By default, all bodies in an Explicit Dynamics analysis system are discretized and solved in a Lagrangian reference frame. The Explicit Dynamics solver offers two alternative solver formulations to overcome the problems of extreme deformations: the Eulerian and the Particle reference frames.
Switching the reference frame of any solid body in a 3D Explicit Dynamics system, or a surface body in a 2D Explicit Dynamics system, from Lagrangian to Eulerian will result in the automatic creation of a virtual Multi-Material Eulerian domain. The domain will have properties such as dimensions and cell size determined by the Euler Domain Controls the Analysis Settings. All solid bodies with the reference frame set to Eulerian will be mapped into the virtual Multi-Material Eulerian background grid at solve time and the material associated with these bodies will be solved in the virtual Eulerian reference frame. The creation of the virtual Multi-Material Eulerian domain as well as the mapping of the bodies are further described in the Eulerian (Virtual) Reference Frame in Explicit Dynamics section within the theory chapter.
Note: Enhancements to the Eulerian solver in Explicit Dynamics are exposed as a Beta feature, such as remapping results from 2D Multi-Material Eulerian analyses to 3D Multi-Material Eulerian analyses. For more information, see Explicit Dynamics Blast Analysis in Mechanical and Virtual Eulerian Surface Bodies for a description of these enhancements.
Note: The LS-DYNA system uses S-ALE Domain and S-ALE Fill Reference Frames for Euler analyses. For more information, see ALE Workflow in the LS-DYNA User's Guide.
The supported material properties are Density, Specific Heat, Isotropic Elasticity, Bilinear Isotropic Hardening, Multilinear Isotropic Hardening, Johnson Cook Strength, Cowper Symonds Strength, Steinberg Guinan Strength, Zerilli Armstrong Strength, Drucker-Prager Strength Linear, Drucker-Prager Strength Stassi, Drucker-Prager Strength Piecewise, Johnson-Holmquist Strength Continuous, Johnson-Holmquist Strength Segmented, RHT Concrete, MO Granular, Ideal Gas EOS, Bulk Modulus, Shear Modulus, Polynomial EOS, Shock EOS Linear, Shock EOS Bilinear, Explosive JWL, Explosive JWL Miller, Compaction EOS Linear, Compaction EOS Non-Linear, P-alpha EOS, Plastic Strain Failure, Tensile Pressure Failure, Johnson Cook Failure, and Grady Spall Failure.
Sometimes, the multimaterial Euler solver exhibits a behavior called checkerboarding, where the face values of Euler elements are correct, but the Euler element values (for example, pressure) are switching between positive and negative values from element to element. This can be seen when the smoothing of the contour values is switched off—the plot will show a checkerboard pattern. This introduces incorrect pressure values, which will result in wrong coupling forces on a Lagrangian flexible or rigid body.
The magnitude of the effect of this limitation on the solution may be large and easy to observe. For example, when the flow or distortion of the material in Euler shows overall incorrect behavior.
The limitation's effect may also be small and more difficult to recognize. For example, in cases where the pressure switches locally, but the overall average pressure is still correct.
Common solutions for this problem are:
A refinement of the mesh
Reduction of the timestep safety factor to a value of 0.333
A body with the reference frame set to Particle must be meshed with a Particle Method in Mechanical, which will generate a cloud of particles within the body.
Contact between SPH bodies is treated using the standard algorithm for coupling between different materials modeled with SPH. Contact between SPH bodies and Lagrange and shell bodies can also be accounted for using Body Interaction objects.
There is no material strength (tensile or shear) across the SPH/Lagrange surface (but bonded contact regions can be used to connect SPH with Lagrange bodies).
Interaction between SPH particles and Lagrange faces are detected using the Proximity based or Trajectory Contact algorithms. The contact detection in both cases is asymmetric node to segment contact where the particles act as the nodes and the Lagrange faces are the segments.
When using proximity-based contact, the gap size used for SPH-Lagrange interactions is always half the local SPH smoothing length, which may be different to the gap size used for Lagrange-Lagrange interactions.
Boundary conditions supported with Particle reference frames are Displacement, Velocity, and Limit Boundaries. They can be scoped to whole bodies, or selections of nodes. Limit Boundary is not supported for LS-DYNA.
Under certain conditions, the SPH algorithm can exhibit tensile instability. This instability often arises either at boundaries or when particles are unevenly spaced. The instability can be seen in practical calculations, when pairs of particles clump together and separate from their other neighbors. For LS-DYNA, you can use the Total Lagrangian Formulation particle approximation to avoid tensile instability.
The SPH formulations do not satisfy the consistency criteria for SPH particles that lack neighbors or whose neighbors are unevenly distributed (for example, at free surface).
The limitations in the current SPH technology may give rise to poor energy conservation. It is recommended to monitor the energy conservation to assess the effects of the known limitations (of instability and lack of consistency) on the results of the simulations. For simulations including SPH regions, note that the maximum energy error wrap-up criteria have been hard-wired to a large value of 50%.
Performing an analysis with the SPH solver is typically more computationally efficient than the equivalent setup using an Eulerian grid, but will be less computationally efficient than an equivalent setup using the Lagrange processor (if appropriate for the scenario).
For more information about the LS-DYNA SPH solver, see SPH Workflow in the LS-DYNA User's Guide.