## 7.7 Modellierung und Simulation

### Filtern

#### Dokumenttyp

- Vortrag (18)
- Zeitschriftenartikel (8)
- Beitrag zu einem Tagungsband (3)
- Dissertation (2)
- Posterpräsentation (2)

#### Schlagworte

- Concrete (3)
- Damage (3)
- Explicit dynamics (3)
- Impact simulation (3)
- Isogeometric analysis (3)
- Structural analysis (3)
- Brückenmonitoring (2)
- Continnum damage model (2)
- Cycle jump (2)
- Demonstrator (2)

#### Organisationseinheit der BAM

The main challenge using numerical models as digital twins in real applications is the calibration and validation of the model based on uncertain measurement data. Therefore, model updating approaches which are inverse optimization processes are applied. This requires a huge number of computations of the same numerical model with slightly different model parameters. For that reason, model updating becomes computationally very expensive for real applications.
Model reduction, e.g. the proper generalized decomposition method, is a popular concept to decrease the computational effort of complex numerical simulations. Therefore, a reduced model of the structure of interest is derived and will be used as surrogate model in a Variational Bayesian procedure to create a very efficient digital twin of the structure.
An efficient model updating approach by means of a PGD reduced model with random field material stiffness parameters is shown. The random field allows, to calibrate the model considering parameter changes over the spatial direction. These changes can be caused by local damages as well as by production. As an exemplary application a demonstrator bridge is used. Digital twins can reduce the costs for maintenance and inspections especially for the costly civil infrastructure with high requirements at their performance over the whole lifetime. Currently, the current state of the structure is determined by regular manual and visual inspections within constant intervals. However, the critical sections are often not directly accessible or impossible to be instrumented at all. In this case, model-based approaches where a digital twin is set up can improve the process. Based on this digital twin, a prognosis of the future performance of the structure, e.g. the failure probability, can be computed.
The influences of the reduction degree, the mesh discretization as well as the correlation length in the PGD Bayesian approach are studied by means of the digital twin of a simple pre-stressed concrete two field bridge.

Many of today’s problems in engineering demand reliable and accurate prediction of failure mechanisms of mechanical structures. Herein it is necessary to take into account the often heterogeneous structure on the fine scale, to capture the underlying physical phenomena. Despite ever increasing Computational resources, dissolving the fine scales in a direct numerical simulation is prohibitive. This work aims to develop an efficient approach to modeling nonlinear heterogeneous structures using the variational multiscale method (VMM) and model order reduction (MOR).
The VMM, introduced in, assumes an additive split of the solution into coarse and fine scale contributions. In, the VMM is applied to a damage mechanics–based material model for concrete-like materials. Herein, suitable boundary conditions for the fine scale which enable localization phenomena to evolve are discussed. As such, zero jump conditions between fine scale solutions are proposed which are enforced pointwise by a Lagrange type method leading to a coupled solution procedure.
In this contribution, possible extensions of the VMM with reduced order modeling are presented. In the linear case, assuming the fine scale solution to be zero on coarse scale element boundaries allows for static condensation and a decoupled solution procedure. Based on this, an efficient localized Training strategy will be developed. For the nonlinear case, the situation of coupled non-conforming spaces, i. e. finite element and reduced order spaces for the fine scales, arises. Thus the imposition of suitable fine scale interface conditions in the weak sense by the use of Lagrange multipliers is investigated. Specific problems in solid mechanics are used to illustrate the performance of the above approaches.
The authors gratefully acknowledge financial support by the German Research Foundation (DFG), Project number 394350870, and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (ERC Grant agreement No. 818473).

Fatigue models that accurately resolve the complex three-dimensional failure mechanisms of concrete are numerically expensive. Especially the calibration of fatigue parameters to existing Wöhler lines requires solving for thousands or millions of cycles and a naive cycle-by-cycle integration is not feasible.
The proposed adaptive cycle jump methods provide a remedy to this challenge.
They greatly reduce the numerical effort of fatigue simulations and provide the basis for a development of those models.

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.”

The quality of a model - and thus its predictive capabilities - is influenced by numerous uncertainties. They include possibly unknown boundary and initial conditions, noise in the data used for its calibration and uncertainties in the model itself. Here, the latter part is not only restricted to uncertain model parameters, but also refers to the choice of the model itself. Inferring these uncertainties in an automatic way allows for an adaption of the model to new data sets and for a reliable, reproducible model assessment. Note that similar concepts apply at the structural level, where a continuously updated digital twin allows virtual measurements at inaccessible positions of the structure and a simulation based lifetime prediction.
This work presents an inference workflow that describes the difference of measured data and simulated model responses with a generic interface that is independent from the specific model or even the geometry and can easily incorporate multiple data sources. A variational Bayesian inference algorithm is then used to a) calibrate a set of models to given data and to b) identify the best fitting one. The developed concepts are applied to a bridge Demonstrator equipped with displacement sensors, force sensors and a stereophotogrammetry system to perform a system identification of the material parameters as well as a real-time identification of a moving load.

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.

The simulation of the structural response for impact scenarios strongly requires an accurate simulation of both the impact event as well as the subsequent wave propagation. The numerical modeling of the impact event is intrinsically ill-posed due to the instantaneous changes of velocities in the contact area, leading to unbounded accelerations for decreasing time steps which causes oscillations in the contact stresses. These oscillations then propagate into the bulk material. Using a rate dependent material model, like concrete, they might lead to signiﬁcant errors and a wrong prediction of the structural response. A regularization is thus required to avoid oscillations in the contact stresses. Another issue is related to the numerical computation of the contact conditions. In impact simulations, the nonlinear contact computation needs to be evaluated in every time step. A segmentation technique of the contact area is accurate but time consuming and may result in a bottleneck for the simulation and implementation, especially for 3D problems. The modeling of the subsequent wave propagation requires small time steps, which is primarily due to accuracy reasons. Implicit schemes are thus not aﬀordable. Explicit time integration schemes are eﬃcient only for diagonal mass matrices, as in this case no solution of a linear system is required. In this work, a coupled ﬁnite element - Non-Uniform Rational B-Spline (FE-NURBS) approach is applied to impact problems. The coupled approach uses an intermediate NURBS layer to compute the contact forces between the contacting bodies discretized by FEs. The advantages of a smooth isogeometric contact formulation are used to compute the contact forces. A segmentation of the contact area is avoided and an eﬃcient element-based integration is used. The impact event is regularized using a mesh dependent nonlinear penalty approach. The penalty function is a polynomial which ensures a smooth transition between the noncontact and the contact state during the impact. For ﬁner meshes, the penalty regularization becomes stiﬀer while still avoiding artiﬁcial oscillations in the contact stresses. Eﬃcient higher order space and time discretizations are used to model the wave propagation. Explicit time integration is combined with higher order spectral element spatial discretization.

One of the most important goals in civil engineering is to guarantee the safety of the construction. Standards prescribe a required failure probability in the order of 10−4 to 10−6. Generally, it is not possible to compute the failure probability analytically.
Therefore, many approximation methods have been developed to estimate the failure probability. Nevertheless, these methods still require a large number of evaluations of the investigated structure, usually finite element (FE) simulations, making full probabilistic design studies not feasible for relevant applications. The aim of this paper is to increase the efficiency of structural reliability analysis by means of reduced order models. The developed method paves the way for using full probabilistic approaches in industrial applications. In the proposed PGD reliability analysis, the solution of the structural computation is directly obtained from evaluating the PGD solution for a specific parameter set without computing a full FE simulation. Additionally, an adaptive importance sampling scheme is used to minimize the total number of required samples. The accuracy of the failure probability depends on the accuracy of the PGD model (mainly influenced on mesh discretization and mode truncation) as well as the number of samples in the sampling algorithm. Therefore, a general iterative PGD reliability procedure is developed to automatically verify the accuracy of the computed failure probability. It is based on a goal-oriented refinement of the PGD model around the adaptively approximated design point. The methodology is applied and evaluated for 1D and 2D examples. The computational savings compared to the method based on a FE model is shown and the influence of the accuracy of the PGD model on the failure probability is studied.

In this paper, the impact problem and the subsequent wave Propagation are considered. For the contact discretization an intermediate non-uniform rational B-spline (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 in combination with a NURBS contact layer the bulk part of the mass matrix is diagonal.