Physics-based models of mechanical structures are widely adopted for assessing and predicting the behaviour of structures. In the context of structural mechanics, the constitutive law that describes the stress-strain relation forms an important modelling component, which suffers from a considerable amount of uncertainties. These uncertainties primarily arise due to the inherent simplifications and assumptions placed in favor of facilitating the modeling process. Bayesian techniques have been proven to be effective for tackling uncertainties associated with the identification of material model parameters and quantifying the confidence level that can be associated with the placed modeling assumptions.

We present a Bayesian framework for the identification of constitutive parameters of quasi-brittle materials suffering strain localization effects, via the use of full-field displacement measurements. The proposed framework explores the idea of force-based Finite Element Model Updating (FEMU-F), which relies on measured full-field displacements and aggregated forces. In particular, the scheme takes advantage of FEMU-F, in contrast to the conventional FEMU, where the information from full-field displacements is directly incorporated into the model. We also address the uncertainties involved in the measured displacements, by treating them as additional unknown variables to be identified, alongside the constitutive parameters. These unknown variables collectively form the inputs to a well-defined objective function, which forms the basis for the Bayesian inference problem. To efficiently solve this Bayesian problem, we employ a variational Bayesian scheme that relies on approximate posteriors represented as multivariate normal distributions. We demonstrate the proposed framework for the parameter identification of a nonlinear path-dependent gradient damage constitutive law, which exhibits strain localization and softening behaviour. The first example illustrates the effectiveness of the inference procedure, highlighting the advantage of FEMU-F in incorporating information about cracks. The second example demonstrates a sub-domain analysis suitable for inferring models with limited domain knowledge; e.g. with uncertain Dirichlet boundary conditions.

Epoxy-based adhesive mortars are applied as bonding materials for the heavy duty fastener in buildings and constructions worldwide. The long-term behavior of the adhesive mortars is a significant influencing factor on the sustained load and lifetime of bonded anchors. An adhesive mortar is a heterogeneous material consisting of resin and fillers. For the analysis of the long-term performance of the bonded anchor, it is fundamental to understand the long-term behavior of the bonding material on the microscale. This contribution presents a novel prediction approach for the long-term load capacity of the epoxy-based bonded anchor by using nanoindentation and FE-simulation. The long-term mechanical properties of the adhesive mortar were measured by using the precise nanoindentation technology on the micro level. Based on the experimental nanoindentation results, the numerical long-term time-independent material parameters were characterized in a concrete model by means of stochastic FE-simulation. For analysis of the imperfection effect of a real bonded anchor, the nanoindentation was employed on the micro level to investigate the error load transfer on the interface between mortar and concrete drillhole without drill-hole cleaning. On the macro level, the macroscale defects of an installed bonded anchor were found by using the computer tomography. It is demonstrated that the FE-model based on the nanoindentation results can correctly predict the long-term performances of a bonded anchorage system.

Joining dissimilar materials to create layered structure enables lightweight, customized designs for complex shapes and specific design requirements that optimize the performance of each material in the structure. An enabling technology for joining dissimilar materials without increasing weight and which overcomes many of the limitations of traditional joining methods is adhesive joining. Adhesive joining uses a polymeric material (adhesive) to bond the two dissimilar materials (adherends) such that the adhesive provides strength and stiffness to the structure. The bondline behavior between the two materials is a critical component in structural reliability and the installation process directly impacts the macroscale performance of an adhesive joint.

It is well established that the surface preparation of the adherends and the application of the adhesive lead to microstructural features and defects in adhesively bonded joints and that this resulting microstructure dictates macroscale mechanical behavior. While the microstructure significantly influences the in-situ macroscale performance, probabilistic characterization of the feature and defect distributions for varying installation conditions and the correlation to macroscale properties are lacking. Peridynamics offers a computational solution to rapidly generate stochastic models from probabilistic distributions of microstructural features and subsequently simulate progressive damage under loading.

A methodology has been developed to generate probabilistic distributions of features (including the surface roughness profile) and defects such as voids from images and to formulate peridynamics models from these distributions. Peridynamics analysis is then performed to simulate progressive damage due to the microstructural defects to statistically correlate microstructure to macroscale behavior. This method will be presented along with validated demonstrations based on physical test data for composite to metal joining.

Mesoscale discrete models, particularly those resolving large mineral grains via tessellation, excel in depicting realistic crack patterns and nonlinear responses of concrete-like materials under mechanical stress. These models excel in portraying progressive damage, inelastic deformations, and energy dissipation, standing out as close approximations for the response of laboratory-sized structures However, adapting these models for real-sized infrastructure is computationally challenging: the sheer number of grains in larger volumes hinders processing on standard computers. Techniques like grain coarsening and selective modeling have been employed to address this.

This presentation showcases an efficient implementation of a damage-based mesoscale discrete model, validated against concrete dog-bone specimen tests. The model accurately matches the response characteristics of specimens, maintaining 2D shape similarity and constant thickness. However, it falls short in fully capturing the experimentally observed strength dependence on structural size, attributed to the model's inability to fully account for statistical size effects due to random material property fluctuations. By modeling material parameters as autocorrelated random fields, we achieve a closer fit to experimental data, though predictions for sizes beyond 2 meters remain unfeasible due to the 2D plane stress simplification and the complex nature of stress redistribution processes.

We propose an analytical model to compute exceedance probabilities over spatially varying thresholds, extending our previous work on extremes of averaged random fields. This model, through the analytical derivation of effective strength as a sliding average of a random field, allows for predictions of strength in larger structures with correct asymptotic behavior, bridging the gap to classical Weibull statistics. Our findings suggest this approach not only matches the mesoscale simulation results but also provides a viable pathway for predicting larger structure strength, underscoring the potential of mesoscale modeling in overcoming computational and theoretical challenges in the field of concrete mechanics.

The inherent variability and imperfections in materials lead to randomness in engineering structures, greatly affecting structural stochastic response analysis and safety assessment. Therefore, it is essential to establish the rational modeling and precise simulation of random sources. The uncertainty in random sources is characterized by three aspects: the randomness of individual variables, the probabilistic dependence among multiple variables, and the spatial correlation of random variables. There are already some models that can effectively describe individual aspects. However, quantifying uncertainty in all these three aspects simultaneously remains a significant challenge. A novel method is proposed for simulating multivariate random fields, which can satisfy each spatial autocorrelation and arbitrary copula dependency given in the modeling condition. The analytical expression for the function regarding the spatial autocorrelation coefficient of variables is derived firstly. The numerical implementation procedures for simulating multivariate fields are introduced. The efficacy of the proposed method is validated with engineering application examples. The results demonstrate the ability of the proposed method in simultaneously capturing spatial parameter variability and probabilistic dependencies. This method furnishes refined stochastic input data for advanced structural stochastic response analysis and safety evaluations. The approach can be extended to simulate non-Gaussian random fields.