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In this work the linear elastic properties of materials containing spherical voids are calculated and compared using finite element simulations. The focus is on homogeneous solid materials with spherical, empty voids of equal size. The voids are arranged on crystalline lattices (SC, BCC, FCC and HCP structure) or randomly, and may overlap in order to produce connected voids. In that way, the entire range of void fraction between 0.00 and 0.95 is covered, including closed-cell and open-cell structures. For each arrangement of voids and for different void fractions the full stiffness tensor is computed. From this, the Young's modulus and Poisson ratios are derived for different orientations. Special care is taken of assessing and reducing the numerical uncertainty of the method. In that way, a reliable quantitative comparison of different void structures is carried out. Among other things, this work shows that the Young's modulus of FCC in the (1 1 1) plane differs from HCP in the (0 0 0 1) plane, even though these structures are very similar. For a given void fraction SC offers the highest and the lowest Young's modulus depending on the direction. For BCC at a critical void fraction a switch of the elastic behaviour is found, as regards the direction in which the Young's modulus is maximised. For certain crystalline void arrangements and certain directions Poisson ratios between 0 and 1 were found, including values that exceed the bounds for isotropic materials. For subsequent investigations the full stiffness tensor for a range of void arrangements and void fractions are provided in the supplemental material.

Quasi-brittle materials exhibit strain softening. Their modeling requires regularized constitutive formulations to avoid instabilities on the material level. A commonly used model is the implicit gradient enhanced damage model. For complex geometries, it still shows structural instabilities when integrated with classical backward Euler schemes. An alternative is the implicit-explicit (IMPL-EX) integration scheme. It consists of the extrapolation of internal variables followed by an implicit calculation of the solution fields. The solution procedure for the nonlinear gradient enhanced damage model is thus transformed into a sequence of problems that are algorithmically linear in every time step. Therefore, they require one single Newton-Raphson iteration per time step to converge. This provides both additional robustness and computational speedup. The introduced extrapolation error is controlled by adaptive time stepping schemes. Two novel classes of error control schemes that provide further performance improvements are introduced and assessed. In a three dimensional com-1 Titscher, January 30, 2019 pression test for a mesoscale model of concrete, the presented scheme provides a speedup of about 40 compared to an adaptive backward Euler time integration.

Using digital twins for decision making is a very promising concept which combines simulation models with corresponding experimental sensor data in order to support maintenance decisions or to investigate the reliability. The quality of the prognosis strongly depends on both the data quality and the quality of the digital twin. The latter comprises both the modeling assumptions as well as the correct parameters of these models. This article discusses the challenges when applying this concept to real measurement data for a demonstrator bridge in the lab, including the data management, the iterative development of the simulation model as well as the identification/updating procedure using Bayesian inference with a potentially large number of parameters. The investigated scenarios include both the iterative identification of the structural model parameters as well as scenarios related to a damage identification. In addition, the article aims at providing all models and data in a reproducible way such that other researcher can use this setup to validate their methodologies.

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One of the main challenges regarding our civil infrastructure is the efficient operation over their complete design lifetime while complying with standards and safety regulations. Thus, costs for maintenance or replacements must be optimized while still ensuring specified safety levels. This requires an accurate estimate of the current state as well as a prognosis for the remaining useful life. Currently, this is often done by regular manual or visual inspections within constant intervals. However, the critical sections are often not directly accessible or impossible to be instrumented at all. Model-based approaches can be used where a digital twin of the structure is set up. For these approaches, a key challenge is the calibration and validation of the numerical model based on uncertain measurement data. The aim of this contribution is to increase the efficiency of model updating by using the advantage of model reduction (Proper Generalized Decomposition, PGD) and applying the derived method for efficient model identification of a random stiffness field of a real bridge.

Summary A key limitation of the most constitutive models that reproduce a degradation of quasi‐brittle materials is that they generally do not address issues related to fatigue. One reason is the huge computational costs to resolve each load cycle on the structural level. The goal of this paper is the development of a temporal integration scheme, which significantly increases the computational efficiency of the finite element method in comparison to conventional temporal integrations. The essential constituent of the fatigue model is an implicit gradient‐enhanced formulation of the damage rate. The evolution of the field variables is computed as a multiscale Fourier series in time. On a microchronological scale attributed to single cycles, the initial boundary value problem is approximated by linear BVPs with respect to the Fourier coefficients. Using the adaptive cycle jump concept, the obtained damage rates are transferred to a coarser macrochronological scale associated with the duration of material deterioration. The performance of the developed method is hence improved due to an efficient numerical treatment of the microchronological problem in combination with the cycle jump technique on the macrochronological scale. Validation examples demonstrate the convergence of the obtained solutions to the reference simulations while significantly reducing the computational costs.

Numerical models built as virtual-twins of a real structure (digital-twins) are considered the future of monitoring systems. Their setup requires the estimation of unknown parameters, which are not directly measurable. Stochastic model identification is then essential, which can be computationally costly and even unfeasible when it comes to real applications. Efficient surrogate models, such as reduced-order method, can be used to overcome this limitation and provide real time model identification. Since their numerical accuracy influences the identification process, the optimal surrogate not only has to be computationally efficient, but also accurate with respect to the identified parameters. This work aims at automatically controlling the Proper Generalized Decomposition (PGD) surrogate’s numerical accuracy for parameter identification. For this purpose, a sequence of Bayesian model identification problems, in which the surrogate’s accuracy is iteratively increased, is solved with a variational Bayesian inference procedure. The effect of the numerical accuracy on the resulting posteriors probability density functions is analyzed through two metrics, the Bayes Factor (BF) and a criterion based on the Kullback-Leibler (KL) divergence. The approach is demonstrated by a simple test example and by two structural problems. The latter aims to identify spatially distributed damage, modeled with a PGD surrogate extended for log-normal random fields, in two different structures: a truss with synthetic data and a small, reinforced bridge with real measurement data. For all examples, the evolution of the KL-based and BF criteria for increased accuracy is shown and their convergence indicates when model refinement no longer affects the identification results.