人工神经网络辅助增量多尺度有限应变孔隙弹性模型
ANN-aided incremental multiscale-remodelling-based finite strain poroelasticity
摘要：
有限应变下多孔弹性介质的力学模型通常通过忽略复杂的微观-宏观尺度相互依赖的唯象模型来进行。一个原因是，数学双尺度分析是简单的假设无限小应变理论。利用人工神经网络的潜力，快速和可靠的放大和本地化程序，我们提出了一个增量的数值方法，考虑重新安排的细胞属性的基础上，其当前的变形，这导致每个时间增量后的宏观模型的重塑。这种计算框架是有效的有限应变和大变形问题，同时它确保无限小的应变增量内的时间步长。第一次考虑了宏观和微观尺度的性质和响应之间的相互依赖性的全部影响，提供了更准确的流体饱和多孔介质的预测分析，通过数值固结的例子进行了研究。此外，在流体过滤数值分析中捕获了与达西定律的（非线性）偏差。最后，对脑组织在单轴循环试验下的力学响应进行了仿真研究。
英文摘要：
Mechanical modelling of poroelastic media under finite strain is usually carried out via phenomenological models neglecting complex micro-macro scales interdependency. One reason is that the mathematical two-scale analysis is only straightforward assuming infinitesimal strain theory. Exploiting the potential of ANNs for fast and reliable upscaling and localisation procedures, we propose an incremental numerical approach that considers rearrangement of the cell properties based on its current deformation, which leads to the remodelling of the macroscopic model after each time increment. This computational framework is valid for finite strain and large deformation problems while it ensures infinitesimal strain increments within time steps. The full effects of the interdependency between the properties and response of macro and micro scales are considered for the first time providing more accurate predictive analysis of fluid-saturated porous media which is studied via a numerical consolidation example. Furthermore, the (nonlinear) deviation from Darcy's law is captured in fluid filtration numerical analyses. Finally, the brain tissue mechanical response under uniaxial cyclic test is simulated and studied.
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