Surrogate-model-assisted uncertainty treatment practices have been the subject of increasing attention and investigations in recent decades for many symmetrical engineering systems. This paper delivers a review of surrogate modeling methods in both uncertainty quantification and propagation scenarios. To this end, the mathematical models for uncertainty quantification are firstly reviewed, and theories and advances on probabilistic, non-probabilistic and hybrid ones are discussed. Subsequently, numerical methods for uncertainty propagation are broadly reviewed under different computational strategies. Thirdly, several popular single surrogate models and novel hybrid techniques are reviewed, together with some general criteria for accuracy evaluation. In addition, sample generation techniques to improve the accuracy of surrogate models are discussed for both static sampling and its adaptive version. Finally, closing remarks are provided and future prospects are suggested.

Modelling and simulation are very important for revealing the relationship between process parameters and internal variables like grain morphology in solidification, precipitate evolution, and solid-state phase transformation in laser additive manufacturing. The impact of the microstructural changes on mechanical behaviors is also a hot topic in laser additive manufacturing. Here we reviewed key developments in thermal modelling, microstructural simulations, and the predictions of mechanical properties in laser additive manufacturing. A volumetric heat source model, including the Gaussian and double ellipsoid heat sources, is introduced. The main methods used in the simulation of microstructures, including Monte Carlo method, cellular automaton, and phase field method, are mainly described. The impacts of the microstructures on mechanical properties are revealed by the physics-based models including a precipitate evolution based model and dislocation evolution based model and by the crystal plasticity model. The key issues in the modelling and simulation of laser additive manufacturing are addressed.

Phase-field modeling of fracture has gained popularity within the last decade due to the flexibility of the related computational framework in simulating three-dimensional arbitrarily complicated fracture processes. However, the numerical predictions are greatly affected by the presence of uncertainties in the mechanical properties of the material originating from unresolved heterogeneities and the use of noisy experimental data. The objective of this work is to apply the Bayesian approach to estimate bulk and shear moduli, tensile strength and fracture toughness of the phase-field model, thus improving accuracy of the simulations with the help of experimental data. Conventional approaches for estimating the Bayesian posterior probability density function adopt sampling schemes, which often require a large amount of model estimations to achieve the desired convergence, thus resulting in a high computational cost. In order to alleviate this problem, we employ a more efficient approach called sampling-free linear Bayesian update, which relies on the evaluation of the conditional expectation of parameters given experimental data. We identify the mechanical properties of cement mortar byconditioningon the experimental data of the three-point bending test (observations) in an online and offline manner. In the online approach the parameter values are sequentially updated on the fly as the new experimental information comes in. In contrast, the offline approach is used only when the whole history of experimental data is provided once the experiment is performed. Both versions of estimation are discussed and compared by validating the phase-field fracture model on an unused set of experimental data.

Carbon fiber reinforced plastics (CFRPs) gained high interest in industrial applications because of their excellent strength and low specific weight. The stacking sequence of the unidirectional plies forming a CFRP laminate, and their thicknesses, primarily determine the mechanical performance. However, during manufacturing, defects, e.g., pores and residual stresses, are induced, both affecting the mechanical properties. The objective of the present work is to accurately measure residual stresses in CFRPs as well as to investigate the effects of stacking sequence, overall laminate thickness, and the presence of pores on the residual stress state. Residual stresses were measured through the incremental hole-drilling method (HDM). Adequate procedures have been applied to evaluate the residual stresses for orthotropic materials, including calculating the calibration coefficients through finite element analysis (FEA) based on stacking sequence, laminate thickness and mechanical properties. Using optical microscopy (OM) and computed tomography (CT), profound insights into the cross-sectional and three-dimensional microstructure, e.g., location and shape of process-induced pores, were obtained. This microstructural information allowed for a comprehensive understanding of the experimentally determined strain and stress results, particularly at the transition zone between the individual plies. The effect of pores on residual stresses was investigated by considering pores to calculate the calibration coefficients at a depth of 0.06 mm to 0.12 mm in the model and utilizing these results for residual stress evaluation. A maximum difference of 46% in stress between defect-free and porous material sample conditions was observed at a hole depth of 0.65 mm. The significance of employing correctly calculated coefficients for the residual stress evaluation is highlighted by mechanical validation tests.

Additives such as nucleating agents are often used in the processing of plastic products not only for improving production efficiency but also for enhancing mechanical performance. In this work, the short- and long-term tensile strength, the morphology as well as the residual stresses of the welded polypropylene (PP) samples with different fillers (carbon black and special beta-nucleating agents) and different dimensionless joining paths are analyzed. Results obtained are then compared with those that are representative of the initial, filler-free samples. It is shown that, upon using the special beta-nucleating agent, superior long-term tensile strength can be achieved compared to the samples without additives or with carbon black agent (e.g., for the dimensionless joining path of 0.95, the long-term tensile strength of a PP nature sample is characterized by around 400 MPa, whereas by adding beta-nucleating agent 1% the value can be increased by 400% to reach around 2050 MPa). However, adding beta-nucleating agent 1% yields inferior short-term tensile strength. The hole drilling method (HDM) is used for the analysis of residual stresses. It is found that the residual stresses in the weld seam are characterized by low values of the tensile stresses. The residual stresses in the weld seam also can be converted from tensile into compressive stresses by adding the beta nucleating agent. However, this has the disadvantage that with a higher proportion by weight of the beta nucleating agent, the short-term tensile strength of the welded joint becomes lower than that of the other tested bonds.