We address numerical solvers for a poromechanics model particularly adapted for soft materials, as it generally respects thermodynamics principles and energy balance. Considering the multi-physics nature of the problem, which involves solid and fluid species, interacting on the basis of mass balance and momentum conservation, we decide to adopt a solution strategy of the discrete problem based on iterative splitting schemes. As the model is similar (but not equivalent to) the Biot poromechanics problem, we follow the abundant literature for solvers of the latter equations, developing two approaches that resemble the well known undrained and fixed-stress splits for the Biot model. A thorough convergence analysis of the proposed schemes is performed. In particular, the undrained-like split is developed and analyzed in the framework of generalized gradient flows, whereas the fixed-stress-like split is understood as block-diagonal $L^2$-type stabilization and analyzed by means of a relative stability analysis. In addition, the application of Anderson acceleration is suggested, improving the robustness of the split schemes. Finally, we test these methods on different benchmark tests, and we also compare their performance with respect to a monolithic approach. Together with the theoretical analysis, the numerical examples provide guidelines to appropriately choose what split scheme shall be used to address realistic applications of the soft material poromechanics model.

我们解决了特别适用于软材料的多孔力学模型的数值求解器，因为它通常尊重热力学原理和能量平衡。考虑到该问题的多物理性质，涉及固体和流体物种，在质量平衡和动量守恒的基础上相互作用，我们决定采用基于迭代分裂方案的离散问题的求解策略。由于该模型类似于（但不等同于）Biot 多孔力学问题，我们遵循了后一个方程求解器的大量文献，开发了两种类似于众所周知的 Biot 模型不排水和固定应力分裂的方法。对所提出的方案进行了彻底的收敛分析。特别是，${升}^2$型稳定性并通过相对稳定性分析进行分析。此外，建议应用安德森加速，提高分裂方案的鲁棒性。最后，我们在不同的基准测试中测试了这些方法，并且我们还比较了它们相对于整体方法的性能。Together with the theoretical analysis, the numerical examples provide guidelines to appropriately choose what split scheme shall be used to address realistic applications of the soft material poromechanics model.