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Evaluation of LS-DYNA Concrete Material Model 159

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Chapter 1. Introduction

Three million human injuries and 42,000 premature deaths occur annually as a result of motor vehicle crashes.⁽¹⁾ To help reduce the toll of this problem, the Federal Highway Administration (fhwa) has set a strategic goal to improve the safety of our Nation's roadways. One way this is being accomplished is by expanding the use of the ls-dyna finite element code to replicate three-dimensional motor vehicle crashes into roadside safety structures.⁽²⁾ The objective is to protect the vehicle occupants from serious injury by making the structures more crashworthy. Roadside safety structures include bridge rails, barriers, and guardrails. One important bridge, barrier, and guardrail material is concrete (with reinforcement).

The roadside safety community supplements measured crash test data with ls-dyna simulations performed on the computer. The accuracy of the simulations depends, in part, on the material models formulated to simulate the behavior of the roadside structures and vehicle materials. A comprehensive concrete material model was developed, implemented in the ls-dyna finite element code, and evaluated for simulating the deformation and damage to reinforced concrete structures from dynamic impact. For ease of use, default material properties for standard concrete are incorporated into the model as a function of concrete compressive strength and maximum aggregate size. Correlations with drop tower, bogie vehicle, and pendulum impact tests are used to evaluate the model and finalize the default material properties.

The calculations of chapters 1 through 7, chapter 9, and appendix B of this evaluation report were conducted and documented by the developer of the concrete material model, referred to here as the "developer." The calculations of chapter 8, chapter 9, and appendix A were conducted and documented by a potential end user of the concrete material model, referred to here as the "user." Conclusions and recommendations from both the developer and user are discussed in chapter 10.

Model Theory

The concrete model was primarily developed to simulate the deformation and failure of concrete in roadside safety structures impacted by vehicles. Examples are bridge rails and safety barriers. The concrete model is commonly referred to as a smooth or continuous surface cap model. Hence, model 159 is implemented in keyword format as mat_cscm for Continuous Surface Cap Model. A smooth and continuous intersection is formulated between the failure surface and hardening cap. The main features of the model are:

• Isotropic constitutive equations.
• Three stress invariant yield surface with translation for prepeak hardening.
• A hardening cap that expands and contracts.
• Damage-based softening with erosion and modulus reduction.
• Rate effects for increasing strength in high-strain rate applications.

General discussions of these types of formulations are given in references by Murray, Lewis, and Schwer.^(3,4,5) Thorough details of the concrete model theory, a user's guide, and example input are documented in the companion manual to this report titled FHWA HRT 05-062 Users Manual for ls-dyna Concrete Model 159.⁽⁶⁾

Concrete structures typically contain steel reinforcement. Steel reinforcement exhibits rate effects, and yields in a ductile manner until it breaks at an ultimate strain greater than about 20 percent. The reinforcement model plays an important role in modeling reinforced concrete behavior. Our approach is to explicitly model the reinforcement (beam elements) separately from the concrete (hex elements) using an elastoplastic material model with yielding, hardening, rate effects, and plastic strain-based failure (such as mat_piecewise_linear_plasticity).

Model Input

There are two methods for setting up the model input. The traditional method is to supply all material parameters, such as moduli, strengths, hardening, softening, and rate effects parameters (mat_cscm). A more convenient method is to request default parameters (mat_cscm_concrete). Default parameters are provided for the concrete model based on three input specifications: the unconfined compression strength (grade), the aggregate size, and the units. The parameters are fit to data for unconfined compression strengths between about 20 and 58 megapascals (MPa) (2,901 and 8,412 pounds per square inch (lbf/inch²)), and aggregate sizes between 8 millimeters (mm) (0.3 inches) and 32 mm (1.26 inches). The unconfined compression strength affects all aspects of the fit, including stiffness, three-dimensional yield strength, hardening, and damage-based softening. The aggregate size affects only the softening behavior of the damage formulation.

The suite of material properties was primarily obtained through use of the Comite Euro-International Du Beton-Fédération Internationale de la Précontrainte Model (CEB-FIP) Code,⁽⁷⁾ supplemented through correlations with the drop tower, bogie vehicle, and pendulum impact tests. This code is a synthesis of research findings and contains a thorough section on concrete classification and constitutive relations. Various material properties, such as compressive and tensile strengths, stiffness, and tensile fracture energy, are reported as a function of grade and aggregate size. A thorough discussion of the model input parameters is documented in the concrete model user's manual.⁽⁶⁾

Limitations of Material Property Data

Limitations of published laboratory test data for setting the default material properties include:

• No direct measurements of the softening behavior (fracture energy) in pure shear stress. The fracture energy is an area under the stress-displacement curve (from peak stress to zero stress).
• Limited information on rate effects for stress states other than uniaxial tensile stress and uniaxial compression stress. This includes the effect of rate on fracture energy as well as strength.

Our methodology is to estimate the missing material property values through ls-dyna correlations with static and impact data provided by the user. Hence the ls-dyna simulations discussed in this document serves not only to evaluate the material model but also to set default material property values.

Evaluation Process

Calculations were compared with a wide variety of test data to evaluate the performance of the concrete material model and the accuracy of the default material parameters. The evaluation of the concrete model proceeded in two steps. The first step was to evaluate the model as a user-defined material, which the developer accomplished. This means that the model was hooked up to the ls-dyna code (version 970) as material model #42 via an interface. The developer retained access to the concrete model source code in order to enhance the formulation and adjust the default parameters during the evaluation process.

Once the evaluation was near completion and all default parameters were tentatively selected, the concrete model was forwarded to Livermore Software Technology Corporation (lstc) for permanent implementation into the ls-dyna code. lstc and the developer implemented the model into a beta 971 version of ls-dyna as material model 159.

The second step was to evaluate the concrete model as material model 159 in the ls-dyna code. Both the developer and the user accomplished this step. One objective was to check the permanent implementation to make sure that material model 159 produced the same results as the user-defined material. Adjustments in the lstc implementation were made until agreement was achieved. A second objective was to make sure that the model produced the same or similar results on different computer platforms. Generally, results agree by platform until erosion occurs, at which time they diverge slightly (see appendix A). A third objective was to allow a potential end user access to the model for independent evaluation. Calculations performed by the developer were conducted using LS-DYNA beta version 971 (revisions 1432 and 2582) on a PC using Microsoft^® (MS) Windows^® XP. Calculations performed by the user were conducted using LS-DYNA beta version 971 with MS-Windows (release 1612 single precision) and Linux^TM Intel 32 bit architecture (release 1708 single precision). Minor adjustments in the model theory and default parameters were finalized with lstc before documenting this effort. Results and conclusions from both the developer and user are included at the end of this document.

Evaluation Calculations

Evaluation of the model requires two general types of test data: basic material property data of plain concrete for determining input parameters to the model and impact tests of reinforced concrete for evaluation of the model formulation. Most of the tests simulated are intended to produce failure conditions in the concrete that replicate the failure conditions in roadside safety applications. Evaluation simulations performed are:

• Single element simulations to check the implementation of the model via examination of the stress versus displacement behavior.
• Single material simulations (cylinders in tension and compression) to check simulation of the damage modes and to check convergence of the model with mesh refinement. Computed damage modes are compared with measured damage modes discussed in the general literature.
• Drop tower impact simulations of plain and reinforced concrete beams. Computed results are compared with test data on ⅓-scale beams in dynamic four-point bending. The test data were specifically generated for use on this project.
• Bogie vehicle impact simulations of full-scale reinforced concrete beams in dynamic four-point bending. Computed results are compared with test data specifically generated for this project.
• Pendulum impact simulations of the Texas T4 bridge rail parapet and deck section with two base-plate configurations (test 3-11 of National Cooperative Highway Research Program (NCHRP) Report 350). Computed results are compared with test data generated by the user on a separately funded project.⁽⁸⁾
• Quasi-static simulations of a New Jersey profile concrete safety-shaped barrier. Computed results are compared with test data generated by the user on a separately funded project.⁽⁹⁾

All calculations discussed in this report were performed with knowledge of the test results. This is because correlations with test results were used to set various default parameters and to help refine the model. Future calculations performed by roadside safety analysts will assess the predictive capability and provide a more thorough evaluation and validation of the concrete material model. Analysts include those at FHWA, National Highway Traffic Safety Administration, National Crash Analysis Center (ncac), and FHWA-organized Centers of Excellence for Finite Element Crash Analysis. Accurate predictions, in which the analyst is unaware of the measured results before the simulation, build more confidence in a model than accurate correlations.

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