A hydromechanically coupled finite element method (FEM) algorithm following a mixed continuous Galerkin formulation for displacement and pore pressure is adopted for modeling of spherical indentation in a poro-elasto-plastic medium. The fully saturated porous medium is assumed to be isotropic and elasto-perfectly plastic, obeying a Drucker-Prager yield criterion with an associative or non-associative flow rule. The Newton-Raphson method with the tangent stiffness scheme is employed to deal with plasticity in the solid skeleton. A stabilization scheme, which permits equal-order interpolation for the displacement and pore pressure fields and suppresses pore pressure oscillation in the incompressible or nearly incompressible limit, is incorporated in this FEM algorithm. The FEM algorithm is extensively benchmarked with poroelastic analytical solutions to the problems of Terzaghi, Mandel, Cryer, and De Leeuw and an analytic solution for one-dimensional poro-elasto-plastic consolidation. Numerical simulations of poroelastic spherical indentation via step displacement loading are conducted to show that the normalized indentation force as a function of dimensionless time has only relatively weak dependence on material properties through a single derived parameter $\omega$. Such universality is shown for three types of surface drainage conditions. For indentation in a poro-elasto-plastic medium, it is shown that even though plasticity occurs immediately at the undrained limit, if cohesion is within a certain range, there is no plastic strain accumulation during the transient period and the normalized force relaxation behavior could be approximated as poroelastic.

中文翻译：

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多孔弹塑性介质中球形压痕的有限元建模，通过阶跃位移加载

采用流体力学耦合有限元法 (FEM) 算法，该算法遵循位移和孔隙压力的混合连续 Galerkin 公式，用于模拟多孔弹塑性介质中的球形压痕。完全饱和的多孔介质被假定为各向同性和完全弹塑性的，遵守带有关联或非关联流动规则的 Drucker-Prager 屈服准则。使用具有切线刚度方案的 Newton-Raphson 方法来处理实体骨架中的塑性。该 FEM 算法中包含一个稳定方案，该方案允许位移和孔隙压力场的等阶插值并抑制不可压缩或几乎不可压缩极限内的孔隙压力振荡。FEM 算法广泛采用了 Terzaghi、Mandel、Cryer 和 De Leeuw 问题的多孔弹性解析解以及一维多孔弹塑性固结的解析解作为基准。通过阶跃位移加载对多孔弹性球形压痕进行数值模拟，以表明作为无量纲时间函数的归一化压痕力通过单个导出参数对材料特性的依赖性相对较弱$\omega$. 三种类型的地表排水条件都显示了这种普遍性。对于多孔弹塑性介质中的压痕，表明即使在不排水极限处立即发生塑性，但如果内聚力在一定范围内，则在瞬态期间没有塑性应变积累，并且规范化力松弛行为可以近似为多孔弹性。