ABSTRACT The unloaded configuration of a body without residual stresses is generally used as the starting point to compute the displacement field but may be unknown for some applications. In this paper, we propose a novel inverse formulation to identify the unloaded configuration of a deformed hyperelastic body using finite element based discretization schemes. The inverse problem consists of finding a domain that is geometrically defined by its boundary such that it deforms in a way consistent with the measurements taken on its deformed configuration. The coordinates of boundary nodes in the deformed configuration can be measured and are assumed to be known for the inverse problem. Since only the coordinates of boundary nodes in the unloaded configuration are updated in each step of the inverse analysis, re-meshing is essential to continue the optimization process. The Akin’s method is employed to map the mesh used for the unloaded configuration in the previous step for the updated one. Both numerical and experimental data sets are used in 2D/3D to demonstrate the effectiveness of the proposed inverse technique. This work could have practical applications in the design of elastomeric parts or to recover the unloaded configuration of soft tissues in vivo.

中文翻译：

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一种识别变形超弹性体卸载构型的新方法

摘要 没有残余应力的物体的卸载配置通常用作计算位移场的起点，但在某些应用中可能是未知的。在本文中，我们提出了一种新的逆公式，以使用基于有限元的离散化方案来识别变形超弹性体的卸载配置。逆问题包括找到一个域，该域由其边界几何定义，使其变形的方式与其变形配置所进行的测量一致。可以测量变形配置中边界节点的坐标，并假设它对于逆问题是已知的。由于在逆分析的每一步中只更新卸载配置中边界节点的坐标，重新划分网格对于继续优化过程至关重要。使用 Akin 方法来映射用于更新配置的上一步中卸载配置的网格。在 2D/3D 中使用数值和实验数据集来证明所提出的逆技术的有效性。这项工作可以在弹性部件的设计或在体内恢复软组织的卸载配置方面具有实际应用。