We consider L-scheme and Newton-based solvers for Biot model under large deformation. The mechanical deformation follows the Saint Venant-Kirchoff constitutive law. Furthermore, the fluid compressibility is assumed to be non-linear. A Lagrangian frame of reference is used to keep track of the deformation. We perform an implicit discretization in time (backward Euler) and propose two linearization schemes for solving the non-linear problems appearing within each time step: Newton’s method and L-scheme. Each linearization scheme is also presented in a monolithic and a splitting version, extending the undrained split methods to non-linear problems. The convergence of the solvers, here presented, is shown analytically for cases under small deformation and numerically for examples under large deformation. Illustrative numerical examples are presented to confirm the applicability of the schemes, in particular, for large deformation.

对于大变形下的Biot模型，我们考虑L方案和基于牛顿的求解器。机械变形遵循Saint Venant-Kirchoff本构定律。此外，流体可压缩性被认为是非线性的。拉格朗日参考系用于跟踪变形。我们在时间上执行隐式离散化（向后欧拉），并提出了两种线性化方案来解决每个时间步长中出现的非线性问题：牛顿法和L-方案。每种线性化方案还以整体式和拆分形式提供，将不排水的拆分方法扩展到非线性问题。对于小变形情况下的解析器，此处给出了求解器的收敛性；对于大变形情况下的示例，则以数值方式表示。给出了说明性的数值示例，以证实该方案的适用性，特别是对于大变形。