Finite element forming simulation for non-crimp fabrics using a non-orthogonal constitutive equation

In the sintering of advanced ceramics, a digital twin consisted of a finite element model can predict the final shape and microstructure of a sintered ceramic. However, to minimise uncertainties, it is essential to continually update the mechanical properties in the digital twin using data collected from the manufacturing process. One promising approach for achieving this is through artificial neural networks (ANN). This study introduces a machine learning strategy to update the constitutive behaviour of advanced ceramics in finite element analysis of sintering deformation. A major challenge in implementing machine learning in material processing is the huge amount of data required by the training and validation of an ANN, which are often unavailable or incomplete in a real manufacturing process. This study demonstrates that the data requirement can be reduced by employing a two-step training technique. Firstly, the ANN is trained using a nonlinear constitutive law, which describes a general relationship between the strain rates and stresses. Subsequently, the weights and biases of the ANN are transferred for the retraining using limited experimental data for an actual ceramic. It is shown that such approach can successfully capture the nonlinear constitutive behaviour of fine-grained alumina without demanding for large amount of experimental data. A case study is provided, highlighting the feasibility of implementing the ANN in a commercial finite element package, to replace the constitutive law and predict the shrinkage and distortion of a sintering part. In particular, the sintered dumb-bell shape part, simulated using the retrained ANN, showed grain size and relative density that markedly different from those using the nonlinear constitutive law. It is important to note that the proposed methodology is generic and can be used to create ANNs to replace constitutive laws in finite element analysis in digital twins for a wide range of other engineering processes.

Predicting low velocity impact damage and Compression-After-Impact (CAI) behaviour of composite laminates

Low-velocity impact damage can drastically reduce the residual mechanical properties of the composite structure even when there is barely visible impact damage. The ability to computationally predict the extent of damage and compression after impact (CAI) strength of a composite structure can potentially lead to the exploration of a larger design space without incurring significant development time and cost penalties. A three-dimensional damage model, to predict both low-velocity impact damage and compression after impact CAI strength of composite laminates, has been developed and implemented as a user material subroutine in the commercial finite element package, ABAQUS/Explicit. The virtual tests were executed in two steps, one to capture the impact damage and the other to predict the CAI strength. The observed intra-laminar damage features, delamination damage area as well as residual strength are discussed. It is shown that the predicted results for impact damage and CAI strength correlated well with experimental testing.

Due to their high deformation capabilities, polymeric materials are widely used in several industries. However, polymers exhibit a complex behaviour with strain rate, temperature and pressure dependencies. Numerous constitutive models were developed in order to take into account their specific behaviour. Among these models, the ones proposed by Richeton et al Polymer 46:6035–6043 (2005a), Polymer 46:8194–8201 (2005b) seem to be particularly suitable. They proposed expressions for the Young modulus and the yield stress with strain rate and temperature dependence. Moreover, these models were also implemented in a finite elastic-viscoplastic deformation approach using a flow rule based on thermally activated process. The increase of computational capabilities allowed simulating polymer forming processes using finite element (FE) codes. The aim of the study is to implement the proposed constitutive model in a commercial FE code via a user material subroutine. The implementation of the model was verified using compressive tests over a wide range of strain rates. Next, FE simulations of an impact test and of a plane strain forging process were carried out. The FE predictions are in good agreement with the experimental results taken from the literature.

Picture frame shear tests are state of the art for determining the shear force vs. shear angle behaviour for in-plane deformation of most technical textiles, such as woven fabrics. Many publications describe this test and the used picture frames. Benchmark tests showed that the measured shearing behaviour for one sample depends on the picture frame used. The shearing rigidity of most textiles is very small compared to the in-plane tensile stiffness, so slight imperfections on the experimental setup have a significant effect on the measured results. During the picture frame test, wrinkles may form on the sample surface during the motion of the picture frame above a critical shear angle. These wrinkles can be described as local fabric buckling. If forming of wrinkles leads to a lower level of internal energy compared to a further shearing of the fabric, local wrinkles occur due to the principle of least action. Because of this effect, the measured shear force above the first formation of wrinkles is inaccurate for describing the exact shearing behaviour of textiles. Another possibility for measuring the shear force vs. shear angle behaviour is the bias-extension test. Here, higher shear angles can be achieved without the formation of wrinkles. Both methods are compared in this paper for different textile samples. The relationship of the shear angle and the applied shear force is an important mechanical value and one of the most important input parameter in numerical drape simulations. The analysis of wrinkles, which occur during textile draping, demands exact input parameters for the simulation. Most important for the drape simulation of technical high-performance textiles are accurate values for the bending and shear behaviours. This paper presents simulation results of the wrinkling during a picture frame shear test. Results show that the input parameter for the shear rigidity delivered by the picture frame shear test do not exactly reproduce the formed wrinkles and are, therefore, not suitable for an exact drape simulation. The underestimation of the shear force vs. shear angle behaviour will be shown with a finite element simulation model. The adaptation of the picture-frame and bias-extension parameters for a proper use in numerical drape simulations are examined.

Bending of unidirectional non-crimp-fabrics: experimental characterization, constitutive modeling and application in finite element simulation

Formability prediction of advanced high strength steels using constitutive models characterized by uniaxial and biaxial experiments

A novel arterial constitutive model in a commercial finite element package: Application to balloon angioplasty

Prediction of in-plane stiffness properties of non-crimp fabric laminates by means of 3D finite element analysis

Intelligent finite element method: An evolutionary approach to constitutive modeling

The paper investigates the mechanical properties of coated polyester fabrics in biaxial monotonic tensile tests. The nonlinear behaviors of the constitutive parameters within the full-stress range were in detail analyzed, and a new constitutive model based on the specific coupling relationships between the uniaxial and biaxial flexibilities was proposed to describe the complex tensile behaviors of coated fabrics under plane stresses. Finally, the accuracy of the nonlinear model in numerical simulations was verified, and special attention was devoted to the finite element (FE) implementation of the model as an ABAQUS user material (UMAT) subroutine. It was found that the constitutive parameters of the material varied noticeably with the stress level and ratio. The stiffnesses in the larger-stress direction are nearly stress-dominated, and the stress ratios exert a more significant effect on Poisson’s ratios than that on stiffnesses in the lower-stress direction. The proposed constitutive model, considering the material nonlinearities, is validated by the good correlations between the numerical and experimental results. Additionally, the FE simulation results using the UMAT are consistent with the experiments which reveals that the constitutive model proposed and the results obtained in this work are reliable.

Numerical study of steel plate shear walls with diverse construction configurations

Through-the-thickness stress distributions near edges of composite laminates using stress recovery scheme and third order shear and normal deformable theory

The cup‐drawing of a strongly anisotropic sheet metal is simulated using a commercial finite element software along with a user material subroutine. In order to accurately describe the plastic anisotropy of the material the well‐known recent yield function ‘Yld2004‐18p’ is extended. Regarding the experimental characterization of the considered material the occurrence of dynamic strain aging lead to an oscillating signal of the width change of the tensile samples, which prevented a reliable determination of plastic strain ratios (r‐values). Thus, an improved measurement concept was developed that leads to a very robust and reproducible determination of r‐values. Furthermore, a novel plane‐strain tensile test sample is presented which is used for the characterization of the plastic anisotropy in biaxial loading states. A quantitative comparison with measured earing profiles of deep drawn cups illustrates the predictive capabilities of the numerical simulation.

Constitutive modeling and finite element procedure development for stress analysis of prismatic high temperature gas cooled reactor graphite core components