A nonlinear block-coupled Finite Volume methodology is developed for large displacement and large strain regime. The new methodology uses the same normal and tangential face derivative discretisations found in the original fully coupled cell-centred Finite Volume solution methodology for linear elasticity, meaning that existing block-coupled implementations may easily be extended to include finite strains. Details are given of the novel approach, including use of the Newton-Raphson procedure on a residual functional defined using the linear momentum equation. A number of 2-D benchmark cases have shown that, compared with a segregated procedure, the new approach exhibits errors with many orders of magnitude smaller and a much higher convergence rate.

中文翻译：

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大应变大位移问题的块耦合有限体积方法

针对大位移和大应变状态开发了一种非线性块耦合有限体积方法。新方法使用与原始完全耦合的以单元为中心的有限体积解决方案方法相同的法向和切向面导数离散化，用于线性弹性，这意味着现有的块耦合实现可以轻松扩展到包括有限应变。给出了新方法的详细信息，包括在使用线性动量方程定义的残差函数上使用 Newton-Raphson 过程。许多二维基准案例表明，与隔离程序相比，新方法的误差要小许多数量级，收敛速度要高得多。