Whitepaper Numisheet 2025 Industrial & Scientifid Benchmarks: How AutoForm Won Both

This whitepaper describes the industrial and scientific Numisheet benchmarks that AutoForm won in 2025. Numisheet is a leading international conference series dedicated to the numerical simulation of sheet metal forming processes. It takes place every three years and brings together researchers, engineers, and industry experts to present advancements in material modeling, process simulation, tribology, tool and geometry optimization, and validation methods. As a central forum in this field, Numisheet fosters the exchange of ideas, supports collaboration across academia and industry, and highlights emerging trends in digital engineering and lightweight manufacturing.

Numisheet Benchmarks

The Numisheet benchmarks are a central component of the international conference, where innovative methods and solutions in sheet metal forming are tested and compared. At each conference, the organizers usually prepare two or three such benchmarks. They perform experiments and share the input needed to model them, such as material test results, tool geometries, and processing conditions. Benchmark participants receive this information before the conference, simulate the problem to the best of their ability, and submit the results, usually in terms of predicted strain distribution, forces, and final geometries. Only during the conference are the experimental results compared with the submitted numerical results, and a winner is announced based on the best numerical predictions.

These benchmarks can therefore be thought of as a “competition” of modeling approaches. They are designed to reflect real-world challenges from industrial practice and to provide a platform for scientific exchange. In this way, they enable an objective comparison of different approaches and software solutions.

At Numisheet 2025 in Munich, there were two benchmarks: an “Industrial Benchmark” and a “Scientific Benchmark.” For the Industrial Benchmark, the task was to develop an optimal method for a forming process under specific boundary conditions. In the Scientific Benchmark, a material card was created from various material tests (micro- and macroscale tests), and the simulation results using this material card were verified on a stretch-forming process (MUC test). The benchmark was evaluated based on simulated strain and forming force, which the participants did not know beforehand.

Industrial Benchmark

Task Definition

The NUMISHEET 2025 Industrial Benchmark focuses on designing a forming-cutting process chain for the Mercedes-Benz T-Node, a stylized geometry of the lower B-pillar joint in a car body. The part is to be formed from stainless steel (1.4301) with a sheet thickness of 1.5 mm.

The aim of the benchmark is to design a forming and trimming process that results in the target geometry after springback. The target geometry was provided as an STL mesh.

The process is evaluated based on the following points [1]:

• High material utilization is a key factor influencing the product’s environmental footprint (minimizing blank size relative to part weight)
• Manufacturing of the B-pillar’s lower joint must be repeatable and precise
• Defect categories to be avoided include tears and wrinkles
• The focus is on minimal thinning for reliable process control and high material utilization to conserve resources

Material Card Generation and TriboForm Model

The following parameters were provided for material card creation:

• Flow curve and Lankford parameter in 6 directions (0°, 22.5°, 45°, 67.5°, and 90°)
• FLC from Nakajima Test
• Cyclic Tensile Test to determine the Elastic Modulus reduction over strain
• Disk Compression Test to estimate the biaxial r-value r_b
• Smily Test and Plane Strain Test to estimate the Yield Surface

From these data, a material card with a BBC 2005 M = 6 yield locus was created. The AutoForm model was used to account for kinematic hardening. The Young’s Reduction Factor and Rate were determined by best fitting the data from the Cyclic Tensile Test (Figure 1) and the formula

Empirical values were used for the Transient Softening Rate and Stagnation Ratio.

Figure 1: Determination of the Young’s Reduction Factor and Rate by best fitting the data from the Cyclic Tensile Test

The friction card was created using TriboForm. The following parameters from the benchmark description were considered:

• Stainless Steel 1.4301 with Roughness S_a = 0.18 µm
• Drawing Oil: OEST Platinol B Amount = 0.5 g/m²
• Tool Steel (Punch S_a = 0.28 µm, Blankholder S_a = 0.56 µm, Die S_a = 0.49 µm)

As expected, velocity, temperature, and pressure strongly influence the friction coefficient, and these effects are considered in the TriboForm model.

Although we adhered to the benchmark definition, there were two details that we reinterpreted:

1. “The material utilization ratio is commonly defined as the ratio of the component weight divided by the blank weight.” In our work, this definition was updated to component weight divided by coil weight.
2. “The focus is on minimal thinning for reliable process control…” Especially for stainless steel alloys, very high thinning is possible under biaxial tension. Therefore, Max Failure value was used as the main measure of feasibility.

Figure 2 shows the procedure for method planning with AutoForm software. First, a crashform process and a deep drawing process are compared. Since both proved infeasible, a coining process based on crash forming was investigated further.

Figure 2: Determining the optimal process with the help of AutoForm software

Comparison of Crashform and Deep Drawing Processes

Two different methods were compared (Figure 3):

• Deep Drawing Process
• Crashform Process

Since both a left and right part are required, the component is manufactured as a double part in both cases. The methods were developed with AutoForm DieDesigner. The final tool geometries were designed in DieDesignerPlus.

In the deep drawing process, a rectangular blank is used. With the help of a step bead, the sheet metal was stretched to reduce the blank size.

The crashform process uses a form blank centered by two pilots. First, the blank is held and bent with a pad. In the subsequent trimming operation, the parts are separated and holes are pierced. The blank boundary was determined as a Target Blank using AutoForm Trim Optimizer. The pad force was set high enough to prevent the pad from opening. In addition, a commercially available spring was used to provide sufficient installation space.

Figure 3:  Comparing a deep drawing process with a crash forming process

Utilization was evaluated with the AutoForm Nesting Tool (Figure 4). For the rectangular blank in the deep drawing process, at least 8.0 mm of overmeasure is required. The form blank also requires a margin of about 8.0 mm in the blanking process. Material utilization for the deep drawing and crashform processes is nearly the same:

• Deep Drawing: Part weight / Coil weight = 0.791
• Crashform: Part weight / Coil weight = 0.793

Figure 4:  Comparing embedding and nesting of both processes

The Trim Check (Figure 5) in AutoForm shows that the deep drawing part is not trimmable with tools. Laser cutting or the use of many cams is required. This is not economical for large series. For this reason, only the crashform process was pursued further.

Figure 5: Combined trim and shear angle limit of a deep drawing part

Springback Compensation

One goal of the benchmark is to achieve the target geometry after trimming and springback. With AutoForm Compensator, the crashform tool was compensated based on the distance between the target geometry and the springback result. This leads to a backdraft tool (Figure 6). Changing the tipping of the part cannot resolve this issue because the backdraft walls are parallel. As a result, geometric compensation is not feasible.

Figure 6: Backdraft in two opposite walls after geometric springback compensation

Reducing Springback by Coining

One way to reduce part springback is coining. This means the offset in the radii is smaller than the material thickness (Figure 7). The applied normal stresses reduce the bending moment through the sheet thickness, which leads to lower springback. To account for normal stresses in the simulation, the thick shell element TS-11 (11 integration points through thickness) is used.

Figure 7: Reducing springback by coining in the radii

A possible issue is that the coining process may not be robust with respect to variation in sheet thickness in real production. For that reason, we conduct an RSPI (Robust Sigma Process Improvement) study with AutoForm Sigma, which allows variation of simulation parameters. Variation in the uncontrollable parameters (thickness variation, yield stress variation, blank position variation, etc.) shows the robustness of the process and helps identify the optimum controllable parameter (the radii in our case).

Figure 8:  Definition of the evaluation area for optimizing the coining radii

As the evaluation area, only the backdraft regions after springback compensation are of interest (Figure 8). As the issue definition, the maximum springback that can be compensated without backdraft problems is specified, corresponding to a material displacement of 0.75 mm in the normal direction.

The result of the RSPI analysis (Figure 9 ) is the process window for the optimized coining radius, which leads to a robust process that is geometrically compensatable.

Figure 9:  Process window determined for the coining radii with the help of an AutoForm Sigma RSPI study

With AutoForm ProcessDesigner, the optimized coining radii were introduced into the upper tool. Afterwards, springback compensation was carried out. The upper and lower tool geometry was compensated based on the distance between the scanned STL mesh and the springback part. Springback compensation is an iterative process. A new simulation is carried out with the compensated tools. This continues until the distance between the sprung-back part and the STL mesh no longer improves. Figure 10 shows the results of the springback compensation.

Figure 10: Iterative springback compensation process

Elastic Tool Deflection in the Coining Process

A drawback of the coining process is the high forming force. At the end of the crashform process, the force rises to about 1100 tons due to the normal stresses required for coining.

Figure 11: Ram force exceeds 1100 tons in the coining process

AutoForm Elastic Tool Deflection (ETD) was used to evaluate the effect of this high forming force on tool deflection, taking press stiffness into account. The following production press data were assumed:

• Ram and bolster plate size: 1000 mm x 1000 mm
• The tool substructure and ribbing geometry were generated in AutoForm

The resulting tool deflection is shown below. The maximum deflection is about 0.07 mm, so overcrowning of the tools was judged unnecessary.

Figure 12: Determination of elastic tool deflection in the coining process

Process Robustness Study

After springback compensation, the max failure value at the most critical point was above 0.8. The max failure value indicates the distance to the forming limit curve. A value of 1 means that the strain distribution of the element lies exactly on the forming limit curve, while a value above 1 means that the component has cracked. To account for uncertainties such as batch variations, the max failure value should be below 0.8. In a robustness study, this limit can be raised to 0.9 because process fluctuations are already taken into account.

The parameter variation used in the robustness study is shown in Figure 13. Several robust springback compensation projects have shown that these parameters have the greatest influence on the forming result.

Figure 13: Parameter variation for the robustness study

Figure 14 shows the Cpk value for the max failure value, along with a dependency plot at the most critical point of the component. The higher this value, the more likely it is that production will remain within specification. The robustness analysis shows that the part as a whole is reliable with respect to splits. In the dependency plot, the max failure value is plotted against the parameter with the greatest influence in the critical region. In this case, anisotropy (r-value) has the strongest effect on the max failure value. Each point represents one simulation result, clearly showing how the results are distributed across the relevant parameters.

Figure 14: Cpk value of the max failure value (advanced)

Figure 15 shows the Cpk value of the distance to the reference result. Unlike the max failure value, the distance to reference has both an upper and a lower limit:

Lower Specification Limit: LSL = -0.5 mm

Upper Specification Limit: USL = 0.5 mm

In some regions, the Cpk value is less than 1.0, which means the process is unreliable or unacceptable. This is not critical here for two reasons:

1. The critical regions are located in radii. These areas are not contact surfaces, so a higher tolerance is acceptable.
2. The part has already been compensated to compare the distance between the sprung-back part and the reference geometry. If scatter in the springback result is taken into account, the springback would have to be compensated to nearly zero. Since there will always be some deviation between simulation and reality, that would amount to overengineering. This becomes clear in the dependency plot.

The recommendation is therefore to check the Cp value for the springback result. The Cp value does not consider upper and lower limits, but rather a tolerance range. In this case, that tolerance range would be 1.0 mm. The Cp value for the distance to the reference result shows that the part as a whole is reliable.

Figure 15: Cpk value of the resultant distance to the reference

Cold Forming with Temperature Effects

As described in the task definition, the part is formed from stainless steel (1.4301). One property of stainless steel is that temperatures above 40 °C affect its strength. The Coldforming with Temperature Effects option considers thermal effects in cold forming processes. In cold forming, both the sheet and the tools heat up due to plastic work in the sheet and friction at the sheet-tool interface. In “cold forming with temperature effects,” the heating of the 3D tools is approximated with a so-called “smart ramp-up” step, in which only heat conduction in the 3D tools is computed repeatedly. Once a steady state has been reached, a second forming simulation is carried out with heated tools. The flow curve was scaled using temperature-dependent flow curves from the AutoForm material database.

In addition to strength, the influence of temperature on friction is considered in the TriboForm friction card (Figure 16). The following diagram shows the influence of temperature and velocity on the friction coefficient.

Figure 16: Friction dependency of temperature and velocity

The goal is to find the maximum stroke rate at which the process is robust without cracks. As velocity increases, temperature and friction also increase. With the help of a Robust Systematic Process Improvement (RSPI) analysis, as in the coining section, the maximum press velocity is determined. In addition to the normally distributed parameters from the robustness analysis, velocity is varied. In this case, Press Stroke Velocity is a controllable parameter and is evenly distributed. The velocity range is from 50 to 500 mm/s. A velocity of 500 mm/s corresponds to a stroke rate of >15 parts per minute.

The Cpk value of the max failure value is shown in Figure 17. The dependency plot clearly shows the influence of press stroke velocity on the max failure value. The RSPI study shows that the process is robust at this high forming velocity (500 mm/s) without tool cooling.

Figure 17: Cpk value of the max failure value and dependency plot of max failure value over forming motion stroke rate

Benchmark Results of All Participants

Ten teams from five countries (Germany, China, USA, Italy, and the UK) participated, including universities, software developers, and technical consultants. The approaches varied greatly in terms of the geometry of the initial blank and the process parameters (e.g. holding force, drawing depth, and coefficient of friction). The blank shapes ranged from simple to complex geometries.

Figure 18: Map showing the origin of the NUMISHEET 2025 Industrial Benchmark participants [1]

According to the benchmark definition, our approach was declared the winner of the benchmark, and we had the opportunity to present our process, demonstrating how different AutoForm solutions interacted in the development of an optimal method.

Scientific Benchmark

Introduction

The aim of this benchmark was to simulate a stretch forming process and predict forming forces as well as strain distribution. The material used was the steel alloy DP800 HHE (High Hole Expansion). Benchmark participants received raw material characterization test results and the necessary geometries to model the forming process. Therefore, the main task was to generate an accurate material card. Then, using this material card, the stretch forming process was simulated, and the predicted tool forces and strain distributions were submitted.

Material Card Generation

Macroscale material characterization test results used for material card generation are as follows:

• Uniaxial Tensile Test (Flow Curve and Lankford Parameters)
• Tensile Test – Cyclic Load (results were not considered)
• Tension-Compression Test (kinematic hardening parameter with the help of the AutoForm Material Generator)
• Plane Strain Test (calibrate the yield locus at plane strain points)
• Shear Test (calibrate the yield locus at the shear point)
• Hydraulic Bulge Test (extrapolate the flow curve)
• Layer Compression Test (determine biaxial r-value r_B)
• Nakajima Test to generate the Forming Limit Diagram (FLD)

Uniaxial Tension Test: Determination of Flow Curve and Lankford Parameter (r-value)

First, the flow curve is determined from the uniaxial tensile test in the rolling direction. The flow curve describes the relationship between the true yield stress σ and the plastic strain ε_p of a material under specified conditions (e.g. temperature and defined strain rate). It captures strain hardening, that is, how much a material becomes harder with increasing plastic deformation. Without a correctly calibrated flow curve, the material response in the FE model becomes inaccurate, and predictions of strain and forces become unreliable.

The force and displacement from the uniaxial tensile test are required to generate the flow curve. Because the flow curve describes the plastic behavior of the material, it is defined from the yield point onward. It is generally assumed that plastic deformation begins at 0.2% strain. To determine the exact point of plastic deformation, temperature was measured in addition to force and distance. The left diagram in Figure 19 shows the stress-strain plot and the temperature profile over strain. On the right side, the initial phase of the uniaxial tension test is shown, including the transition from elastic to plastic material behavior. The decrease in temperature under elastic loading and the increase in the plastic range (Joule-Thomson effect) are clearly visible here. The yield strength at 0.02% strain amounts to 550.4 MPa. The yield strength at minimum temperature is 498.7 MPa. For the final material card, a yield stress of 498.7 MPa (the stress at the lowest temperature) is used.

Figure 19: Determination of yield strength at 0.02% strain and minimum temperature

Figure 20 shows the hardening curves in the rolling direction at 0° (red), 45° (green), and 90° (blue). The solid curves represent the experimental results from the tensile test, while the dashed curves are calculated using the stress ratios σ₄₅/σ₀ and σ₉₀/σ₀. These stress ratios are necessary for yield locus determination and can be calculated using either the initial yield strength R_p0.2 or the tensile strength R_m. On the left side of the figure, the ratio of the yield strength in the diagonal and transverse directions relative to the rolling direction was used. At low elongation, the dotted curve fits the tensile test result well. At larger elongation, however, there are significant differences between the extrapolated curve and the test result. For this reason, the tensile strength ratio was used instead. On the right side of Figure 20, it becomes clear that the extrapolated hardening curve fits the tensile test result much better.

Figure 20 : Scaling the flow curve using yield stress and tensile strength

The Lankford parameter, or r-value, is a measure of a material’s anisotropic behavior, specifically its resistance to thinning or thickening under tensile or compressive forces in the plane of a sheet. It is defined as the ratio of true width strain to true thickness strain during plastic deformation. The left side of Figure 21 shows the r-value over true longitudinal strain. After uniform elongation at Ag = 10%, diffuse necking begins in the sample, and the r-value can no longer be evaluated. Between true strain ε_l = 0.04 and A_g, the r-value is relatively constant. Therefore, the r-value was calculated as the average over this range. After that, the average of three different samples was used.

Figure 21: r-value determination over strain: left, average value over longitudinal strain; right, linear regression over longitudinal strain

Figure 21 also shows another method for determining the r-value. In this approach, the r-value is calculated from the linear regression curve of true width strain over true longitudinal strain in the plastic strain range up to uniform elongation. From the gradient b of the linear regression curve, the r-value can be calculated as follows:

Figure 22 shows the variation of the r-value with angle to the rolling direction for both approaches. The variation of the r-value in the rolling direction and perpendicular to the rolling direction is significantly smaller. The largest differences between the two methods occur at 45° to the rolling direction. This is also where the greatest variation between the individual samples was observed. For the final material card, the average of both approaches was used (orange points in Figure 22).

Figure 22: r-value variation for different angles to the rolling direction and evaluation methods

Flow Curve Extrapolation with Bulge Test (DIN EN ISO 16808)

In tensile tests, the flow curve can only be recorded up to uniform elongation. After that, the tensile specimen begins to neck locally, and the strain distribution becomes uneven. For this reason, the flow curve beyond uniform elongation must be extrapolated. In this case, uniform elongation is only A_g = 10%.

The advantage of the bulge test is that flow curves can be obtained at higher strains. However, because of the different stress states in the bulge test and the uniaxial tensile test, the stress-strain curve from the bulge test cannot be used directly as the flow curve. In DIN EN ISO 16808 [3], Attachment D describes a procedure for determining the equibiaxial stress ratio and adapting the bulge test results to determine the uniaxial stress-strain curve beyond uniform strain.

Figure 23 shows the flow curves from the tensile test in the rolling direction up to uniform elongation, from the bulge test, and the calculated combined flow curve. The uniform strain of the tensile specimen in the rolling direction, together with the corresponding true yield stress, serves as the reference. For this purpose, the corresponding reference point is determined in the bulge data set so that both sides match the reference state in terms of plastic work. A biaxial stress factor is derived from the ratio of bulge reference stress to tensile reference stress. In this case, the calculated adjustment factor f_bi = 0.9957 is nearly one. Using this factor, the entire equibiaxial bulge curve is converted into an equivalent uniaxial stress-strain curve and appended to the tensile curve beyond uniform elongation. This creates a continuous strain hardening curve up to high strains. For strains below the uniform elongation A_g = 10%, the flow curve from the tensile test in the rolling direction was used.

Figure 23: Flow curve extrapolation according to DIN EN ISO 16808

Layer Compression Test

The result of the layer compression test was used to determine the biaxial r-value r_b. The layer compression test was described in [2]. Eleven plates were stacked centered between two parallel plates and compressed vertically. This loading configuration led to deformation in the horizontal direction. The side lengths of the three inner layers in the rolling and transverse directions, as well as their thickness, were measured before and after the layer compression test. Based on these measurements, the degree of deformation can be determined in the three main directions. The r_b value is defined as the ratio of the plastic strain in the transverse direction to the plastic strain in the rolling direction:

The mean of all tests yields an r_b value of 0.81.

Tension-Compression Test: Determination of Kinematic Hardening

The tension-compression test is used to characterize the behavior of a material under tensile and compressive loading. A specimen is first subjected to a tensile load and then compressed in the opposite direction. A detailed description of the test can be found in [2]. The aim is to examine the material’s behavior during load reversal, with particular focus on the Bauschinger effect, namely, the reduction in yield stress when the loading direction changes from tension to compression. In simulations, this effect can significantly influence springback results when tension-compression load reversals occur during the forming process. This typically occurs, for example, when the sheet is drawn through a geometric draw bead. For the MUC test, no influence of the kinematic hardening parameters on the simulation result is expected.

Figure 24 shows the engineering stress-strain curves from the seven tension-compression tests. These hysteresis curves were used to fit the kinematic hardening parameters with the AutoForm Material Generator. The resulting parameters are as follows:

Figure 24: Stress-strain curves from tension compression tests

Plane Strain Test: Determination of the Plane Strain Point

The plane strain test was used to calibrate the yield locus under plane strain conditions. In the test, a notched specimen oriented in three directions relative to the rolling direction (0°, 45°, and 90°) was stretched. Force-displacement curves and strain distribution data on the specimen were provided. A detailed description of the test can be found in [2]. The yield locus calibration was performed by reverse engineering. For this purpose, the experimental plane strain test was replicated in a simulation model, and both the strain distribution and the forming force were compared. Figure 25 shows the strain distribution of the notched specimen. As can be seen, the plane strain state could only be reached in the middle of the specimen, where the minor strain is zero.

Figure 25: Comparison of major and minor strain from experiment and simulation

Figure 26 shows a section plot in the middle of the plane strain specimen. The gray curves are the test results, and the red curve is the simulation result. The length of the plane strain region is about one-third of the sample. At the edge of the specimen, the stress and strain state of uniaxial tension prevails.

Figure 26: Section plot in the middle of the plane strain specimen

Yield Loci Variation

In the following, simulations of the plane strain test are carried out using different yield loci. The simulation results for major strain and the force-displacement curve are then compared with the experimental results. The following yield loci were used for reverse engineering:

• BBC2005 M6: Banabic-Balan-Comsa yield criterion. M=6 is the default yield locus curvature for steel materials.
• Vegter2017: Abspoel & Scholting parameter prediction for Vegter yield locus. Only three tensile tests at 0°, 45°, and 90° to the rolling direction are required.
• Vegter Standard (2006): The yield locus was optimized so that the simulation results match the force-displacement curve. s_ps0/s₀ represents the minimum value; otherwise, the 3D stress space becomes concave.

The material cards described above differ only in the yield locus. The various yield loci are shown in Figure 27.

Figure 27: Different yield loci used for reverse engineering of the plane strain test

The yield locus definition of the Vegter Standard (2006) model is very flexible. The plane strain point can be freely defined for 0°, 45°, and 90°. However, forming simulations require a convex yield locus. For this reason, the Vegter Standard (2006) yield locus was defined so that the force-displacement curves from simulation and experiment match as closely as possible. This is clearly shown in the left diagram in Figure 28. The three gray curves represent the experimental force-displacement curves. The blue curve, corresponding to the Vegter Standard (2006) yield locus, provides the best fit to the experimental data. A further reduction of the plane strain point is not possible, as this would result in a concave yield locus. All other simulation results predict higher forces. The Vegter2017 and BBC2005 M6 yield loci show similar behavior.

The middle plot of Figure 28 shows a section view of the major strain distribution at the force maximum. The gray curves again represent the experimental results. The simulation results using the optimized Vegter Standard (2006) yield locus show the largest deviation from the experimental data. The history plot in Figure 28 shows the same trend. It tracks the major strain at a point in the middle of the specimen over the entire test.

These results show that adjusting only the plane strain point in the yield locus is not sufficient. A good prediction of force leads to poor agreement in strain, and vice versa.

Figure 28: Comparison of simulation and experimental results for the plane strain test (RD 0°)

BBC2005 M-Value variation

In the following, the influence of the M value of the BBC2005 yield locus is investigated. Figure 29 shows the BBC2005 yield loci for different M values. A lower M value shifts the plane strain point outward, while a higher M value shifts it inward.

Figure 29: BBC2005 yield loci with different M values

If the plane strain point is further outward, the resistance to deformation under plane strain increases. This effect is reflected in the test results (Figure 30). The smaller the M value, the higher the forming force, and vice versa. A smaller M value also leads to lower major strain in the plane strain region of the specimen. As a result, the simulation results do not match the experimental data.

Figure 30: Plane strain test results in the rolling direction for BBC2005 yield loci with different M values

Strain Rate Sensitivity

None of the yield loci showed good agreement for both measured forces and strains. For this reason, the influence of strain rate is investigated below. In AutoForm, strain rate dependence can be modeled using:

where σ₀(ε) is the quasi-static reference hardening curve. For strain rate values below εstatic , the static hardening curve is used. This means that in regions with higher strain rates, the stress increases, and thus the forming force also increases. At the same time, strain peaks are reduced because the surrounding material is softer and deformation is redistributed there. Using strain rate-dependent flow curves also requires consideration of the forming velocity in the plane strain test.

No strain rate-dependent tensile test data were provided in the benchmark definition. Therefore, the following empirical values were assumed:

• m = 0.01
• εstatic = 0.001 1/s

Figure 31 shows the force-displacement curves from the simulations with and without strain rate dependency, compared with the experimental results. As expected, a slight increase in forming force is observed for both yield loci.

Figure 31: Force-displacement plot comparing results with and without strain rate-dependent material models

Figure 32 shows the strain distribution of the sample in a section plot (left) and the evolution of strain over displacement in a history plot (right). The two yield loci, BBC2005 M = 6 and Vegter Standard (2006), are compared using both strain rate-dependent and strain rate-independent flow curves. The major strain is significantly lower in the strain rate-dependent simulations and is closer to the experimental results. This effect is particularly evident for the BBC2005 M = 6 model in the history plot.

Figure 32: Section and history plots of the plane strain sample showing major strain

Conclusion: Material Card Generation

Table 1 summarizes the material parameters determined directly from the material tests.

Table 1: Material parameters for steel DP800 HHE

The reverse engineering study of the plane strain test showed good agreement between simulation and experiment with the following material parameters:

• Yield surface model: BBC 2005 M = 6
• Use of strain rate dependency with the following parameters: m = 0.01 and εstatic = 0.001 1/s

Simulation Setup of the MUC Test

Element Type, Time Step, and Mesh Refinement

The MUC test is described in detail in [2]. The simulation was performed using AutoForm version R12.0.3 with an implicit solver. This software was available to all AutoForm customers at the time of the benchmark. The element type was an elastic-plastic shell element with 11 integration points through the thickness (EPS-11).

To balance accuracy and computational efficiency, the final mesh was divided into distinct zones with tailored element sizes. The area outside the bead used a coarse mesh without refinement. In contrast, the bead region used FV mesh settings to better capture localized deformation behavior. For the wall area of the sample, a constant element size of approximately 1.2 mm was used. The top surface of the sample was meshed more finely, with a constant element size of approximately 0.6 mm to improve the resolution of strain measurements in this critical region. In addition, symmetry was applied to improve computational efficiency. The number of elements and computation times are summarized in Table 2.

Table 2: Computation times and number of elements

Comparison of Experimental and Numerical Results

Figures 33 to 35 show the minor and major strain for two planes of the three different MUC tests. The blue curves represent the experimental results, while the red curves show the AutoForm simulation results. Figure 36 compares the experimental and simulated force-displacement curves.

In a benchmark study or in practical method planning, it is important to compare simulation results with experimental data to identify limitations and improve accuracy in future applications. The force-displacement curves (Figure 36), as well as the major and minor strain results for the MUC 110 mm and 230 mm tests, show good agreement between simulation and experiment (Figures 34 and 35).

The major strain results for the MUC 70 mm test show less agreement. It was found that friction has a significant influence on the strain results in the MUC test. As described earlier, the TriboForm friction card for the punch was created based on the sheet metal surface, and friction on the punch side was reduced using foil. Based on this information and prior experience, an existing friction map for uncoated DP steel was adjusted toward a lower friction coefficient.

In Figure 37, the green surface shows the friction coefficient as a function of pressure and strain for the TriboForm friction card used in the benchmark. In addition to strain and pressure, velocity also influences friction, while temperature effects are not considered here.

The blue surface in Figure 37 shows the friction coefficient with less adjustment. The yellow curves in Figures 33 to 35 show the strain results obtained with the modified friction card. The simulation results for the MUC 70 mm test show improved agreement with the experimental data, while the results for the MUC 110 mm and 230 mm tests change only slightly. also shows that modifying the friction map for the punch has little influence on the punch force. However, the friction adjustment was carried out after the MUC test results had been published.

Overall, the benchmark shows that the forming simulation results are very close to the experimental results. However, achieving this level of accuracy requires significant effort in material card creation. Further improvements can be achieved through a more detailed description of friction and strain rate dependence.

Figure 33: Experimental and AutoForm strain results for MUC test, 70 mm, 45° to rolling direction

Figure 34: Experimental and AutoForm strain results for MUC test, 110 mm, 90° to rolling direction

Figure 35: Experimental and AutoForm strain results for MUC test, 230 mm, rolling direction

Figure 36: Experimental and AutoForm force-displacement curves

Figure 37: Benchmark and modified TriboForm friction card

Benchmark Results

A total of 17 international teams from industry, academia, and software development participated in the benchmark. In the blind benchmark, each participant submitted simulation results for punch force and major/minor strain at two sections from three different MUC tests (with varying blank sizes and rolling directions). The error value was calculated based on the difference between the simulation and experimental results. A detailed description of the error calculation can be found in [4].

Figure 38 compares the error values for all participants. As in the Industrial Benchmark, AutoForm secured first place among all participants.

Figure 38: Mean error value of the 17 benchmark participants with corresponding standard deviation compared to experimental data

Summary

The requirements for participants in the Industrial and Scientific Benchmarks differ significantly. The Industrial Benchmark requires experience in process planning, as well as software that supports methodological development. The Scientific Benchmark requires strong expertise in material card generation and a reliable solver.

These results reflect the contributions of many AutoForm employees. Winning both benchmarks demonstrates that the AutoForm team has extensive expertise in process planning and material modeling in sheet metal forming. In addition, the software supports users in methodological development by providing reliable solver results.

References