Abstract WYPiWYG hyperelasticity is a data-driven, model-free computational procedure for finite element analysis of soft materials. The procedure does not assume the shape of the stored energy function and does not employ material parameters, predicting accurately any smooth prescribed behavior from a complete set of experimental tests. However, fuzzy experimental data may yield useless highly oscillatory, unstable stored energy functions, and classical curvature smoothing gives frequently unsatisfactory results. Aside, the possibility of having experimental data from different specimens for the same test was not considered in previous procedures. In this work we present a novel technique based on spline regression and smoothing penalization using stability conditions. In general, this procedure reduces noisy experimental data or data from multiple specimens for ulterior determination of the stored energy. The procedure only needs the solution of a linear system of equations. Instead of classical curvature-based smoothing, we employ a novel stability-based smoothing, determining for each branch of the uniaxial stress-strain curve the most restrictive stability condition during uniaxial and equibiaxial tests. The resulting stored energy functions are smooth and stable. The procedure has little sensitivity to the number of spline segments or to the choice of the penalization parameter, which are computed automatically.

中文翻译：

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超弹性的实验数据简化

摘要 WYPiWYG 超弹性是一种用于软材料有限元分析的数据驱动、无模型计算程序。该程序不假设储能函数的形状，也不使用材料参数，从一组完整的实验测试中准确预测任何平滑的规定行为。然而，模糊的实验数据可能会产生无用的高度振荡、不稳定的存储能量函数，并且经典曲率平滑经常给出不令人满意的结果。此外，在以前的程序中没有考虑从不同样本获得相同测试的实验数据的可能性。在这项工作中，我们提出了一种基于样条回归和使用稳定性条件平滑惩罚的新技术。一般来说，该程序减少了噪声实验数据或来自多个样本的数据，以便进一步确定存储的能量。该过程只需要求解线性方程组。我们采用了一种新颖的基于稳定性的平滑，而不是经典的基于曲率的平滑，为单轴应力-应变曲线的每个分支确定单轴和等双轴测试期间最严格的稳定性条件。由此产生的储能函数是平滑和稳定的。该过程对样条段的数量或对自动计算的惩罚参数的选择几乎不敏感。我们采用了一种新颖的基于稳定性的平滑，为单轴应力-应变曲线的每个分支确定了单轴和等双轴试验期间最严格的稳定性条件。由此产生的储能函数是平滑和稳定的。该过程对样条段的数量或自动计算的惩罚参数的选择几乎不敏感。我们采用了一种新颖的基于稳定性的平滑，为单轴应力-应变曲线的每个分支确定了单轴和等双轴试验期间最严格的稳定性条件。由此产生的储能函数是平滑和稳定的。该过程对样条段的数量或对自动计算的惩罚参数的选择几乎不敏感。