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首页> 外文期刊>Journal of Biomechanics >A MATHEMATICAL APPROXIMATION FOR THE SOLUTION OF A STATIC INDENTATION TEST
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A MATHEMATICAL APPROXIMATION FOR THE SOLUTION OF A STATIC INDENTATION TEST

机译：静态指示测试的数学逼近

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The classical contact problem of the indentation of a thin compressible linear elastic layer bonded to a rigid substrate is considered. Closed-form mathematical approximations of the deformation are presented for the cases of plane indentation by a rectangular block and three dimensional indentation by a plane-ended (axisymmetric) cylinder. The approximations are analyzed in the context of a static indentation test by comparison of applied load values to those obtained using a classical integral transform solution. In the case of plane indentation, the mathematical and classical predictions agree to within 2% relative error for aspect ratios between 0.1 and 1.0 and apparent Poisson ratio between 0.0 and 0.3. Comparisons for the axisymmetric case indicate a similar pattern. The main advantage of the new approach is that it yields closed-form approximations of the static indentation solution which can also capture the essential singular behavior. (C) 1997 Elsevier Science Ltd. [References: 14]
机译：考虑了粘合到刚性基底上的可压缩线性弹性薄层的压痕的经典接触问题。对于矩形块的平面压痕和平面端的（轴对称）圆柱体的三维压痕，给出了变形的闭合形式数学近似值。通过将施加的载荷值与使用经典积分变换解决方案获得的载荷值进行比较，在静态压痕测试的情况下分析了近似值。在平面压痕的情况下，对于0.1至1.0的纵横比和0.0至0.3的表观泊松比，数学和经典预测均在2％的相对误差范围内。轴对称情况的比较表明相似的模式。新方法的主要优点是，它可以得出静态压痕解决方案的闭合形式的近似值，该近似值也可以捕获基本的奇异行为。 （C）1997 Elsevier Science Ltd. [参考：14]

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