displacement

Pressure in Fluids Div Displacement

Max shear stress Pressure in Fluids Max Shear stress

Pressure in Fluids Max Shear stress

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

Maximum tensile stress in different sizes stones

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

10 mm12 mm