Stretch-based hyperelastic constitutive metamodels via Gradient Enhanced Gaussian Predictors

作者：Nathan Ellmer, Rogelio Ortigosa, Jesús Martínez‐Frutos, Roman Poya, Johann Sienz, Antonio J. Gil · 发表于：Computer Methods in Applied Mechanics and Engineering · 年份：2024 · DOI：10.1016/j.cma.2024.117408 · 被引用次数：2 · 研究领域：Elasticity and Material Modeling、Robotic Mechanisms and Dynamics、Probabilistic and Robust Engineering Design

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....