# Presentation: 661801

## 

Greg Bessette and Jason Libersky
Computational Physics Research and Development (9231)
Sandia National Laboratories
Albuquerque NM

8th US National Congress on Computational Mechanics
Austin TX
25 – 27 July 2005

**Greg Bessette and Jason Libersky**
**Computational Physics Research and Development (9231)**
**Sandia National Laboratories**
**Albuquerque NM**
**8****th**** US National Congress on Computational Mechanics**
**Austin TX**
**25 – 27 July 2005**

- Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company,for the United States Department of Energy under contract DE-AC04-94AL85000.

**A ****Coupled Euler-Lagrange ****Approach for Modeling Penetration and Blast/Structure Interaction**

## Zapotec Collaborators

**John Prentice (SCI-TAC LLC)**
**Paul Yarrington (SNL, 9902)**
**Courtenay Vaughan (SNL, 9224)**
**Ray Bell (SNL, 9231)**
**Sue Goudy (SNL, 9224)**
**Steve Attaway (SNL, 9134)**
**Steward Silling (SNL, 9231)**
**Richard Koteras (SNL, 9142)**
**Bob Cole (Orion International Technologies)**
**And others ....**

## Motivation 

**Motivation **

**Penetration and blast/structure interaction characterized by:**
**Transient wave propagation, large material deformations, high strain rates, multi-body contact, etc.**
**Materials exhibiting vastly differing strengths and degrees of deformation**
**Many regimes of interest cannot be modeled using traditional methods**
**Coupled solution approach can fill the void**

**Earth Penetration**

**Blast Loading on a Building**

**Notes:**
We use a coupled approach to solve a class of problems not readily handled by Eulerian or Lagrangian methods alone.  The class of problems we want to solve with Zapotec usually involve large material deformations, high strain rates, and multi-body contact.  Also, the materials in the problem generally exhibit vastly differing strengths and degrees of deformation.  It is the later physical characteristic which drives the need for a coupled solution approach.

## Coupled Methods

**Many coupled approaches available for modeling penetration and blast/structure interaction**
**Engineering models/FE, CEL, FE/SPH, ALE, etc. **
**One-way vs. loosely-coupled methods**
**Present discussion focused on coupled Euler-Lagrange (CEL) approach embedded in the Zapotec code**

**Notes:**
We use a coupled approach to solve a class of problems not readily handled by Eulerian or Lagrangian methods alone.  The class of problems we want to solve with Zapotec usually involve large material deformations, high strain rates, and multi-body contact.  Also, the materials in the problem generally exhibit vastly differing strengths and degrees of deformation.  It is the later physical characteristic which drives the need for a coupled solution approach.

## Coupled Euler-Lagrange computer code

Directly couples two production codes
CTH: Eulerian shock physics code
Pronto3D: Explicit, Lagrangian FE code

Zapotec couples interaction between Lagrangian and Eulerian materials

Only handles 3D problems

**Directly couples two production codes**
**CTH: Eulerian shock physics code**
**Pronto3D: Explicit, Lagrangian FE code**
**Zapotec couples interaction between Lagrangian and Eulerian materials**
**Only handles 3D problems**

**What is Zapotec?**

**Notes:**
There are many implementations of coupled methods.  With Zapotec, we tightly couple two existing, production codes: CTH and Pronto3D. 

In the problem development, we define materials as Lagrangian or Eulerian.  The coupling algorithm then handles the interaction between the two material types.

## Zapotec Background The Coupled Algorithm in Time

**CTH and Pronto3D are run sequentially, cycle by cycle**
**Algorithm permits Pronto3D subcycling**

**Notes:**
Before discussing the details of the coupling algorithm, it is first useful to look at the coupled treatment in time.  At time tn, we get data from CTH and Pronto, work on that data, then send back the updated data to the two codes.  CTH and Pronto then move forward in time independently to tn+1.  In general, CTH will have a larger stable time step.  We permit Pronto subcycling to improve efficiency and accuracy.

## The Zapotec Coupling Algorithm

**Coupled treatment conducted in two steps, referred to as material insertion and force application**
**Material insertion step updates CTH data**
**Force application step updates Pronto3D data**

**Notes:**
Zapotec performs two steps in the coupled treatment.  We refer to these as material insertion and force application.

## The Zapotec Coupling AlgorithmMaterial Insertion Step

**Remove pre-existing Lagrangian material from the CTH mesh**
**Get updated Lagrangian data**
**Insert Lagrangian material into CTH mesh**
- Compute volume overlaps
- Map Lagrangian data – mass, momentum, sound speed, stress, internal energy

- CTH Mesh

- tn

- L1

- L2

- PL,inserted = (VO,L1 PL1 + VO,L2 PL2) / VO

- Voverlap = VO = VO,L1 + VO,L2

**Notes:**
At the beginning of the coupled treatment, we have Lagrangian material that was previously inserted into the CTH mesh.  We remove this material so that the CTH mesh contains only Eulerian materials.  Once this is done, we get the current (updated) Lagrangian data and insert it into the CTH mesh.  Material insertion first involves computing the overlap of Lagrangian elements with CTH cells.  After the element/cell overlaps are determined, we insert the Lagrangian data (mass, momentum, sound speed, stress, internal energy) into the CTH mesh.  In general, we have CTH cells that are overlapped by several Lagrangian elements.  We weight the Lagrangian data, usually by volume, for cell insertion.  For example, consider pressure where we weight the Lagrangian pressures by their volume-fraction overlap prior to insertion.

## The Zapotec Coupling AlgorithmForce Application Step

**Remove pre-existing Lagrangian material from the CTH mesh**
**Get updated Lagrangian data**
**Insert Lagrangian material into CTH mesh**
**Compute volume overlaps**
**Map Lagrangian data**
**Compute external force on Lagrangian surface**
- Determine surface overlaps
- Compute surface tractions based on Eulerian stress state
- Compute normal force on element surface (element-centered force)
- If friction, compute tangential force as **f**t = fn**s**
- Distribute forces to nodes

- CTH Mesh

- tn

**f**n = (**t** · **n**L ) Aoverlap **n**L

**f**I = NI **f**n

**Notes:**
With the material insertion step, we have updated the CTH data.  Now we need to assess the loading on the Lagrangian materials.  

First determine the overlap of Lagrangian surface elements with cells in the CTH mesh.  For a given surface element, we compute the surface tractions based on the stress state in the neighboring Eulerian material.  The surface normal and element area is known, allowing us to readily compute the normal force on a surface element.  These forces are element-centered.  We distribute these forces to the nodes in standard FE fashion.  Once this is done for all surface elements, we pass the data back to Pronto as a set of external nodal forces.

## Highlight of Zapotec Capabilities

**Supports several Pronto3D element types for material insertion**
**8-node hexahedral element**
**8-node tetrahedral element**
**4-node shell element**
**Compatible with CTH-AMR capability**
**Can model response of complex, thin-shell structures**
**Element death (a.k.a. erosion) accounted for in the force application step**
**Parallel implementation **

## Parallel Implementation

- Pronto3D

- Master
-  processor

- CTH

- Zapotec

**• ****CTH and Pronto3D have different mesh decompositions**
**•**** ****Data resides on different processors**
**• **** ****Lagrangian data communicated for coupled calculations**

## Processor Interactions Between CTH and Pronto3D

**Processor Interactions**
**CTH**** / ****PRONTO**** ****        Total**
**1**** - ****7, 8, 9, 10**** ****	****4**
**2**** - ****6, 7, 8, 9****	****	****4**
**5**** - ****5, 7****	****	****2**
**6**** - ****1, 2, 3, 4, 5, 6, 7****	****7**
**10**** - ****0, 1, 2****	****	****3**

- 1

- 2

- 3

- 4

- 5

- 0

- 6

- 7

- 8

- 9

- 10

- 0

- 4

- 1

- 2

- 3

- 7

- 6

- 5

- 12

- 9

- 8

- 10

- 13

- 14

- 11

- 15

- CTH Mesh Decomposition

- Pronto3D Mesh
- Decomposition

-  Overlapping data owned by
-   different processors
-  Pronto3D data and CTH mesh
-   coordinates communicated to idle
-   processors to load balance work

## Example Problems

**Ballistic penetration**
**Air blast loading on a thin plate**
**Blast loading on a buried structure**

## Ballistic Penetration

**Normal impact of 4340 steel penetrator into 6061-T651 aluminum plate**
**Piekutowski, Forrestal, Poorman, and Warren, “Penetration of Aluminum Plates with Ogive-nose Steel Rods at Normal and Oblique Impacts”, *****Int.***** *****J. Impact Engng*****, Vol. 18, pp. 877-887 (1996)**
**Penetrator characteristics**
**Ogive nose (3CRH), 88.9 mm long, 12.9 mm diameter**
**Impact velocities range from 282 to 863 m/s**
**Pitch/yaw generally less than one degree**
**Plate dimensions: 304 x 304 x 26.3 mm**
**Drivers for coupled modeling**
**Disparity in material response**
**Relatively low impact velocities**

**Notes:**
These experiments considered a wide range of impact velocities, as well as the effect of nose shape on penetration.  This was done experimentally by considering three different nose shapes:  hemi-spherical, ogive (3 CRH), and conical.

Hemi-spherical nose penetrator L/D = 10.5

DOP = depth of penetration

## Ballistic Penetration

**Penetrator is Lagrangian, plate is Eulerian**
**AOA modeled in some instances**
**Model friction with a velocity-dependent friction model where friction coefficient is specified as a function of sliding velocity**
**No data available for steel-aluminum contact, but data is available for steel-steel contact**
**Bowden and Persson, “Deformation, heating, and melting of solids in high-speed friction”, *****Proc. Royal Society*****, Vol. 160, pp. 433-458 (1961)**
**Friction coefficients range from 5 to 18 percent at sliding velocities  of 600 and 20 m/s, respectively**
**Zapotec utilizes a piecewise linear fit to the data**
**Comparisons with measured residual velocity**

**(Courtesy: Bowden and Persson)**

## Ballistic Penetration

**Plate response modeled using EP and Johnson-Cook constitutive models with Mie-Gruneisen EOS**
**AOA (combined pitch and yaw) also considered**

## Air Blast Loading on a Thin Plate

**Air blast on 5-mm-thick flat steel plate**
**Boyd, “Acceleration of a Plate Subject to Explosive Blast Loading – Trial Results”, DSTO-TN-0270 (2000)**
**Charge suspended over plate**
**Plate bolted into support structure**
**Drivers for coupled modeling**
**Disparity in material response**
**Varying length scales**
**Varying time scales**

**Notes:**
Shell mesh composed of uniform mesh, with element size of 20 mm.  Two variations in CTH cell size will be considered to assess convergence and investigate potential interplay between the Lagrangian and Eulerian domains.   The CTH cell sizes considered were 5 and 20 mm.

Shells expanded along top direction (i.e., direction towards impinging blast wave) to half of true thickness.  Shells scaled along bottom direction to two times the effective thickness.

Loads applied to top surface of plate and support block.

Characteristic time associated with blast is much less that the response time of the structure.  So CTH portion of calculation cutoff after loading was essentially over.  Pronto calculation allowed to proceed to capture late-time response (i.e., the permanent deflection).  The choice of 300 msec was arbitrary, and as it turns out, far more than needed.

## Air Blast Loading on a Thin Plate

**Charge and air are Eulerian**
**Plate and support are Lagrangian**
**Plate modeled with 4-node shell elements**
**Block modeled with 8-node hex elements**
**Joint modeled as clamped BC**
**CTH calculation cutoff after 400 ********sec**
**Pronto3D calculation run to 100 msec**
**Run with and without CTH-AMR**
**Phenomenological-based indicators**
**Charge: Volume fraction > 0**
**Shock: Pressure difference histogram**
**Plate: V****mag**** > 10 cm/s**
**Comparisons for centerline displacements**

**Air**

**Charge**

## Air Blast Loading on a Thin Plate

**Air Blast Loading on a Thin Plate**

**Notes:**
One notes a significant increase in accelerations with mesh refinement, and only a marginal increase in the displacements.  The calculated acceleration correlates directly with the strength of the shock impinging on the plate.  As the mesh is refined, the peak pressures increase as the shock front and pressure gradients are better resolved.  In contrast, the displacement results vary as a weak function of the mesh resolution.  This is not surprising, as this measurement correlates more with the impulse delivered to the plate, which is less affected by resolution.

The reason for the under-predicted peak displacements is unknown.  It may be tied with resolution of the shell mesh; however, this was not tested.  For both CTH meshes, there is an over-prediction of the permanent deflection.  However, the deflections are reasonably closed to the measured value. 

## Air Blast Loading on a Thin Plate

## Blast Loading on a Buried Structure

**Conventional Weapon Effects Backfill (CONWEB) Test 1**
**Hayes, “Backfill Effects on Response of Buried Reinforced Concrete Slabs”, TR-SL-89-19**
**15.4-lb cased C-4 charge at 5-ft standoff in clay backfill**
**Test Structure**
**Reinforced concrete (RC) slab bolted to reusable reaction structure**
**Slab thickness: 4.3 inches**
**Reaction Structure: 15 ft long, 65 inches high, 4 ft deep**
** ****Structure and soil instrumented**
**Drivers for coupled modeling**
**Disparity in material response**
**Load duration**

## Blast Loading on a Buried Structure

**Soil and charge are Eulerian**
**Charge: JWL Library EOS for C-4**
**Steel case: Elastic-plastic **
**Soil: P-alpha EOS with Geologic (GEO) strength model**
**Structure is Lagrangian**
**Reinforcement and bolted connections explicitly modeled**
**Concrete: K&C model**
**Reinforcement: Rebar model**
**Displacement-based death criterion         used to model breach (d/CS > 0.3)**
**Comparisons**
**Free-field soil stress and velocity**
**Structure velocities**
**Interface pressures**

**Notes:**
CTH: ~1.7 million cells
Pronto: ~80K elements

## Blast Loading on a Buried Structure 

- AHS-0: Center of RC Slab

- AHS-10: Base of Reaction Structure

- RC Slab:
-     Thickness:        4.3 inches
-     Strength (fc’):     6095 psi
-     Reinforcement:  1.0 %
- Backfill:  Clay

## Blast Loading on a Buried Structure

## Concluding Remarks

**CEL approach well suited for modeling penetration and blast/structure interaction**
**Open issues for coupling algorithm**
**Consistent material modeling for insertion step**
**Overfilled cells**
**Cost of volume/area overlap calculations**