A Modified SPH Method for Dynamic Failure Simulation of Heterogeneous Material

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="808359.fig.007a" src="https://static.hindawi.com/articles/mpe/volume-2014/808359/figures/808359.fig.007a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Strain rate <svg height="16.049999" id="M71" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 42.712502 16.049999" width="42.712502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,29.325,7.613)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.012,-0,0,-.012,36.31,7.613)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="808359.fig.007b" src="https://static.hindawi.com/articles/mpe/volume-2014/808359/figures/808359.fig.007b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Strain rate <svg height="16.049999" id="M72" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 42.712502 16.049999" width="42.712502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,29.325,7.613)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.012,-0,0,-.012,36.31,7.613)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="808359.fig.007c" src="https://static.hindawi.com/articles/mpe/volume-2014/808359/figures/808359.fig.007c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b>Strain rate <svg height="16.049999" id="M73" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 50.875 16.049999" width="50.875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></td></tr></table></td></tr><tr class="fig-image" id="d"><td><img alt="808359.fig.007d" src="https://static.hindawi.com/articles/mpe/volume-2014/808359/figures/808359.fig.007d.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(d) </b>Strain rate <svg height="16.049999" id="M74" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 50.875 16.049999" width="50.875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></td></tr></table></td></tr><tr class="fig-image" id="e"><td><img alt="808359.fig.007e" src="https://static.hindawi.com/articles/mpe/volume-2014/808359/figures/808359.fig.007e.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(e) </b>Strain rate <svg height="16.049999" id="M75" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 59.025002 16.049999" width="59.025002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></td></tr></table></td></tr></table>

<table>Fracture processes and the final failure patterns for the Brazilian splitting test.</table>

Mathematical Problems in Engineering

fig7

Figure 7

Figure 7: A Modified SPH Method for Dynamic Failure Simulation of Heterogeneous Material 