In linear simulations, the loads and deformations behave proportionally to each other. They are used for small deformations and initial estimations. Additionally, modal analyses based on linear calculation models are conducted.

Nonlinear simulations are more complex and require more computational capacity. There are three cases that require nonlinear models:

• When materials do not exhibit linear behavior, such as many metals in the elastic range, special material models need to be used. These can range from simple ideal elastic-ideal plastic models for failure analyses to complex hyperelastic models for elastomers.
• When significant deformations occur in a geometry, geometric nonlinearities arise. These are captured in the calculation model.
• If contact or multiple contacts occur that change the state during the simulation (e.g., open/closed), these conditions are nonlinear.

In static strength analysis, structures are analyzed under static conditions, where there is no time variation in the load or boundary conditions. This simplifies the equation of motion to the displacement component, and time-dependent terms such as damping are not considered. If only certain states of a process are of interest, the dynamic system can be approximated as quasi-static.

In dynamic or transient strength analysis, time-dependent loads are analyzed. The force equilibrium is determined not only by the displacement component but also by mass forces or damping effects. This enables the analysis of vibration responses and crash simulations, among other things.

Linear static simulations are the simplest case where the equation systems can be directly solved in one computational step. If all required boundary conditions are provided, the simulation always converges. However, when considering nonlinearities or dynamic effects, loads must be applied in small increments, and the solution is significantly more time-consuming and challenging.

Strength simulations allow for predicting the behavior of developed products before they are built.

By using simulations at an early stage of development, our technicians, engineers, and designers can simulate different scenarios. This enables the early detection of potential weaknesses and allows for optimization during the design phase.

The Finite Element Method (FEM) serves as a tool for determining technical safety and utilization rates. The utilization rate provides a simple way to visualize where and to what extent a component or structure is being stressed.

This is achieved by calculating stresses and deformations under different loading conditions. By presenting the utilization rates, even project team members who are not specialized in Finite Element Method (FEM) can understand to what extent the current design meets the requirements. Through the use of colors and simple numerical values, it is visualized where and to what extent safety margins exist.

Finite Element Analysis (FEA) is also used for root cause analysis and damage analysis. By conducting FEA simulations, damage patterns can be visualized and causes of failure can be identified. The insights gained from these analyses can be used to optimize future components.

Through damage analysis using FEA, our technicians, engineers, and designers can understand the causes of failure and take appropriate countermeasures.

Often, there are no specific standards available for the design of the components and assemblies to be calculated. Therefore, we categorize the proof requirements into those for metallic components and those for plastic components.

• For metallic components, we provide proofs according to the FKM guidelines (Calculation of Strength – 7th Edition, 2020).
• For plastic components, there are no universally standardized proofs available to date. Therefore, we refer to the current state of the art and rely on our experience. Additionally, we utilize principles based on the approaches by Oberbach, as described in the book "FEM zur Berechnung von Kunststoff- und Elastomerbauteilen" (Finite Element Method for Calculating Plastic and Elastomeric Components - 2nd Edition, 2018).

To ensure a high quality of the results, we verify the FEM results according to NAFEMS ESQMS (Interpretation based on ISO 9001:2015 by NAFEMS). This involves numerically verifying the models (mesh quality, convergence, etc.) and physically validating our results using samples, prototypes, or production parts (load conditions, reaction forces, etc.).

Flow-3D is used in the filling simulation of aluminum die-castings to simulate the behavior of liquid metal during the casting process. It allows for predicting the filling behavior and associated challenges such as porosity, gas entrapment, solidification patterns, oxide formation, and temperature loss.

Through these simulations, technicians, engineers, and designers can explore various design options and process parameters. The geometry of the component, as well as the gating and runner system, can be optimized to maintain an open and stable process window for high-quality components. The CFD analysis also enables evaluating the influence of parameters such as temperature, velocity, and pressure, and optimizing them accordingly.

Squeeze casting is a special process in the field of aluminum die casting. In this process, the liquid metal is poured into a closed mold under higher pressure, but at a slower rate and lower melt temperature. The process combines the advantages of casting and forging, allowing the production of components with high density and low porosity.

In this case as well, Computational Fluid Dynamics (CFD) can be used in the filling simulation to simulate the behavior of the metal during the casting process.

Flow-3D is characterized by its ability to solve CFD simulations involving a fluid with a free surface and two-phase simulations with "low" computational effort.

In practice, this type of analysis is used to study the behavior of fluids during flow and to make geometric optimizations. Examples include toilet flushes, automotive tank systems, weirs and waterfalls, and sand casting.