A finite strain model for fiber angle plasticity of textile fabrics based on isogeometric shell finite elements

TL;DR

This paper develops a finite-strain, surface-invariant elastoplastic model for textile fabrics within an anisotropic Kirchhoff-Love shell framework, focusing on angle plasticity between fiber families. The authors introduce a multiplicative split of the deformation gradient, define relative fiber-angle measures, and formulate a yield function with isotropic hardening, solved via a predictor-corrector return-mapping scheme implemented in isogeometric shell elements. Key contributions include an analytical solution for the picture frame test, thorough FE verification, and calibration/validation against bias extension data across multiple plain weave fabrics, demonstrating accurate prediction of both sticking/sliding and hardening phases. The approach enables robust 3D shell problems with complex draping, wrinkling, and self-contact while avoiding thickness integration, providing a practical framework for textile modeling and optimization. The work advances surface-invariant elastoplasticity for dry textiles and offers a versatile basis for extending to bending, twisting, and cyclic loading in anisotropic shells.

Abstract

This work presents a shear elastoplasticity model for textile fabrics within the theoretical framework of anisotropic Kirchhoff-Love shells with bending of embedded fibers proposed by Duong et al. (2023). The plasticity model aims at capturing the rotational inter-ply frictional sliding between fiber families in textile composites undergoing large deformation. Such effects are usually dominant in dry textile fabrics such as woven and non-crimp fabrics. The model explicitly uses relative angles between fiber families as strain measures for the kinematics. The plasticity model is formulated directly with surface invariants without resorting to thickness integration. Motivated by experimental observations from the picture frame test, a yield function is proposed with isotropic hardening and a simple evolution equation. A classical return mapping algorithm is employed to solve the elastoplastic problem within the isogeometric finite shell element formulation of Duong et al. (2022). The verification of the implementation is facilitated by the analytical solution for the picture frame test. The proposed plasticity model is calibrated from the picture frame test and is then validated by the bias extension test, considering available experimental data for different samples from the literature. Good agreement between model prediction and experimental data is obtained. Finally, the applicability of the elastoplasticity model to 3D shell problems is demonstrated.

Figures (19)

• Figure 1: Shell surface $\mathcal{S}$ with an embedded fiber bundle along curve $\mathcal{C}$shelltextile. Multiple fiber families are distinguished by index $i=1,2,3,..., n_\mathrm{f}$. Vectors $\boldsymbol{\ell}_i$, $\boldsymbol{c}_i$, and $\boldsymbol{n}$ maintain unit length during deformations by definition. The red planes illustrate tangent planes.
• Figure 2: Split of the surface deformation into elastic and plastic parts sauer2019decomF. This introduces the intermediate configuration $\hat{\mathcal{S}}$ between reference and current configurations $\mathcal{S}_0$ and $\mathcal{S}$. The geometrical objects of Sec. \ref{['s:geodescription']} are defined likewise in the three configurations. In particular, fiber angle measures $\Theta_{12} := \boldsymbol{L}_1\cdot\boldsymbol{L}_2=\cos\Theta$, $\theta_{12} := \boldsymbol{\ell}_1 \cdot \boldsymbol{\ell}_2 = \cos\theta$ and $\hat{\theta}_{12} := {\hat{ \boldsymbol{\ell}} }_1\cdot{\hat{ \boldsymbol{\ell}} }_2=\cos\hat{\theta}$ are defined here for a pair of two fiber families $\mathcal{C}_1$ and $\mathcal{C}_2$.
• Figure 3: Picture frame test conducted at Hong Kong University of Science and Technology (HKUST): (a) frame setup, (b) a woven fabric sample at initial configuration, (c) enlargement of a representative fabric cell, (d) fabric sample at deformed configuration. Here, the pictures are taken from Cao2008a and Zhu2007, with permission from Elsevier.
• Figure 4: Picture frame test: A typical shear force curve versus shear angle, approximately subdivided into three phases, where phases I-II result from rotational friction, and phase III is governed by yarn-yarn locking. The shear angle here is defined as $\gamma:=90^\circ- \theta$.
• Figure 5: Characteristics of the proposed yield function: (a) yield surface $f_\mathrm{y} = 0$ from Eq. \ref{['e:fy_general']} and (b) function derivative $f'_{\mathrm{iso}}(q)$ from Eq. \ref{['e:fiso']} versus hardening variable $q$. Here, we have used $\tau_\mathrm{y}=0.1\,\mu_0$, $A=0.05\, \mu_0$, $a= 1$, $B= 0.01\, \mu_0$, $b= 55$, $C= 0.7\, \mu_0$ and $c= 5$, where $\mu_0$ denotes a stress measure.