Nonlinear isogeometric multiscale simulation for design and fabrication of functionally graded knitted textiles

Do, Huy; Tan, Ying Yi; Ramos, Nathalie; Kiendl, Josef; Weeger, Oliver

doi:10.1016/j.compositesb.2020.108416

Cited by 17 publications

(12 citation statements)

References 48 publications

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“…where r is the radius of the rods. The first variation of the contact potential energy (23) gives its contribution to the weak form of the equilibrium equations (15). This contribution takes the form…”

Section: Yarn-to-yarn Contactmentioning

confidence: 99%

“…the reviews [9,10,11]. Twoscale homogenisation often referred to as FE 2 , combined with a yarn-level and a membranelevel finite element model has been also applied to woven and knitted fabrics [12,13,14,15]. The boundary conditions of the microscale representative volume element (RVE) are given by the membrane deformation and in turn the averaged yarn stress in the RVE yields the membrane stress.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Computational modelling and data-driven homogenisation of knitted membranes

Herath,

Xiao,

Cirak

2021

Preprint

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Knitting is an effective technique for producing complex three-dimensional surfaces owing to the inherent flexibility of interlooped yarns and recent advances in manufacturing providing better control of local stitch patterns. Fully yarn-level modelling of large-scale knitted membranes is not feasible. Therefore, we consider a two-scale homogenisation approach and model the membrane as a Kirchhoff-Love shell on the macroscale and as Euler-Bernoulli rods on the microscale. The governing equations for both the shell and the rod are discretised with cubic B-spline basis functions. The solution of the nonlinear microscale problem requires a significant amount of time due to the large deformations and the enforcement of contact constraints, rendering conventional online computational homogenisation approaches infeasible. To sidestep this problem, we use a pre-trained statistical Gaussian Process Regression (GPR) model to map the macroscale deformations to macroscale stresses. During the offline learning phase, the GPR model is trained by solving the microscale problem for a sufficiently rich set of deformation states obtained by either uniform or Sobol sampling. The trained GPR model encodes the nonlinearities and anisotropies present in the microscale and serves as a material model for the macroscale Kirchhoff-Love shell. After verifying and validating the different components of the proposed approach, we introduce several examples involving membranes subjected to tension and shear to demonstrate its versatility and good performance.

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Section: Yarn-to-yarn Contactmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computational modelling and data-driven homogenisation of knitted membranes

Herath,

Xiao,

Cirak

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Using unit cell definition and periodic boundary conditions, FEA under different loading situations lead to identical experiment results. 22 Vassiliadis' work 22 is expended to a multi-scale modeling by O. Weeger et al [23][24] to a multi-scale modeling based on yarns numerically discretized using an isogeometric collocation approach.…”

Section: Introductionmentioning

confidence: 99%

Mechanical behaviour of 3D monofilament knitted fabrics: Modeling, simulation and validation

Cherradi

Kébir

Boukhriss

et al. 2022

Journal of Industrial Textiles

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Three-dimensionally (3D) knitted technology textiles are expanding into industrial and technical applications of textile composites given their geometric, structural, and functional performance. However, there are many challenges in developing computational tools that allow for physics-based predictions while keeping the related computing cost low. The strong interactions between geometrical and physical elements permit determining the behavior of this type of engineering material. In the aim of understanding the specific mechanical behaviors of knitted textiles, a yarn-level simulation model framework was created to predict the nonlinear orthotropic mechanical behavior of monofilament jersey-knitted textiles. The relative contributions of many computational parameters on the global mechanical behavior of knitted fabrics are investigated, specifically, inter-yarn interactions and the boundary conditions effect. The models are saved in a format that can be read directly by Finite Element Analysis FEA software. Yarns are numerically discretized as nonlinear 3D beam components, while input parameters, such as mechanical characteristics of yarns and geometric dimensions of loops in fabrics are established experimentally. Good agreement was relieved by comparing experimental data to simulation results in a wale-wise direction tensile load.

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“…There is an extensive amount of literature on finite element‐based computational homogenization of heterogeneous solids, see, for example, the reviews 9‐11 . Two‐scale homogenization often referred to as FE 2 , combined with a yarn‐level and a membrane‐level finite element model, has also been applied to woven and knitted fabrics 12‐15 . The boundary conditions of the microscale representative volume element (RVE) are given by the membrane deformation and in turn the averaged yarn stress in the RVE yields the membrane stress.…”

Section: Introductionmentioning

confidence: 99%

“…Subsequently, the trained model provides a closed‐form constitutive equation that is used in the macroscale model. As a machine learning model, for instance, neural networks, GPR or polynomial regression have been used 15‐19 . Alternatively, it is possible to formulate the macroscale finite element problem directly on the training data set, bypassing the need to train a machine learning model 20,21 .…”

Section: Introductionmentioning

confidence: 99%

Computational modeling and data‐driven homogenization of knitted membranes

Herath

Xiao

Cirak

2021

Numerical Meth Engineering

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Knitting is an effective technique for producing complex three‐dimensional surfaces owing to the inherent flexibility of interlooped yarns and recent advances in manufacturing, providing better control of local stitch patterns. Fully yarn‐level modeling of large‐scale knitted membranes is not feasible. Therefore, we use a two‐scale homogenization approach and model the membrane as a Kirchhoff‐Love shell on the macroscale and as Euler‐Bernoulli rods on the microscale. The governing equations for both the shell and the rod are discretized with cubic B‐spline basis functions. For homogenization, we consider only the in‐plane response of the membrane. The solution of the nonlinear microscale problem requires a significant amount of time due to the large deformations and the enforcement of contact constraints, rendering conventional online computational homogenization approaches infeasible. To sidestep this problem, we use a pretrained statistical Gaussian process regression (GPR) model to map the macroscale deformations to macroscale stresses. During the offline learning phase, the GPR model is trained by solving the microscale problem for a sufficiently rich set of deformation states obtained by either uniform or Sobol sampling. The trained GPR model encodes the nonlinearities and anisotropies present in the microscale and serves as a material model for the membrane response of the macroscale shell. The bending response can be chosen in dependence of the mesh size to penalize the fine out‐of‐plane wrinkling of the membrane. After verifying and validating the different components of the proposed approach, we introduce several examples involving membranes subjected to tension and shear to demonstrate its versatility and good performance.

show abstract

Nonlinear isogeometric multiscale simulation for design and fabrication of functionally graded knitted textiles

Cited by 17 publications

References 48 publications

Computational modelling and data-driven homogenisation of knitted membranes

Computational modelling and data-driven homogenisation of knitted membranes

Mechanical behaviour of 3D monofilament knitted fabrics: Modeling, simulation and validation

Computational modeling and data‐driven homogenization of knitted membranes

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