**An opportunity to evaluate explicit solver performance in quasi-static phenomena.**

As a matter of fact, nowadays the use of different types of **FEA** (Finite Element Analysis) tools for different applications fields has left very little space for the user’s choice, considering that **each solver is unanimously associated to very specific industrial simulation areas**.

As an example, aerospace static structural analyses are typically carried out with linear and non-linear so-called “implicit solvers” such as Optistruct, NASTRAN, ABAQUS standard; while in an automotive crash simulation “explicit solvers” such as Radioss or LS-Dyna are the reference.

Without going any deeper into the mathematical theory that differentiates implicit vs explicit solving schemes, we can just affirm, in very practical terms, **the typical physical scenario where these two families of solvers (or in other terms, commercial software available) are being used**.

An additional important criterion needed to be considered when facing an industrial simulation problem is run time.

The figure highlights that **whenever we have highly dynamic non-linear phenomena we go towards “explicit”.** However, if our problem is non-linear static, **“implicit” scheme is capable of giving us a fast and precise solution**. Therefore, the question is: what if our problem is borderline, at the limit of those two implicit-explicit domains?

Actually, a superposition area exists for some problems, such as the **ROPS simulation analysis**.

By means of a FEA simulation model, **we can predict and optimize the shape, materials, and properties of a cabin without actually performing experimental tests**. These last will be performed just as a final validation or certification procedure on the structure that has already been optimized by the numerical model with dramatic advantages in terms of reduction of product development time, time to market and, by the consequent overall **cost of the product**, as well as **enhancement of safety standards and overall quality of the product**.

**ROPS analysis mainly consists of a series of simulations of sequential prescribed loads applied to the structure of a cabin of a tractor, earth moving machine, excavator and so on.**

This sequence is prescribed by UNI EN ISO 3471_2008 European standard (which defines precisely the load cases and constraint conditions of the structure subject to the test) and is representative of a real rollover event, with a safety margin.

In reality, the test loads are applied via hydraulic actuators moving at very low speed pushing on the structure of the cabin. **Hence, we can consider the loads as quasi-static.**

Moreover, the damage produced by the sequence of loads is cumulative: this means that after the first load acting on the structure, there are residual deformations due to the plastic behaviour of the material deriving from the large deformations imposed by the actuator. Once this load is released, the next loading phase acts on the deformed structure. And so on for the next loading phase.

The acceptance criteria for those tests prescribe to **measure the distance between the internal part of the structure and a “dummy” which is positioned inside the cabin**. If the measurements are acceptable, under a certain threshold, the test is passed.

**Therefore, in order to summarize what happens in this scenario, we have:**

**multiple contacts (between the loading pads applied to the actuators and the structure)****large deformations of the structure****plastic behaviour of materials****quasi-static loads acting on the structure****cumulative deformation for each loading phase**

Ergo, what about the software tool (solver) should be used for this kind of simulation?

From the summary above one could deduce that the implicit scheme could be suitable for some points and an explicit scheme for others.

**As the literature points out, there are different and opposite choices operated by the structural analysts which cause dilemma with regards to the right choice.**

AXIRO has studied in real industrial projects the advantages and disadvantages concerning the use of implicit or explicit solvers. **The main conclusion is that, if correctly set up, explicit solver provides the best compromise between the capability of accurately representing the physical model by FEA and convergence speed.**

AXIRO’s experience confirms that the most critical problems within this simulation are:

- Management of unwanted dynamic phenomena (management of the kinetic energy of the model during the loading phases)
- Management of the sequence of loading phases (cumulative deformations)

**With Altair Radioss AXIRO has put in place a numerical model capable of providing very good correlation to experimental test and, in the same time, allowing AXIRO to provide its customers with rapid answers to their needs, ensuring a considerable reduction in time and cost of product development.**