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Publication Number: FHWA-HRT-05-063
Date: May 2007

Evaluation of LS-DYNA Concrete Material Model 159

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Appendix A. User Code Verification

Introduction

This task involved repeating the finite element calculations previously performed by the developer using input files supplied by the developer, and comparing the results of these calculations. Five models were supplied to the user by the developer. The models included a single element model (three load cases), concrete cylinder under tension, plain (unreinforced) concrete beam under impact loading, over-reinforced concrete beam under impact loading, and reinforced concrete beam under impact loading by surrogate vehicle.

All the input files incorporate the new material (MAT type 159 or MAT_CSCM) to be released in LS-DYNA version 971. The user obtained a beta binaries release of LS-DYNA version 971 for the following platforms/operating systems: SGI IRIX (version 971 release 1490 double precision ), MS-Windows (version 971 release 1612 single precision), and Linux Intel 32 bit architecture (version 971 release 1708 single precision). The SGI IRIX binary crashed with a floating point exception error during the initialization phase of reading an input file. The researchers believe the crash occurred because the SGI binary beta release (1490) might not be as "bug free" as the other binaries.

Case 1. Single Element Simulations

In this case, a single solid element was used to verify the basic behavior of the material model. There are three loading conditions for this case. The first load case was compression of the element as shown in Figures 148 and 149. The second load case was application of a tensile load to the element as shown in Figures 150 and 151. The last load case was a shear load applied on the element as shown in Figures 152 and 153. For each of these load conditions, the user calculations precisely matched the developer's calculations as Figures 148-153 indicate.

Figure 148. Graph. Single element under pure compressive loading, developer. The Y-axis is Z-stress in units of megapascals, and ranges from negative 5,000 to 0. The X-axis is Time in milliseconds, and ranges from 0 to 0.12. The stress increases linearly from 0 to negative 4,000 megapascals in 0.02 millisecond. Then it gradually softens in a nonlinear manner to 100 megapascals in 0.12 millisecond.

psi = 145.05 MPa

Figure 148. Single element under compressive loading, developer.

Figure 149. Graph. Single element under pure compressive loading, user. </strong> The Y-axis is Z-stress in units of megapascals, and ranges from negative 5,000 to 0. The X-axis is Time in milliseconds, and ranges from 0 to 0.12. The stress increases linearly from 0 to negative 4,000 megapascals in 0.02 millisecond. Then it gradually softens in a nonlinear manner to 100 megapascals in 0.12 millisecond.

psi = 145.05 MPa

Figure 149. Single element under compressive loading, user.

Figure 150. Graph. Single element under tensile loading, developer. The Y-axis is Z-stress in units of megapascals, and ranges from 0 to 350. The X-axis is Time in milliseconds, and ranges from 0 to 0.3. The stress increases linearly from 0 to 320 megapascals in 0.02 millisecond. Then it gradually softens in a nonlinear manner to 20 megapascals in 0.3 millisecond.

psi = 145.05 MPa

Figure 150. Single element under tensile loading, developer.

Figure 151. Graph. Single element under tensile loading, user. The Y-axis is Z-stress in units of megapascals, and ranges from 0 to 350. The X-axis is Time in milliseconds, and ranges from 0 to 0.3. The stress increases linearly from 0 to 320 megapascals in 0.02 millisecond. Then it gradually softens in a nonlinear manner to 20 megapascals in 0.3 millisecond.

psi = 145.05 MPa

Figure 151. Single element under tensile loading, user.

Figure 152. Graph. Single element under pure shear loading, developer. The Y-axis is Z-stress in units of megapascals, and ranges from 0 to 350. The X-axis is Time in milliseconds, and ranges from 0 to 0.3. The stress increases linearly from 0 to 305 megapascals in 0.025 millisecond. Then it gradually softens in a nonlinear manner to 20 megapascals in 0.3 millisecond.

psi = 145.05 MPa

Figure 152. Single element under pure shear loading, developer.

Figure 153. Graph. Single element under pure shear loading, user. The Y-axis is Z-stress in units of megapascals, and ranges from 0 to 350. The X-axis is Time in milliseconds, and ranges from 0 to 0.3. The stress increases linearly from 0 to 305 megapascals in 0.025 millisecond. Then it gradually softens in a nonlinear manner to 20 megapascals in 0.3 millisecond.

psi = 145.05 MPa

Figure 153. Single element under pure shear loading, user.

Case 2. Cylinder Runs

This case consists of a plain unreinforced concrete cylinder subject to tensile loading. The tension loading was simulated by pulling both ends of the cylinder at a constant velocity. An inclined cross section was defined in the model to track force versus time, as shown in Figure 154 below.

Figure 154. Illustration. Concrete cylinder model with inclined cross section. This is a view of the mesh of the cylinder, which is twice as tall as it is wide. A diagonal line extends across the cylinder, beginning near the top left of the cylinder at three-fourths of the height, and extending to the bottom right of the cylinder, ending at one-fourth of the height.

Figure 154. Concrete cylinder model with inclined cross section.

Fringes of the damage to the materials were plotted at various times during the analysis. The damage parameter plotted is the maximum of brittle and ductile damage calculated by the material model. It is noteworthy that damage is a normalized entity from 0 (no damage) to 1.0 (complete damage).

Figures 155-157 show these damage fringe plots at key times. Figures 158 and 159 show the cross-sectional force versus time measured on the inclined plane from the developer calculation and the user calculation, respectively. The user calculations matched the developer's calculations in terms of both damage fringes and cross-sectional force for this model. Two binaries were used for this calculation; however, only the Windows results are presented because there was no significant difference between the computed results.

Figure 155. Illustration. Damage fringe lowercase T equals 13.498 milliseconds. Damage fringes are shown on the outside of the cylinder. Two sets of fringes are shown, and are identical. One is for the developer calculation, and the other for the user calculation. The fringes are located in the central one-third of the cylinder.

Figure 155. Damage fringe t = 13.498 msec.

Figure 156. Illustration. Damage fringe Lowercase T equals 13.598 milliseconds. Damage fringes are shown on the outside of the cylinder. Two sets of fringes are shown and are identical. One set is for the developer calculation, and the other is for the user calculation. The fringes are two horizontal lines, symmetric through the vertical midplane, and residing in the central third of the cylinder.

Figure 156. Damage fringe t = 13.598 msec.

Figure 157. Illustration. Damage fringe at lowercase T equals 40 milliseconds. Damage fringes are shown on the outside of the cylinder. Two sets of fringes are shown, and are identical. One set is for the developer calculation, and the other is for the user calculation. The fringes are one horizontal line, located above the vertical midplane, and residing in the central third of the cylinder.

Figure 157. Damage fringe at t = 40 msec.

Figure 158. Graph. Cross-sectional force (developer). The Y-axis is Z-force in units of megapascals, and ranges from 0 to 14,000. The X-axis is Time in units of milliseconds, and ranges from 0. to 0.04. One curve is shown. It increases linearly from 0 to 13,000 megapascals in about 0.013 millisecond. It rapidly then gradually decays to 500 megapascals in about 0.04 millisecond.

psi = 145.05 MPa

Figure 158. Cross-sectional force (developer).

Figure 159. Graph. Cross-sectional force (user). The Y-axis is Z-force in units of megapascals, and ranges from 0 to 14,000. The X-axis is Time in units of milliseconds, and ranges from 0 to 0.04. One curve is shown. It increases linearly from 0 to 13,000 megapascals in about 0.013 millisecond. It rapidly then gradually decays to 500 megapascals in about 0.04 millisecond. It is identical to the stress history calculated by the user in Figure 158

psi = 145.05 MPa

Figure 159. Cross-sectional force (user).

Case 3. Plain Concrete Beam

In this case, an unreinforced concrete beam was modeled using the CSCM concrete model. Unlike previous cases, this model incorporates element erosion and contact definitions. The element erodes based on a set damage threshold above 0.99. Contacts were defined to represent surface interaction between parts (beam, impact parts, support parts, etc.).

Damage fringes were plotted at simulation times (t) of 1, 4, 20, and 30 msec. Figures 160-163 show the respective damage fringe plots obtained from the developer calculations for these simulation times. Figures 164-167 show the corresponding damage fringes plots from the user's calculations using the Linux binary. Similarly, Figures 168-171 show the respective damage fringe plots from the user's calculations using the Windows binary for the aforementioned simulation times.

At 1 msec of simulation time, the beam was already experiencing damage as shown in Figure 160 (developer), Figure 164 (user Linux), and Figure 168 (user Windows). The damage fringe from all three calculations looks very similar. Some elements were already eroded at t = 4 msec as shown in Figure 161 (developer), Figure 165 (user Linux), and Figure 169 (user Windows). Although the number of eroded elements is different among the three calculations, the fracture pattern is considered to be bounded within expected behavior of concrete. This same degree of variation in cracking patterns is observed among identical laboratory tests.

Figure 160. Illustration. Plain concrete damage fringe at 1 millisecond (developer). This is a view of the damage fringes and erosion in the simulation of the plain beam tested in the drop tower facility. Damage fringes are concentrated in the central region of impact, and at one-fourth of the distance from each end of the beam.

Figure 160. Plain concrete damage fringe at 1 msec (developer).

Figure 161. Illustration. Plain concrete damage fringe at 4 milliseconds (developer). This is a view of the damage fringes and erosion in the simulation of the plain beam tested in the drop tower facility. Damage fringes are concentrated in the central region of impact, and at one-fourth of the distance from each end of the beam. Erosion, part way through the beam thickness, is also evident beneath each impactor point.

Figure 161. Plain concrete damage fringe at 4 msec (developer).

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Figure 162. Plain concrete damage fringe at 20 msec (developer).

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Figure 163. Plain concrete damage fringe at 30 msec (developer).

Figure 164. Illustration. Plain concrete damage fringe lowercase T equals 1 millisecond (user Linux). This is a view of the damage fringes and erosion in the simulation of the plain beam tested in the drop tower facility. Damage fringes are concentrated in the central region of impact, and at one-fourth of the distance from each end of the beam. The damage is nearly identical to that calculated by the developer.

Figure 164. Plain concrete damage fringe t =1 msec (user Linux).

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Figure 165. Plain concrete damage fringe t = 4 msec (user Linux).

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Figure 166. Plain concrete damage fringe t = 20 msec (user Linux).

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Figure 167. Plain concrete damage fringe t = 30 msec (user Linux).

Figure 168. Illustration. Plain concrete damage fringe lowercase T equals 1 millisecond (user Windows). This is a view of the damage fringes and erosion in the simulation of the plain beam tested in the drop tower facility. Damage fringes are concentrated in the central region of impact, and at one-fourth of the distance from each end of the beam. The damage is nearly identical to that calculated by the developer.

Figure 168. Plain concrete damage fringe t = 1 msec (user Windows).

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Figure 169. Plain concrete damage fringe t = 4 msec (user Windows).

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Figure 170. Plain concrete damage fringe t = 20 msec (user Windows).

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Figure 171. Plain concrete damage fringe t = 30 msec (user Windows).

Case 4. Reinforced Concrete Beam

In this case, an over-reinforced concrete beam was modeled using the CSCM concrete model. The setup is similar to the model used in case 3 with the exception that beam elements are added to model the steel reinforcement inside the concrete beam. Both Windows and Linux binaries were used for conducting calculations with this model. Due to their similarity to one another, only one set of results (from the Linux binary) is presented in this report. Figures 172-175 show the damage fringes plots obtained from the developer calculations at simulation times corresponding to 1, 4, 16, and 20 msec, respectively. Figures 176-179 show damage fringe plots from the user Linux's calculations using the same simulation times. Figures 180 and 181 show the displacement history plot of a node on the impacting heads using the developer and user calculations, respectively.

Due to the over-reinforced nature of the beam, element erosion did not initiate in this analysis case. Close correlation was obtained between the user and the developer calculations for both the damage fringes and the displacement history of the impactor node. The minor variations that exist are well within the anticipated range of behavior.

Figure 172. Illustration. Reinforced concrete damage fringe lowercase T equals 1 millisecond (developer). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested in the drop tower facility. Damage fringes are concentrated in the central region of impact, and at one-fourth of the distance from each end of the beam.

Figure 172. Reinforced concrete damage fringe t = 1 msec (developer).

Figure 173. Illustration. Reinforced concrete damage fringe lowercase T equals 4 milliseconds (developer). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested in the drop tower facility. Damage fringes are concentrated in the central region, but also spread out and join those previously formed at one-fourth of the distance from each end of the beam.

Figure 173 Reinforced concrete damage fringe t = 4 msec (developer).

Figure 174. Illustration. Reinforced concrete damage fringe lowercase T equals 16 milliseconds (developer). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested in the drop tower facility. Damage fringes are concentrated in the central region, but also spread out and join those previously formed at one-fourth of the distance from each end of the beam. The beam is deflecting in flexure.

Figure 174. Reinforced concrete damage fringe t = 16 msec (developer).

Figure 175. Illustration. Reinforced concrete damage fringe lowercase T equals 20 milliseconds (developer). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested in the drop tower facility. Damage fringes are concentrated in the central region, but also spread out and join those previously formed at one-fourth of the distance from each end of the beam. The beam is deflecting in flexure, but has started to rebound.

Figure 175. Reinforced concrete damage fringe t = 20 msec (developer).

Figure 176. Illustration. Reinforced concrete damage fringe lowercase T equals 1 millisecond (user Linux). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested in the drop tower facility. Damage fringes are concentrated in the central region of impact, and at one-fourth of the distance from each end of the beam. The damage is nearly identical to that calculated by the developer.

Figure 176. Reinforced concrete damage fringe t = 1 msec (user Linux).

Figure 177. Illustration. Reinforced concrete damage fringe lowercase T equals 4 milliseconds (user Linux). This is a view of the damage fringes and erosion in the simulation of the reinforced beam tested in the drop tower facility. Damage fringes are concentrated in the central region, but also spread out and join those previously formed at one-fourth of the distance from each end of the beam. The damage is nearly identical to that calculated by the developer.

Figure 177. Reinforced concrete damage fringe t = 4 msec (user Linux).

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Figure 178. Reinforced concrete damage fringe t = 16 msec (user Linux).

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Figure 179. Reinforced concrete damage fringe t = 20 msec (user Linux).

Figure 180. Graph. Displacement of node 49,072 in millimeters (developer). The Y-axis is Y-displacement in millimeters, and ranges from negative 30 to 0. The X-axis is Time in milliseconds, and ranges from 0 to 0.02. One curve is shown that originates at the origin. It gradually decreases to negative 27 millimeters in about 0.013 millisecond, then begins to rebound.

mm = 0.039 inch

Figure 180. Displacement of node 49,072 in millimeters (developer).

Figure 181. Graph. Displacement of node 49,072 in millimeters (user Linux). The Y-axis is y-displacement in millimeters, and ranges from negative 30 to 0. The X-axis is Time in milliseconds, and ranges from 0 to 0.02. One curve is shown that originates at the origin. It gradually decreases to negative 27 millimeters in about 0.013 millisecond, then begins to rebound. It is identical to that calculated by the developer in Figure 180.

mm = 0.039 inch

Figure 181. Displacement of node 49,072 in millimeters (user Linux).

Case 5. Bogie Impact Tests

In the final case, another steel-reinforced concrete beam was modeled using the CSCM concrete model. The loading condition represents a bogie vehicle impacting the reinforced beam at a speed of 33 km/h (20.5 mi/h). Figures 182-185 show the damage fringes plots from developer calculations at simulation times of 4, 8, 48, and 80 msec, respectively. Figures 186-189 show damage fringes plots from user Windows binary calculations at these same simulation times. Figures 190-193 show the corresponding damage fringes plots from user Linux binary calculations.

As for the beam analyzed in case 3, the damage fringes for the impacted beam in the user calculations developed similarly to those obtained from the developer calculations, and the subsequent element erosion pattern representing the cracking and failure of the beam shows differences for each calculation. However, the element erosion/fracture patterns are bounded within the same physical regions of the beam and the differences are considered to be within normal variability and range of behavior expected of a concrete member of this type.

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Figure 182. Bogie damage, t = 4 msec (developer).

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Figure 183. Bogie damage t = 8 msec (developer).

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Figure 184. Bogie damage, t = 48 msec (developer).

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Figure 185. Bogie damage, t = 80 msec (developer).

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Figure 186. Damage fringes t = 4 msec (user Windows).

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Figure 187. Damage fringe t = 8 msec (user Windows).

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Figure 188. Damage fringe t = 48 msec (user Windows).

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Figure 189. Damage fringe t = 80 msec (user Windows).

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Figure 190. Damage, t = 4 msec (user Linux).

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Figure 191. Damage, t = 8 msec (user Linux).

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Figure 192. Damage, t = 48 msec (user Linux).

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Figure 193. Damage t = 80 msec (user Linux).

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