壓痕試驗(indentation test)因其試驗方法簡單而被廣泛運用於測量彈性材料或是彈塑性材料的機械性質，然而若欲預測如孔彈材料性質這種相對複雜的材料在壓痕試驗下的行為是非常困難的，孔彈材料本身以及所含之孔隙液體的流動狀況皆會影響材料的行為，且若材料本身是由多層材料組成的話，在分析上則更有挑戰。本研究利用位移函數法和漢克-拉普拉斯轉換建立均質及多層孔彈材料的平面壓痕問題分析，求解在拉普拉斯轉換域下由混和邊界條件如接觸條件所形成的對偶積分方程，再經由數值反轉換得到時域下的固定下壓量之壓痕機反力。位移函數法所得之結果與有限元素分析進行比對。壓痕機反力鬆弛預期受層厚、材料係數及邊界條件影響，本研究選定三種不同的表面以及兩種不同的底面進行分析，而在多層材料問題中則探討滲透係數差異對於鬆弛行為的影響。由研究結果得知，孔彈性材料無摩擦平面壓痕問題之穩態反力與瞬時反力的比值只與材料的厚度以及底部邊界條件有關而與材料的滲透係數無關，而材料的滲透係數會影響壓痕機反力鬆弛行為達到穩態的時間。

Indentation tests are widely used to characterize the mechanical properties of elastic and elastoplastic materials due to simplicity. However, for poroelastic materials, interpreting the indentation problem is difficult, because the solid network and the drainage of the pore fluid both affect the deformation. The interpretation of multilayered poroelastic materials is even more challenging. This thesis develops the analysis of the flat indentation on a uniform or multilayered poroelastic material by displacement functions and Hankel-Laplace transform. By solving the dual integral equations attributed to the mixed boundary conditions such as contact condition in Laplace domain, the force of the indenter at a fixed displacement in time domain is obtained through numerical inversion. The results calculated by displacement function method are compared with those of finite element simulations. It is expected that the force relaxation is affected by layer thickness, material properties and boundary conditions. The force relaxation is then analyzed for three drainage conditions on the top and two conditions on the bottom of the material. The effect of the difference in permeability coefficients on the force relaxation of a multilayered material is also discussed. The results show that the ratio of the force at steady state to that at initial state only depends on the bottom conditions and layer thickness. The material permeability affects only the time for the indenter force to reach steady state.

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