Computational modeling and data‐driven homogenization of knitted membranes

Abstract

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.

Topologically optimal design and failure prediction using conditional generative adversarial networks

“…Machine learning and one of its main subsets deep learning have gained increasing popularity in various research communities, certainly not limited to material modeling, 27‐29 computer vision, 30,31 and image processing 11,14,22 . Convolution neural networks (CNNs) are a subset of deep Learning algorithms which take in an image, designate various learnable features/objects in the image and predict desired output.…”

Nonlinear response modelling of material systems using constrained Gaussian processes

“…Furthermore, GPR has been used merely as an interpolation technique in a plethora of research studies. Multiscale homogenisation of knitted 3 and woven 39 textiles; validating computational fluid dynamics experimentation by a GPR-inspired method, 40 GPR-based estimation of CO2 adsorption 41 ; autonomous materials discovery guided by GPR using a synchrotron beamline based synthetic and experimental tests 42 are a few among many interesting uses of GPR modelling. Departing from the established approach to GPR as given in Rasmussen and Williams , 37 constrained GPR (commonly referred to as CGPR) has now gained increasing popularity in various research communities.…”

“…In this article, the nonlinear homogenisation of a representative volume element (RVE) in a weft-knitted technical textile is considered (see Figure 1 for boundary value problem definitions). 3,5,58 The experimental results 58 and validated finite element results 3 are used to train the CGPR models. In Figure 1, individual yarns are modelled as 1D finite deformable beam elements with a radius 0.0923 mm, Young's modulus of 800 MPa, course and wale spacings 0.4875 and 0.8327 mm, respectively.…”

“…Therefore, such simulations are cost‐ and labour‐intensive which motivates the use of data‐driven techniques in approximating the macroscale nonlinear response. In this article, the nonlinear homogenisation of a representative volume element (RVE) in a weft‐knitted technical textile is considered (see Figure 1 for boundary value problem definitions) 3,5,58 . The experimental results 58 and validated finite element results 3 are used to train the CGPR models.…”

“…In recent decades, the fields of materials science and various engineering disciplines have undergone a transformative shift towards the adoption of data‐driven (data‐centric) approaches for modelling nonlinear responses. As the conventional empirical, analytical and experiment‐based models fail to capture the complex behaviours exhibited by novel material systems such as; metamaterials, 1 micro‐lattices, 2 hierarchical materials, 3,4 interlaced and interwoven composites, 5–7 data‐driven techniques have been established to unveil the underlying kinematic patterns and relationships 8 . This transformation is fueled by sophisticated material response simulators, physics‐conforming computational methods and high‐performance computing facilities leading towards the exponential growth of data generation coupled with the latest advancements in machine learning techniques 9 .…”