Stretch-Based Hyperelastic Constitutive Metamodels Via Gradient Enhanced Gaussian Predictors - Nathan Ellmer (Computer Methods in Applied Mechanics and Engineering, 2024)
This paper introduces a new Gradient Enhanced Gaussian Predictor (Kriging) constitutive metamodel based on the use of principal stretches for hyperelasticity. The model further accounts for anisotropy by incorporating suitable invariants of the relevant symmetry integrity basis. The use of stretches is beneficial since it aligns to experimental practices for data gathering, removes the challenge associated with stress projections in isotropy, and increases the range of available constitutive models. This paper presents three significant novelties. The first arises from the proposed approach highlighting the need to enforce physical symmetries and resulted in the authors altering the standard Radial Basis style correlation function to incorporate invariants which naturally uphold these symmetries. The invariants used are both the commonly employed invariants of the right Cauchy–Green strain tensor and the lesser used invariants of the stretch tensor. Note that one may consider using invariants in the correlation function to be the same as using invariants for inputs to the metamodel and this would be true if Ordinary Kriging was used. But the derivatives used in the chain rule clearly result in a new formulation. Secondly, the authors compare two approaches to the infill strategies, one consisting of the error in stress and the other utilising uncertainty provided by Kriging directly. This enables Kriging to guide the user as to most efficient data to insert into the dataset. The final novelty involves the integration of calibrated constitutive metamodels into Finite Element simulations thereby showcasing the accuracy yielded even when handling highly complex deformations such as bending, wrinkling and pinching. Furthermore, the constitutive models are calibrated with data from both isotropic and anisotropic materials such as rank-one laminates, making the accuracy achieved with the small calibration sets even more impressive. The formulation is shown to perform equally well for both synthetic and experimental type of collected data.