Quadratic approximations shrunk the model without speeding it up.

Simulating complex materials can overwhelm computers because calculating stress and deformation takes massive computing effort. To fix this, researchers paired a method called Empirically Corrected Cluster CubatureCubaturea mathematical method that approximates an integral by adding up values at a few chosen points, each multiplied by a weight., or E3C, with model reduction techniques. E3C works by cutting down the number of integration points needed to solve the equations in strain space. The researchers tested E3C alongside both linear and quadratic approximation spaces on an example porous hyperelastic material sample. They found that E3C considerably improved performance compared to alternative methods from their previous work, regardless of whether linear or quadratic spaces were used. The quadratic setup built smaller spaces with equal accuracy compared to the linear setup. However, this smaller size did not actually improve the tradeoff between runtime and accuracy.

Why it matters

Engineers who simulate how materials like rubber deform need to balance speed and accuracy. This work shows that using a more sophisticated mathematical description (quadratic) to reduce the model size doesn't always lead to faster simulations. It means choosing the right tool isn't just about theory—practical results matter.

Questions answered