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where $\mathbf{x}_i$ are the current nodal positions.
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The potentials $T$, $U$, and $R$ are then integrated numerically over each element using appropriate Gaussian quadrature rules.
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The potentials $T$, $U$, and $R$ are then integrated exactly over each element.
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The resulting dynamics are discretized in time using the general [implicit-stage formulation](../../dynamics.md#mechanical-variables), with a slight modification to accommodate the strain rate in the viscoelastic damping term.
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During stage $i$, the strain rate is approximated as
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