Ahmadi Masoud, McBride Andrew, Steinmann Paul, Saxena Prashant
Glasgow Computational Engineering Centre, James Watt School of Engineering, University of Glasgow, Glasgow, G12 8LT UK.
Institute of Applied Mechanics, Friedrich-Alexander University Erlangen-Nürnberg, D-91052 Erlangen, Germany.
Acta Mech. 2025;236(7):3975-3994. doi: 10.1007/s00707-025-04310-z. Epub 2025 May 30.
Modelling the large deformation of hyperelastic solids under plane stress conditions for arbitrary compressible and nearly incompressible material models is challenging. This is in contrast to the case of full incompressibility where the out-of-plane deformation can be entirely characterised by the in-plane components. A rigorous general procedure for the incorporation of the plane stress condition for the compressible case (including the nearly incompressible case) is provided here, accompanied by a robust and open source finite element code. An isochoric/volumetric decomposition is adopted for nearly incompressible materials yielding a robust single-field finite element formulation. The nonlinear equation for the out-of-plane component of the deformation gradient is solved using a Newton-Raphson procedure nested at the quadrature point level. The model's performance and accuracy are made clear via a series of simulations of benchmark problems. Additional challenging numerical examples of composites reinforced with particles and fibres further demonstrate the capability of this general computational framework.
对任意可压缩和近不可压缩材料模型，在平面应力条件下对超弹性固体的大变形进行建模具有挑战性。这与完全不可压缩的情况形成对比，在完全不可压缩情况下，面外变形可完全由面内分量表征。本文提供了一种将平面应力条件纳入可压缩情况（包括近不可压缩情况）的严格通用程序，并附带一个强大的开源有限元代码。对于近不可压缩材料，采用等容/体积分解，得到一个强大的单场有限元公式。使用在积分点级别嵌套的牛顿-拉夫逊法求解变形梯度面外分量的非线性方程。通过一系列基准问题模拟，该模型的性能和准确性得以明确。用颗粒和纤维增强的复合材料的其他具有挑战性的数值例子进一步证明了这个通用计算框架的能力。
