A computationally tractable framework for nonlinear dynamic multiscale modeling of membrane fabric [article]

Philip Avery, Daniel Z. Huang, Wanli He, Johanna Ehlers, Armen Derkevorkian, Charbel Farhat
2020 arXiv   pre-print
A general-purpose computational homogenization framework is proposed for the nonlinear dynamic analysis of membranes exhibiting complex microscale and/or mesoscale heterogeneity characterized by in-plane periodicity that cannot be effectively treated by a conventional method, such as woven fabrics. The proposed framework is a generalization of the "Finite Element squared" method in which a localized portion of the periodic subscale structure – typically referred to as a Representative Volume
more » ... ment (RVE) – is modeled using finite elements. The numerical solution of displacement-driven problems using this model furnishes a mapping between the deformation gradient and the first Piola-Kirchhoff stress tensor. The approach involves the numerical enforcement of the plane stress constraint. Finally, computational tractability is achieved by introducing a regression-based surrogate model to avoid further solution of the RVE model when data sufficient to fit a model capable of delivering adequate approximations is available. For this purpose, a physics-inspired training regimen involving the utilization of our generalized FE^2 method to simulate a variety of numerical experiments – including but not limited to uniaxial, biaxial and shear straining of a material coupon – is proposed as a practical method for data collection. The proposed framework is demonstrated for a Mars landing application involving the supersonic inflation of an atmospheric aerodynamic decelerator system that includes a parachute canopy made of a woven fabric. Several alternative surrogate models are evaluated including a neural network.
arXiv:2007.05877v1 fatcat:gpfxqsdjpbepbcupymlxmt3mfq