The Finite Element Method (FEM) is a well-established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with a discretisation error that can be an be quantified with \emph{a posteriori} error estimates. The practical relevance of error estimates for biomechanics problems, especially for soft tissue where the response is governed by large strains, is rarely addressed. In this contribution, we propose an implementation of \emph{a posteriori} error estimates targeting a user-defined quantity of interest, using the Dual Weighted Residual (DWR) technique tailored to biomechanics. The proposed method considers a general setting that encompasses three-dimensional geometries and model non-linearities, which appear in hyperelastic soft tissues. We take advantage of the automatic differentiation capabilities embedded in modern finite element software, which allows the error estimates to be computed generically for a large class of models and constitutive laws. First we validate our methodology using experimental measurements from silicone samples, and then illustrate its applicability for patient-specific computations of pressure ulcers on a human heel.

翻译：有限元方法是求解偏微分方程描述的确定性工程问题的一种成熟计算近似解的方法。有限元法能产生解的离散近似值，其离散化误差可通过后验误差估计进行量化。误差估计在生物力学问题中的实际应用价值鲜少被探讨，尤其是在软组织这类响应受大应变主导的领域。本文针对用户定义的关注量，提出一种采用适用于生物力学的对偶加权残差技术实现后验误差估计的方案。该方法考虑了包含三维几何体和非线性模型的通用设置，这些特征常见于超弹性软组织中。我们利用现代有限元软件内置的自动微分功能，从而能够对大量模型和本构方程进行通用化的误差估计计算。首先采用硅胶试样的实验测量数据验证了该方法的有效性，随后通过人体足跟压力性损伤的个性化计算案例展示了其适用性。