LS-DYNA & DYNA3D Experience in
Modeling Geomaterials: Concrete, Rocks and Soils

Rock, concrete, and soil are the three most common examples of geo-materials encountered in engineering applications. They are all characterized as ‘frictional materials’ in that their shear strength depends on the confinement of the material. Also, these geo-materials can undergo a significant amount of volume change under hydrostatic or combined loading, i.e. compaction. These similarities in physical behavior have led to the development of rather general constitutive models for this class of geo-materials referred to as cap models.

Dr. Schwer has been using and developing numerical constitutive models for frictional materials since starting his profession career at SRI International in 1976. The majority of this work has focused on the computational aspects of rock mechanics with a goal of applying these models to the response of underground, and deep underground, tunnel facilities to conventional and nuclear attack. With the exception of the early work at SRI International, all of Dr. Schwer constitutive model use and development has been with DYNA3D. The early work at SRI International started with the NONSAP code, which was later commercialized into the current ADINA code, this work is partially documented in the peer reviewed publication:

Florence, A.L., and L.E. Schwer, ``Axisymmetric Compression of a Mohr-Coulomb Medium Around a Circular Hole,'' International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 2, No. 4, pp. 367-379, October-December 1978.

Where the role of the intermediate principal stress is documented through an comparison of analytical solutions and their numerical replication using a three invariant constitutive model developed by Dr. Schwer. This publication also is a good demonstration of the type of constitutive model verification effort that is essential in developing numerical algorithms. Another closely related verification, and validation, of numerical constitutive modeling is the peer reviewed publication:

Senseny, P.E., H.E. Lindberg, and L.E. Schwer, ``Elastic-Plastic Response of a Circular Hole to Repeated Loading,'' International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 13, No. 5, pp. 459-476, September-October 1989.

Where an analytical solution and results from supporting laboratory experiments of the repeat loading of a rock specimen containing a tunnel are compared with the numerical results generated using the above mentioned Mohr-Coulomb model developed by Dr. Schwer. Before leaving SRI International in 1985, with the help of Dr. John Hallquist, this Mohr-Coulomb material model was implemented in DYNA3D where it continued to be used by SRI International engineers.

In 1985 Dr. Schwer began working on numerical simulation of earth penetrators as part of Lockheed Missile and Space Corporation’s contract with the US Air Force to develop a Hard Target Weapon; an air delivered steel cased bomb that could penetrate up to six feet of reinforced concrete in a shallow buried target. The modeling and simulation efforts were initially focused on using DYNA2D in an axisymmetric mode to model the normal impact of the penetrator with the target. The now rather simple DYNA2D ‘Soil and Crushable Foam’ (Model 5) was used to model both the concrete target and soil when present; reinforcement was not important in these simulations as the amount of reinforcement was typical of civil structures and thus small in terms of a 10-12 inch diameter penetrator impacting at close to 2000 feet/second. In part, this work is documented in the peer reviewed publication:

Schwer, L.E., R. Rosinsky, and J. Day, ``Axisymmetric Lagrangian Technique for Predicting Earth Penetration Including Penetrator Response,'' International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 12, No. 3, pp. 235-262, May-June 1988.

Dr. Schwer’s direct involvement in this penetration simulation work continue for several years and the scope expanded from nominal impact of concrete targets to the oblique impact of concrete and thin steel targets and thus the analysis shifted focus from DYNA2D to DYNA3D. A portion of this work is documented in the peer reviewed publication:

Schwer, L.E. and J. Day, ``Computational Techniques for Penetration of Concrete and Steel Targets by Oblique Impact of Deformable Projectiles,'' Nuclear Engineering and Design, Vol. 125, pp. 215-238, 1991.

Dr. Schwer’s work on computational rock mechanics was renewed in the early 1990’s as the former Defense Nuclear Agency (DNA), then Defense Special Weapons Agency (DSWA) and now the Defense Threat Reduction Agency (DTRA), interest in deep underground and shallow tunnel facilities became an agency focus. One new aspect of the tunnel response problem that was of interest to DSWA, was the response of the tunnel in the presence of joints in the rock mass which might cause significant increases in tunnel deformation under various attack scenarios. Dr. Schwer used DYNA3D and it’s robust slide-surface feature to demonstrate one approach to numerically simulating such a scenario and this work is documented in the peer reviewed publication:

Schwer, L.E. and H.E. Lindberg, ``A Finite Element Slideline Approach for Calculating Tunnel Response in Jointed Rock,'' International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 16, pp. 529-540, 1992.

Dr. Schwer served as the Program Manager and Principal Investigator for the DNA sponsored 3D Calculations (Contract DNA 001-91-C-0140) effort of the Underground Technology Program, a $750,000 four year program. Dr. Schwer’s research activities focused on the development of constitutive models for geo-mechanical materials, especially rocks under dynamic loading. The results of these efforts led to the development of a new cap model which has been incorporated in the Lawrence Livermore National Laboratories finite element codes DYNA2D and DYNA3D, referred to as the Smooth Cap Model, or as Material Model Type 37. These efforts are partially documented in the peer reviewed publications:

Schwer, L.E., ``A Viscoplastic Augmentation of the Smooth Cap Model,'' Nuclear Engineering and Design, Vol. 150, pp. 215-223, 1994.
Schwer, L.E. and Y.D. Murray, ``A Three-Invariant Smooth Cap Model with Mixed Hardening,'' International Journal for Numerical and Analytical Methods in Geomechanics, Volume 18, pp. 657-688, 1994.

Dr. Schwer’s work on computational rock mechanics continues to the present. He serves as a consultant to two DTRA prime contractors, Weidlinger Associates and Titan Corporation, on the continuation of this program to simulated the response of tunnels to conventional weapon attack.

In 1997 Dr. Schwer was part of a successful team proposal to DSWA for an effort entitled “Advanced Numerical Prediction of Target Response” contract DSWA-97-C-0171 ($1.4 million over 3 years), which will develop mesh free methods for simulation of conventional weapons effects on structures. The team members and roles are Professors Ted Belytschko and Wing Liu of Northwestern University developing appropriate meshfree methods, Dr. Robert Whirley of TransMotive Technologies Inc provides the DYNA3D implementation knowledge, and Dr. Schwer performs the code verification, validation, and applications. The program currently has a coupled code comprising the Northwestern Element Free Galerkin code and DYNA3D. The primary application of this coupled code capability is the numerical simulation of reinforced concrete structures subjected to weapon induced damage and failure.