In this paper, numerical methods of fatigue life prediction for elastomers subjected to multidirectional, variable amplitude loadings are presented. Because experiments and numerical methods use different stress measures in large deformation, transformation between nominal stress and the second Piola–Kirchhoff stress is performed before fatigue life calculation. In order to incorporate the Mullins effect, the material properties of elastomers are calculated after an initial transition period. An efficient interpolation scheme using load stress/strain curves under unidirectional loading is proposed based on the fatigue characteristic of elastomers. A rainflow counting method with multi‐stress components is developed for variable amplitude loadings, and the critical plane method is applied to find the plane with the maximum damage parameter. Fatigue life predictions using the proposed numerical method are validated against experimental results. As a practical example, the fatigue life of a rubber engine mount is predicted using the proposed numerical method.

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Large sampling uncertainty is generally introduced in the calculation of a low percentile of fatigue crack growth life due to a small number of coupon tests. It is often desirable to estimate a low percentile (for example, 10th percentile) with a certain coverage probability (for example, 95%) using the confidence bound approach. An equally competing objective is not to have overly conservative bounds.The performance of two bootstrap-based methods are investigated for calculating a one-sided 95% confidence bound on a low percentile of lognormal and gamma fatigue crack growth life distributions. A comparison is also made with the classical tolerance interval method and nonparametric (Hanson-Koopmans) method. These confidence bounds methods are tested to estimate B-basis fatigue crack growth design life using material properties estimated from coupon test samples ranging from 8 to 64.

Image segmentation for quantifying damage based on Bayesian updating scheme is proposed for diagnosis and prognosis in structural health monitoring. This scheme enables taking into account the prior information of the state of the structures, such as spatial constraints and image smoothness. Bayes' law is employed to update the segmentation with the spatial constraint described as Markov Random Field and the current observed image acting as a likelihood function. Segmentation results demonstrate that the proposed algorithm holds promise of searching a crack area in the SHM image and focusing on the real damage area by eliminating the pseudo-shadow area. Thus more precise crack estimation can be obtained than the conventional K-means segmentation by shrinking the fuzzy tails which often exist on both sides of the crack tips.

In the first paper of this two-part study basic theories were introduced for several new methodologies developed in the Automotive Research Center (a US Army TACOM Center of Excellence for Modelling and Simulation of Ground Vehicles at the University of Michigan) for the simulation and design of advanced structures and materials for next-generation ground vehicles. These new methodologies include: (1) an advanced topology optimisation technique for innovative conceptual design of vehicle structures and materials; (2) a systematic design optimisation process with efficient analysis and sensitivity analysis capabilities for detailed design modifications to improve the vibration and noise characteristics of a complex vehicle structure; (3) a reduced-order modelling technique that can be used to systematically generate low-order models for the prediction of vehicle vibration, power flow, and the effects of parameter uncertainties; and (4) an efficient and accurate energy boundary element analysis method for highfrequency noise analysis outside the vehicle. In this second paper, an extensive case study is presented to demonstrate how the methodologies presented in the first paper can be applied to a vehicle system. A pick-up truck equipped with an advanced hybrid propulsion system is considered in this paper, and various example design and prediction problems are discussed, which provide proofof-concept for the methodologies developed.