One can compute the final deformation of a known geometry under specific boundary conditions using the constitutive laws of mechanics that describe their stress strain behavior. In such cases the initial geometry is known, and all operators mapping the deformation are defined on the reference domain. However, there are situations in which the final configuration of a deformation might be known but not the initial. The inverse formulation allows one to determine the initial geometry of a domain, given its final deformation state, the material behavior law and a set of boundary conditions. In the present work we propose a method to reconstruct the mesoscale geometry of a textile based on its mechanical response during compaction. To do so, stress boundary conditions are acquired by means of a pressure-sensitive film. By adopting an appropriate material law, the thickness and width information of the yarns are deduced from the pressure field experienced by the compacted textile. Unlike 3D scanning techniques such as $\mu$ -CT, the proposed method can be applied on any domain size, allowing long-range variability to be captured. To the best of the authors' knowledge, there are no previous works that use a pressure-sensitive film on a large domain to capture the input data for a shape reconstruction. This example application serves as a demonstration of a methodology which could be applied to other classes of materials.

可以使用描述应力应力行为的力学本构定律，计算特定边界条件下已知几何形状的最终变形。在这种情况下，初始几何是已知的，并且映射变形的所有算子都在参考域上定义。但是，在某些情况下，可能知道变形的最终构造，但不知道初始变形。逆公式可以确定一个域的初始几何形状，并给出其最终变形状态，材料行为定律和一组边界条件。在当前的工作中，我们提出了一种基于压实过程中的机械响应来重构纺织品的中尺度几何形状的方法。为此，借助于压敏膜获得应力边界条件。通过采用适当的材料定律，可以从压实的纺织品所经历的压力场中得出纱线的粗细和宽度信息。不像3D扫描技术，例如$\mu$-CT，所提出的方法可以应用于任何域大小，从而可以捕获远距离变化。就作者所知，以前没有作品在大范围内使用压敏胶片来捕获输入数据以进行形状重构。此示例应用程序演示了可以应用于其他类别材料的方法。