Inverse methodology as applied to reconstruct local textile features from measured pressure field

doi:10.1016/j.jmst.2020.09.010

Abstract

Abstract:

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 μ -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.

Key words: Textiles, Pressure sensors, Inverse method, Digital twin, Geometry reconstruction, Hyperelasticity

S. Bancora, C. Binetruy, S. Advani, S. Comas-Cardona. Inverse methodology as applied to reconstruct local textile features from measured pressure field[J]. J. Mater. Sci. Technol., 2021, 71: 241-247.

Figures/Tables 13

Fig. 1. UDT400 fabric.

Fig. 2. Schematic of Yarn cross section where w is the width and h is the thickness subjected to normal distributed traction vector $\text{ }\!\!\Gamma\!\!\text{ }{{e}_{2}}$.

Fig. 3. Single yarn compression device.

Fig. 4. Camera recorded yarn compression.

Fig. 5. Stress/stretch best curve fitting provided the model coefficients: $\text{ }\!\!\alpha\!\!\text{ }=44.8178,\text{ }\!\!\beta\!\!\text{ }=0.1857,\text{ }\!\!\mu\!\!\text{ }=0.8341\text{MPa}$ in Eq. (2).

Table 1 Measured reference cross-section area ${{\text{A}}_{0}}$ from an 8 samples population.

Yarn sample	1	2	3	4	5	6	7	8
${{A}_{0}}\left[ \text{m}{{\text{m}}^{2}} \right]$	1.10	1.11	1.11	1.09	1.12	1.08	1.04	1.12

Fig. 6. Flowchart to create the stress/initial geometry database.

Fig. 7. Finite element yarn compression, ${{\text{ }\!\!\sigma\!\!\text{ }}_{2}}$ stress field on a quarter of yarn.

Fig. 8. ${{\text{ }\!\!\Gamma\!\!\text{ }}_{\text{num}}}$ database for imposed final h=0.25 mm, half yarn normalized width (vertical symmetry). Units in legend are [mm].

Fig. 9. Visual validation of yarn geometry reconstruction (left) and pressure print of one yarn (right).

Fig. 10. (a) Pressure field used for the UDT400 textile reconstruction. Nodes are marked at the crossover regions. (b) Inter crossover sampling on yarn i (c) Longitudinally averaged pressure profile $\text{ }\!\!\Gamma\!\!\text{ }_{\text{meas}}^{i}$.

Table 2 Comparison of reconstructed vs measured yarn geometries [mm].

Specimen	$w_{0}^{\text{meas}}$	$h_{0}^{\text{meas}}$	$w_{0}^{\text{calc}}$ (err)	$h_{0}^{\text{calc}}$ (err)
1	2.94	0.35	3.192(8.5 %)	0.34(2.8 %)
2	3.39	0.33	3.392(0.05 %)	0.32(3%)
3	2.7	0.41	2.65(1.8 %)	0.405(1.2 %)
4	2.7	0.41	2.77(2.6 %)	0.4(4.8 %)
5	3.42	0.34	3.39(1%)	0.32(5.8 %)
6	2.75	0.39	2.855(3.8 %)	0.38(2.6 %)

Fig. 11. Synoptic comparison of real and reconstructed geometry of a 98×98mm UDT400 textile. (a) Picture of the real material (intra-yarn gaps highlighted) (b) Prescale pressure field (c) Reconstructed material.

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