Abstract
The anisotropic properties and pressure sensitivity are intrinsic features of the constitutive response of fiber network materials. Although advanced models have been developed to simulate the complex response of fibrous materials, the lack of comparative studies may lead to a dubiety regarding the selection of a suitable method. In this study, the pressure-sensitive Hoffman yield criterion and the Xia model are implemented for the plane stress case to simulate the mechanical response under a bi-axial loading state. The performance of both models is experimentally assessed by comparison to bi-axial tests on cruciform-shaped specimens loaded in different directions with respect to the material principal directions. The comparison with the experimentally measured forces shows the ability of the Hoffman model as well as the Xia model with shape parameter k≤2 to adequately predict the material response. However, this study demonstrates that the Xia model consistently presents a stiffer bi-axial response when k≥3 compared to the Hoffman model. This result highlights the importance of calibrating the shape parameter k for the Xia model using a bi-axial test, which can be a cumbersome task. Also, for the same tension-compression response, the Hill criterion as a special case of the Hoffman model presents a good ability to simulate the mechanical response of the material for bi-axial conditions. Furthermore, in terms of stability criteria, the Xia model is unconditionally convex while the convexity of the Hoffman model is a function of the orthotropic plastic matrix. This study not only assesses the prediction capabilities of the two models, but also gives an insight into the selection of an appropriate constitutive model for material characterization and simulation of fibrous materials. The UMAT implementations of both models which are not available in commercial software and the calibration tool of the Xia model are shared with open-source along with this work.
Highlights
Bio-based materials are broadly used in modern industry due to their competitive bending stiffness vs. price, sustainability, lightness, and relatively good mechanical properties (Jungstedt et al, 2020; Wang et al, 2021)
The small fibers bonded to each other due to hydrogen bonds (Roberts, 1996; Verma et al, 2014) are the main constitutive components of the Fiber Network (FN). This FN presents heterogeneity (Hagman and Nygårds, 2017; Hristopulos and Uesaka, 2004), structural disorderliness (Alzweighi et al, 2021; Lahti et al, 2020), and anisotropy (Considine et al, 2014) which result in difficulties in accurately predicting its mechanical performance
The simulation and experimental results are presented for the MDCD Test and the 45-Rot Test in Figs. 14(a) and (b), respectively
Summary
Bio-based materials are broadly used in modern industry due to their competitive bending stiffness vs. price, sustainability, lightness, and relatively good mechanical properties (Jungstedt et al, 2020; Wang et al, 2021). The small fibers bonded to each other due to hydrogen bonds (Roberts, 1996; Verma et al, 2014) are the main constitutive components of the FN This FN presents heterogeneity (Hagman and Nygårds, 2017; Hristopulos and Uesaka, 2004), structural disorderliness (Alzweighi et al, 2021; Lahti et al, 2020), and anisotropy (Considine et al., 2014) which result in difficulties in accurately predicting its mechanical performance. The complexity of the micro-mechanical models, difficulties in characterizing the properties of the fibers at the micro-level, and the prohibitive computational cost, limit the usage of direct FN simulations Overcoming these limitations is crucial for the proper product scale design and reliability assessment (Hu et al, 2021) of fibrous materials
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