Three-dimensionally (3D) knitted technical textiles are spreading into industrial applications, since their geometric, structural and functional performance can be tailored and optimized on fibre-, yarnand fabric levels by customizing yarn materials, knit patterns and geometric shapes. The ability to simulate their complex mechanical behaviour is thus an essential ingredient in the development of a digital workflow for optimal design and manufacture of 3D knitted textiles. Here, we present a multi-scale modelling and simulation framework for the prediction of the nonlinear orthotropic mechanical behaviour of single jersey knitted textiles and its experimental validation. On the meso-scale, representative volume elements (RVEs) of the fabric are modelled as single, interlocked yarn loops and their mechanical deformation behaviour is homogenized using periodic boundary conditions. Yarns are modelled as nonlinear 3D beam elements and numerically discretized using an isogeometric collocation method, where a frictional contact formulation is used to model inter-yarn interactions. On the macro-scale, fabrics are modelled as membrane elements with nonlinear orthotropic material behaviour, which is parameterized by a response surface constitutive model obtained from the meso-scale homogenization. The input parameters of the yarn-level simulation, i.e., mechanical properties of yarns and geometric dimensions of yarn loops in the fabrics, are determined experimentally and subsequent meso-and macro-scale simulation results are evaluated against reference results and mechanical tests of knitted fabric samples. Good agreement between computational predictions and experimental results is achieved for samples with varying stitch values, thus validating our novel computational approach combining efficient meso-scale simulation using 3D beam modelling of yarns with numerical homogenization and nonlinear orthotropic response surface constitutive modelling on the macroscale.
This paper summarizes the literature on reconciliation of finite element analyses with in-plane bending experiments on piping elbows. It then describes in detail two four-point-bending tests on straight pipes and two in-plane bending tests on elbows and the corresponding nonlinear finite element analyses. Using a new procedure for obtaining a stress-strain curve for stainless steel using only values for E,Sy, and Su and a representative stress-strain curve from a test on a similar material specimen, the nonlinear responses of the piping components tested are shown to be simulated more accurately than previously published results.
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