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Paper des Monats
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In this paper, a new methodology based on the Hill–Mandel lemma in an FE² sense is proposed that is able to deal with localized deformations. This is achieved by decomposing the displacement field of the fine scale model into a homogeneous part, fluctuations, and a
cracking part based on additional degrees of freedom (X¹)—the crack opening in normal and tangential directions. Based on this decomposition, the Hill–Mandel lemma is extended to relate coarse and fine scale energies using the assumption of separation of scales such
that the fine scale model is not required to have the same size as the corresponding
macroscopic integration point. In addition, a procedure is introduced to mimic periodic
boundary conditions in the linear elastic range by adding additional shape functions for the boundary nodes that represent the difference between periodic boundary conditions and pure displacement boundary conditions due to the same macroscopic strain. In order to decrease the computational effort, an adaptive strategy is proposed allowing different
macroscopic integration points to be resolved in different levels on the fine scale.
Concrete is one of the most important building materials world wide. The safety of constructions build from concrete is of utmost importance in daily life. As a consequence, accurate predictions of the structural behavior over the entire lifetime of concrete structures are required to ensure a prescribed safety level. A lack of exact models and/or stochastically varying constitutive parameters are compensated by large safety factors.
The nonlinear structural performance is strongly related to the constitutive behavior of concrete. Arbitrary complex models can be used to describe the macroscopic constitutive behavior of concrete. The parameters in these models often lack any physical meaning. Consequently, the fitting can only be performed by an inverse analysis. In contrast, models on finer scales are able to simulate the physical phenomena more accurately and are thus better suited to understand the failure mechanisms. In addition, the macroscopically observed strong nonlinearities can at least partially be explained by the direct modeling of the material heterogeneities on finer scales.
The presentation discusses several phenomena that are strongly related to the internal microstructure of concrete. This includes the discrepancy between the unique results of a numerical model and the stochastic scatter observed in real experiments. A short discussion on the generation of random mesoscale geometries to model aggregates and mortar matrix explicitly and random fields are given. The strong nonlinearities especially for stresses close to the peak strength are usually the result of failure in the mortar matrix or the interfacial transition zone, whereas the aggregates are inert and often can accurately be modeled by a linear elastic model. The different constitutive properties lead to eigenstresses that strongly in uence the macroscopic behavior. In addition, this effect is even more pronounced when dealing with multiphysics phenomena such as drying, creep and shrinkage, fatigue or thermal problems. It will be demonstrated for several examples that simple models on the fine scale can be superimposed and coupled to obtain a macroscopically nonlinear behavior, where the superposition principle does not hold any longer. Finally, a short discussion on upscaling techniques to couple mesoscale models with large scale structural problems is given.
A regularized model for impact in explicit dynamics applied to the split Hopkinson pressure bar
(2016)
In the numerical simulation of Impact phenomena, artificial oscillations can occur due to an instantaneous change of velocity in the contact area. In this paper, a nonlinear penalty regularization is used to avoid these oscillations. Aparticular focus is the investigation of higher order methods in space and time to increase the computational efficiency. The spatial discretization is realized by higher order spectral element methods that are characterized by a diagonal mass matrix. The time integration scheme is based on half-explicit Runge–Kutta scheme of fourth order. For the conditionally stable scheme, the critical time step is influenced by the penalty regularization. A framework is presented to adjust the penalty stiffness and the time step for a specific mesh to avoid oscillations. The methods presented in this paper are applied to 1D-simulations of a split Hopkinson pressure bar, which is commonly used for the investigation of materials under dynamic loading.
In this paper, the impact problem and the subsequent wave propagation are considered. For the contact discretization an intermediate NURBS layer is added between the contacting finite element bodies, which allows a smooth contact formulation and efficient element‐based integration. The impact event is ill‐posed and requires a regularization to avoid propagating stress oscillations. A nonlinear mesh dependent penalty regularization is used, where the stiffness of the penalty regularization increases upon mesh refinement. Explicit time integration methods are well suited for wave propagation problems, but are efficient only for diagonal mass matrices. Using a spectral element discretization and the coupled FE‐NURBS approach the bulk part of the mass matrix is diagonal.
In this work, a probabilistic framework for identification of traffic loads on concrete Bridge structures is presented using data from a FE structural model in combination with a finite volume approach for traffic load modelling. The identification approach uses Bayesian Inference to identify traffic loads from measured sensor data from travelling load experiments performed at BAM. The work focuses on the load identification part of the Framework utilizing global structural response measurements only. The obtained information on traffic loads can be forwarded to further analysis such as fatigue and structure state estimation or model updating.
A safe and robust performance is a key criterion when building and maintaining structures and component. Ensuring this criterion at different stages of the lifetime can be supported by applying continuous monitoring concepts. The latter usually can serve multiple purposes, including the determination of material parameters for the design phase, the evaluation of the actual loading/environmental conditions (instead of using conservative estimates that are usually larger) and evaluating or predicting the true performance of the structure (thus decreasing the model bias). In this context, a digital twin of the structure has many benefits. It allows to introduce virtual sensors to “measure” sensor information that is e.g. inaccessible or unmeasureable. In order to efficiently use monitoring techniques in the context of a digital twin, it is important to consider the complete chain of information including the choice of sensors, the data processing and structuring, the modelling assumptions, the numerical simulation and finally the stochastic nature of the model prediction. In this presentation, challenges in this context are discussed with a specific focus on Bayesian model updating of the digital twin, accounting for both parameter updates as well as model bias that results from the limitations of modelling assumption. A bottleneck in this approach is the computational effort related to sampling methods such as Markov chain Monte Carlo methods that require many evaluations of the forward model. An alternative to the expensive computation of the forward model for updating the digital twin is the combination with model reduction techniques such as the Proper General Decomposition [1, 2]. The results are illustrated for several examples and scale, ranging from digitals twin for material tests in the lab over lab scale structural digital twins up to damage identification in field experiments.
A safe and robust performance is a key criterion when building and maintaining structures and components. Ensuring this criterion at different stages of the lifetime can be supported by applying continuous monitoring concepts. The latter usually can serve multiple purposes, including the determination of material parameters for the design phase, the evaluation of the actual loading/environmental conditions (instead of using conservative estimates that are usually larger) and evaluating or predicting the true performance of the structure (thus decreasing the model bias). In this context, a digital twin of the structure has many benefits. In addition, it allows to introduce virtual sensors to “measure” sensor information that is e.g. inaccessible or unmeasureable. In the limit, the remaining useful life of a structure can be interpreted as a property that can be “measured” indirectly via the numerical model in combination with real sensor data. In order to efficiently use monitoring techniques in the context of a digital twin, it is important to consider the complete chain of information including the choice of sensors, the data processing and structuring, the modelling assumptions, the numerical simulation and finally the stochastic nature of the model prediction. In this presentation, challenges in this context are discussed with a specific focus on Bayesian model updating of the digital twin, accounting for both parameter updates as well as model bias that results from the limitations of modelling assumption. A bottleneck in this approach is the computational effort related to sampling methods such as Markov chain Monte Carlo methods that require many evaluations of the forward model. An alternative to the expensive computation of the forward model for updating the digital twin is the combination with model reduction techniques such as the Proper General Decomposition. The results are illustrated for several examples and scales, ranging from digitals twin for material tests in the lab over lab scale structural digital twins up to damage identification in field experiments.
Simulating high-cycle fatigue with continuum models offers the possibility to model stress-redistributions, consider 3Dstress states and simplifies extensions to multi-physics problems. The computational cost of conventional cycle-by-cycle time integrations is reduced by reformulating the fatigue problem as an ordinary differential equation for the material state and solving it with high-order adaptive time integration schemes. The computational cost of calculating the Change of the material state in one cycle is further reduced by a high-order fatigue-specific time integration. The approach is exemplarily demonstrated for a fatigue extension of the implicit gradient-enhanced damage model in 3D and compared to experimental Wöhler lines.