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Despite the advances in hardware and software techniques, standard numerical methods fail in providing real-time simulations, especially for complex processes such as additive manufacturing applications. A real-time simulation enables process control through the combination of process monitoring and automated feedback, which increases the flexibility and quality of a process. Typically, before producing a whole additive manufacturing structure, a simplified experiment in the form of a beadon-plate experiment is performed to get a first insight into the process and to set parameters suitably. In this work, a reduced order model for the transient thermal problem of the bead-on-plate weld simulation is developed, allowing an efficient model calibration and control of the process. The proposed approach applies the proper generalized decomposition (PGD) method, a popular model order reduction technique, to decrease the computational effort of each model evaluation required multiple times in parameter estimation, control, and optimization. The welding torch is modeled by a moving heat source, which leads to difficulties separating space and time, a key ingredient in PGD simulations. A novel approach for separating space and time is applied and extended to 3D problems allowing the derivation of an efficient separated representation of the temperature.
The results are verified against a standard finite element model showing excellent agreement. The reduced order model is also leveraged in a Bayesian model parameter estimation setup, speeding up calibrations and ultimately leading to an optimized real-time simulation approach for welding experiment using synthetic as well as real measurement data.
Structural build-up describes the stability and early-age strength development of fresh mortar used in 3D printing. lt is influenced by several factors, i.e. the composition of the print able material, the printing regime, and the ambient conditions. The existing modelling approaches for structural build-up usually define the model parameters for a specific material composition with out considering the influence of the ambient conditions. The goal of this contribution is to explicitly include the temperature dependency in the modelling approach. Temperature changes have signifi cant impact on the structural build-up process: an increase of the temperature leads to a faster dissol ution of cement phases and accelerates hydration. The proposed extended model includes temperature dependency using the Arrhenius theory. The new model parameters are successfully calibrated based on Viskomat measurement data using Bayesian inference. Furthermore, a higher impact of the temperature in the re-flocculation as in the structuration stage is observed.
For extrusion-based 3D concrete printing, the early age mechanical behavior is influenced by various time dependent phenomena: structural build-up, plasticity as well as viscosity. The structural build-up is governing the stability and early-age strength development of the fresh printable cementitious materials and with that influencing the printability, buildability, and open time of the printing process. Generally, it is influenced by a number of factors, i.e. composition of the printable material, printing regime, and ambient conditions (temperature, humidity, etc.). There are several approaches to model the structural build-up of cementitious materials. All models are based on a time-dependent internal structural parameter describing the flocculation state, which is assumed to be zero after mixing and increases with time. The approaches differ in the definition of the time dependency (linear, exponential, bi-linear). Usually, the parameters are defined for a specific material composition without considering the influence of ambient conditions.
In this contribution, the bi-linear structural build-up model [Kruger et al., Construction and Building Materials 224, 2019] is extended by the temperature influence. Temperature changes will occur in real life printing processes due to changing ambient conditions (summer, winter, day, night) as well as the printing process (pressure changes etc.) and have a significant impact on the structural build-up process: an increase of the temperature leads to a faster dissolution of cement phases, accelerates hydration and boosts the Brownian motion. For that reason, the model parameters are simulated as temperature dependent using an Arrhenius function. Furthermore, the proposed extended model is calibrated based on measurement data using Bayesian inference. A very good agreement of the predicted model data with the measured control data was reached. Additionally, the structural build-up model is integrated into a viscoelastic and elastoplastic mechanical model, simulating the whole mechanical behavior during layer deposition.
Numerical simulations are essential in predicting the behavior of systems in many engineering fields and industrial sectors. The development of accurate virtual representations of actual physical products or processes (also known as digital twins) allows huge savings in cost and resources. In fact, digital twins would allow reducing the number of real, physical prototypes, tests, and experiments, thus also increasing the sustainability of production processes and products’ lifetime. Standard numerical methods fail in providing real time simulations, especially for complex processes such as additive manufacturing applications.
This work aims to use a reduced order model for efficient wire arc additive manufacturing simulations, calibrations and real-time process control. Model reduction, e.g. the proper generalized decomposition [1,2] method, is a popular concept to decrease the computational effort. A new mapping approach [3] was applied to simulate a moving heat source with the proper generalized decomposition. Using this procedure even complex models can be simulated in real-time. The physical model is later on calibrated with the use of a stochastic model updating process and the reduced order model, leading to an optimized real-time simulation.
In this contribution, a proper generalized decomposition model for a bead-on-plate wire arc additive manufacturing is presented. It is also coupled with a stochastic model updating process identifying the heat source characteristics as well as the boundary conditions of the transient thermal problem, whereas the heat source shape is simulated using a Goldak heat source