<!-- source-page: 191 -->

All of the parameters specified affect only the bubble amplitude; other physical parameters in the problem are independent. You can suppress the effects of wave loss in the bubble dynamics and introduce empirical flow drag, if desired. Detailed information about the bubble mechanical model is given in “Loading due to an incident dilatational wave field,” Section 6.3.1 of the Abaqus Theory Guide.

In an underwater explosion event a bubble migrates upward toward, and possibly reaches, the free water surface. If the bubble migration reaches the free water surface during the specified analysis time, Abaqus applies loads of zero magnitude after this point.

Model data about the bubble simulation are written to the data (.dat) file. During an Abaqus/Standard analysis history data are written each increment to the output database (.odb) file. The history data include the radius of the bubble and the bubble depth below the free water surface. For reference, the pressure and acoustic load quantities at the standoff point are also written to the data file; these load terms include the direct plane-wave term and the spherical spreading (“afterflow”) effect (see “Loading due to an incident dilatational wave field,” Section 6.3.1 of the Abaqus Theory Guide).

For the preferred interface the loading effects due to bubble formation can be defined for spherical incident wave loading using the UNDEX charge property definition. Because the bubble simulation uses spherical symmetry, the incident wave interaction property must define a spherical wave.

<table><tr><td>Input File Usage:</td><td>Use the following options to specify loading effects due to bubble formation using the UNDEX charge property definition:*INCIDENT WAVE INTERACTION PROPERTY, NAME=wave property name, TYPE=SPHERE*UNDEX CHARGE PROPERTY data defining the UNDEX charge*INCIDENT WAVE INTERACTION, PROPERTY=wave property name, UNDEX fluid surface name, source node, standoff node, reference magnitude</td></tr></table>

<table><tr><td>Abaqus/CAE Usage:</td><td>Use the following input to specify loading effects due to bubble formation using the UNDEX charge property definition:Interaction module:Create Interaction Property:Name:wave property name andIncident wave:Definition:Spherical, Propagation model: UNDEX charge, enter data defining the UNDEX chargeCreate Interaction:Incident wave:Definition: UNDEX, Wave property: wave property name, enter data defining the UNDEX chargeUse the following input to specify pressure at the standoff point using tabulated data:Load or Interaction module:Create Amplitude:Name:pressure and selectTabularInteraction module:Create Interaction:Incident wave:select the standoff point:Definition:Pressure, Pressure amplitude:pressure</td></tr></table>

<!-- source-page: 192 -->

Use the following input to specify source node location time histories using tabulated data:

Load or Interaction module: Create Amplitude: Name: name and select Tabular

Load module: Create Boundary Condition: select step:

Displacement/Rotation or Velocity/Angular velocity: select

the source node as the region and toggle on the degree or degrees

of freedom, Amplitude: name

# Modeling incident wave loading on a moving structure

To model the effect of relative motion between a structure (such as a ship) and the wave source during the analysis using the preferred interface, the source node may be assigned a velocity. It is assumed that the entire fluid-solid model is moving at a velocity with respect to the source node during the loading and that the speed of the model’s motion is low compared to the speed of propagation of the incident wave. That is, the effect of the speed of the source is neglected in the computation of the loads, but the change in position of the source is included. This is equivalent to assuming that the relative motion between the source and the model is at a low Mach number. Relative motion can be specified only for transient analyses.

In addition to prescribing boundary conditions at the source node, a small mass element must be defined at the source node.

Input File Usage: Use the following option to assign a velocity to the source node:

\*BOUNDARY, TYPE=DISPLACEMENT or VELOCITY, AMPLITUDE=name

source node, degrees of freedom

Abaqus/CAE Usage: Load module: Create Boundary Condition: select step: Velocity/Angular velocity or Displacement/Rotation: select regions and toggle on the degree or degrees of freedom, Amplitude: name

# Specifying the reflection effects

The waves emanating from the source may reflect off plane surfaces, such as seabeds or sea surfaces, before reaching the specified standoff point. Thus, the incident wave loading consists of the waves arriving from a direct path from the source, as well as those arriving from reflections off the planes. In Abaqus an arbitrary number of these planes can be defined, each with its own location, orientation, and reflection coefficient.

If no reflection coefficient is specified, the plane is assumed to be nonreflective; a zero reflected pressure is applied. If a reflection coefficient is specified, the magnitude of the reflected waves are modified by the reflection coefficient according to the formula:

$$
p _ {r e f l e c t e d} = Q p _ {i n c i d e n t}.
$$

Only real values for are used.

<!-- source-page: 193 -->

The reflection planes are allowed only for incident waves that are defined in terms of fluid pressure values. Only one reflection off each plane is considered. If the effect of many successive reflections is important, these surfaces should be part of the finite element model. Reflection planes should not be used at a boundary of the finite element model if the total wave formulation is used, since in that case the incident wave will be reflected automatically by that boundary.

Input File Usage: Use the following option in conjunction with the \*INCIDENT WAVE INTERACTION option to define an incident wave reflection plane:

\*INCIDENT WAVE REFLECTION

Abaqus/CAE Usage: Incident wave reflections are not supported in Abaqus/CAE.

# Boundary with prescribed pressure

The acoustic pressure degree of freedom at nodes of acoustic elements can be prescribed using a boundary condition. However, since you can use the nodal acoustic pressure in an Abaqus analysis to refer to the total pressure at that point or to only the scattered component, care must be exercised in some circumstances.

When the total wave formulation is used, a boundary condition alone is sufficient to specify a prescribed total dynamic pressure on a boundary.

In an analysis without incident wave loading, the nodal degree of freedom is generally equal to the total acoustic pressure at that point. Therefore, its value can be prescribed using a boundary condition in a manner consistent with other boundary conditions in Abaqus. For example, you may set the acoustic pressure at all of the nodes at a duct inlet to a prescribed amplitude to analyze the propagation of waves along the duct. The free surface of a body of water can be modeled by setting the acoustic pressure to zero at the surface.

When incident wave loading is used, the scattered wave formulation defines the nodal acoustic degree of freedom to be equal to the scattered pressure. Consequently, a boundary condition definition for this degree of freedom affects the scattered pressure only. The total acoustic pressure at a node is not directly accessible in this formulation. Specification of the total pressure in a scattered formulation analysis is nevertheless required in some instances (for example, when modeling a free surface of a body of water). In this case, one of the following methods should be used.

If the fluid surface with prescribed total pressure is planar, unbroken, and of infinite extent, an incident wave reflection plane and a boundary condition can be used together to model the fact that the total pressure is zero on the free surface. A “soft” incident wave reflection plane coincident with the free surface will make sure that the structure is subjected to the incident wave load reflected off the free surface. A boundary condition setting the acoustic pressure in the surface equal to zero will make sure that any scattered waves emitted by the structure are reflected properly. The scattered wave solution in the fluid must be interpreted taking into consideration the fact that the incident field now includes a reflection of the source as well. If the fluid surface with prescribed total pressure is planar but broken by an object, such as a floating ship, this modeling technique may still be applied. However, the reflected loads due to the incident wave are computed as if the reflection plane passes through the hull of the ship; this approximation neglects some diffraction effects and may or may not be applicable in all situations of interest.

<!-- source-page: 194 -->

Alternatively, the free surface condition of the fluid can be eliminated by modeling the top layer of the fluid using structural elements, such as membrane elements, instead of acoustic elements. The “structural fluid” surface and the “acoustic fluid” surface are then coupled using either a surface-based mesh tie constraint (“Mesh tie constraints,” Section 35.3.1) or, in Abaqus/Standard, acoustic-structural interface elements; and the incident wave loading must be applied on both the “structural fluid” and the “acoustic fluid” surfaces. The material properties of the “structural fluid” elements should be similar to those of the adjacent acoustic fluid. In Abaqus/Explicit the thickness of the “structural fluid” elements must be such that the masses at nodes on either side of the coupling constraint are nearly equal. This modeling technique allows the geometry of the surface on which total pressure is to be prescribed to depart from an unbroken, infinite plane. As a secondary benefit of this technique, you can obtain the velocity profile on the free surface since the displacement degrees of freedom are now activated at the “structural fluid” nodes. If a nonzero pressure boundary condition is desired, it can be applied as a distributed loading on the other side of the “structural fluid” elements.

Input File Usage: Use the following options for the first modeling technique with the default scattered wave formulation:

\*BOUNDARY   
\*INCIDENT WAVE REFLECTION

Use the following option for the second modeling technique with the default scattered wave formulation:

\*TIE  
\*INCIDENT WAVE INTERACTION

Use the following option with the total wave formulation:

\*BOUNDARY

Abaqus/CAE Usage: Load module: Create BC: choose Other for the Category and Acoustic pressure for the Types for Selected Step

Defining air blast loading for incident shock waves using the CONWEP model in Abaqus/Explicit

An explosion in air forms a highly compressed gas mass that interacts with the surrounding air, generating an outward-propagating shock wave. The loading effects due to an explosion in air can be defined, for spherical incident waves (air blast) or hemispherical incident waves (surface blast), by empirical data provided by the CONWEP model in conjunction with the incident wave loading definition.

Unlike an acoustic wave, a blast wave corresponds to a shock wave with discontinuities in pressure, density, etc. across the wave front. Figure 34.4.6–3 shows a typical pressure history of a blast wave.

The CONWEP model uses a scaled distance based on the distance of the loading surface from the source of the explosion and the amount of explosive detonated. For a given scaled distance, the model provides the following empirical data: the maximum overpressure (above atmospheric), the arrival time, the positive phase duration, and the exponential decay coefficient for both the incident pressure and the reflected pressure. Using these parameters, the entire time history of both the incident pressure and reflected pressure as shown in Figure 34.4.6–3 can be constructed. Use of a standoff point is not required.

<!-- source-page: 195 -->

![](images/page-195_f63fdafcfdd1b0d0efbf6fbfb2e8ef619fa66f5150e651b2da88cbafef225482.jpg)

<details>
<summary>line</summary>

| Time of detonation | Pressure |
| ------------------ | -------- |
| Time of arrival    | P_max    |
| Time of detonation | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm    |
| Time of arrival    | P_atm, P_atm |
| Time of arrival    | P_atm, P_atm |
| Time of arrival    | P_atm, P_atm |
| Time of arrival    | P_atm, P_atm |
| Time of arrival    | P_atm, P_atm |
| Time of arrival    | P_atm, P_atm |
| Time of arrival    | P_atm, P_atm |
| Time of arrival    | P_atm, P_atm |
|
| Time of arrival    | P_atm, P_atm |
| Time of arrival    | P_atm, P_atm |
| Time of arrival    | P_atm, P_atm |
| Time of arrival    | P_atm, P_atm |
| Time of arrival    | P_atm, P_atm |
| Time of arrival    | P_atm, P_atm |
| Time of arrival    | P_atm, P_atm |
| P_table_P_max     | P_max    |
| P_table_P_atm      | P_atm    |
| P_table_P_atm      | P_atm    |
| P_table_P_atm      | P_atm    |
| P_table_P_atm      | P_atm    |
| P_table_P_atm      | P_atm    |
| P_table_P_atm      | P_atm    |
| P_table_P_atm      | P_atm    |
| P_table_P_atm      | P_atm    |
| P_table_P_atm     | P_atm    |
| P_table_P_atm     | P_atm    |
| P_table_P_atm     | P_atm    |
| P_table_P_atm     | P_atm    |
| P_table_P_atm     | P_atm    |
| P_table_P_atm     | P_atm    |
| P_table_P_atm     | P_atm    |
| P_table_P_atm     | P_atm    |
| P Company_P_atm  | P Company_P_atm |
| P Company_P_atm  | P Company_P_atm |
| P Company_P_atm  | P Company_P_atm |
| P Company_P_atm  | P Company_P_atm |
| P Company_P_atm  | P Company_P_atm |
| P Company_P_atm  | P Company_P_atm |
| P Company_P_atm  | P Company_P_atm |
| P Company_P_atm  | P Company_P_atm |
|
| P Company_P_atm  | P Company_P_atm |
| P Company_P_atm  | P Company_P_atm |
| P Company_P_atm  | P Company_P_atm |
| P Company_P_atm  | P Company_P_atm |
| P Company_P_atm  | P Company_P_atm |
| P Company_P_atm  | P Company_P_atm |
| P Company_P_atm  | P Company_P_atm |
| N Company_P_atm   | N Company_P_atm |
| N Company_P_atm   | N Company_P_atm |
| N Company_P_atm   | N Company_P_atm |
| N Company_P_atm   | N Company_P_atm |
| N Company_P_atm   | N Company_P_atm |
| N Company_P_atm   | N Company_P_atm |
| N Company_P_atm   | N Company_P_atm |
| N Company_P_atm   | N Company P_atm |
| N Company_P_atm   | N Company P_atm |
| N Company_P_atm   | N Company P_atm |
| N Company_P_atm   | N Company P_atm |
| N Company_P_atm   | N Company P_atm |
| N Company_P_atm   | N Company P_atm |
| N Company_P_atm   | N Company P_atm |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
|
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_atm |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
|
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| P Company_P_atm   | P Company_P_at m |
| N Company_P_atm   | N Company_P_at m |
| N Company_P_atm   | N Company_P_at m |
| N Company_P_atm   | N Company_P_at m |
| N Company_P_atm   | N Company_P_at m |
| N Company_P_atm   | N Company_P_at m |
| N Company_P_atm   | N Company_P_at m |
| N Company_P_atm   | N Company_P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at n |
| N Company_P_atm   | N Company P_at n |
| N Company_P_atm   | N Company P_at n |
| N Company_P_atm   | N Company P_at n |
| N Company_P_atm   | N Company P_at n |
| N Company_P_atm   | N Company P_at n |
| N Company_P_atm   | N Company P_at n |
| N Company_P_atm   | N Company P_at n |
|
| N Company_P_atm   | N Company P_at n |
| N Company_P_atm   | N Company P_at n |
| N Company_P_atm   | N Company P_at n |
| N Company_P_atm   | N Company P_at n |
| N Company_P_atm   | N Company P_at n |
| N Company_P_atm   | N Company P_at n |
| N Company_P_atm   | N Company P_at n |
| P Company_P_atm   | P Company P_at m |
| P Company_P_atm   | P Company P_at m |
| P Company_P_atm   | P Company P_at m |
| P Company_P_atm   | P Company P_at m |
| P Company_P_atm   | P Company P_at m |
| P Company_P_atm   | P Company P_at m |
| P Company_P_atm   | P Company P_at m |
| P Company_P_atm   | P Company P_at m |
|
| P Company_P_atm   | P Company P_at m |
| P Company_P_atm   | P Company P_at m |
| P Company_P_atm   | P Company P_at m |
| P Company_P_atm   | P Company P_at m |
| P Company_P_atm   | P Company P_at m |
| P Company_P_atm   | P Company P_at m |
| P Company_P_atm   | P Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company P_at m |
| N Company_P_atm   | N Company N      |
| N Company_P_atm   | N Company N      |
| N Company_P_atm   | N Company N      |
| N Company_P_atm   | N Company N      |
| N Company_P_atm   | N Company N      |
| N Company_P_atm   | N Company N      |
| N Company_P_atm   | N Company N      |
| N Company_P_atm   | N Company N      |
| N Company_P_atm   |
| N Company_P_atm   | N Company N      |
| N Company_P_atm   | N Company N      |
| N Company_P_atm   | N Company N      |
| N Company_P_atm   | N Company N      |
| N Company_P_atm   | N Company N      |
| N Company_P_atm   | N Company N      |
| N Company_P_atm   | N Company N      |
| N Company_P_atm   (Time of detonation) | P_atm    |
| N Company_P_atm   | P_atm    |
| N Company_P_atm   | P_atm    |
| N Company_P_atm   | P_atm    |
| N Company_P_atm   | P_atm    |
| N Company_P_atm   | P_atm    |
| N Company_P_atm   | P_atm    |
| N Company_P_atm   | P_atm    |
| N Company_P_atm   | P_atm    |
| N company_P_atm   | P_atm    |
| N company_P_atm   | P_atm    |
| N company_P_atm   | P_atm    |
| N company_P_atm   | P_atm    |
| N company_P_atm   | P_atm    |
| N company_P_atm   | P_atm    |
| N company_P_atm   | P_atm    |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N Company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_atm, P_atm |
| N company_P_atm   | P_at, P_atm |
| N company_P_atm   | P_at, P_atm |
| N company_P_atm   | P_at, P_atm |
| N company_P_atm   | P_at, P_atm |
| N company_P_atm   | P_at, P_atm |
| N company_P_atm   | P_at, P_atm |
| N company_P_atm   | P_at, P_atm |
| N company_P_a t m   | P_at, P_atm |
| N company_P_a t m   | P_at, P_atm |
| N company_P_a t m   | P_at, P_atm |
| N company_P_a t m   | P_at, P_atm |
| N company_P_a t m   | P_at, P_atm |
| N company_P_a t m   | P_at, P_atm |
| N company_P_a t m   | P_a t m    |
| N company_P_a t m   | P_a t m    |
| N company_P_a t m   | P_a t m    |
| N company_P_a t m   | P_a t m    |
| N company_P_a t m   | P_a t m    |
| N company_P_a t m   | P_a t m    |
| N company_P_a t m   | P_a t m    |
| N company_P_a t m   (Time of detonation) | P_atm    |
| N company_P_a t m   | P_atm    |
| N company_P_a t m   | P_atm    |
| N company_P_a t m   | P_atm    |
| N company_P_a t m   | P_atm    |
| N company_P_a t m   | P_atm    |
| N company_P_a t m   | P_atm    |
| N company_P_a t m   | P_atm    |
| N company_P_a t m   | N Company P_at m |
| N company_P_a t m   | N Company P_at m |
| N company_P_a t m   | N Company P_at m |
| N company_P_a t m   | N Company P_at m |
| N company_P_a t m   | N Company P_at m |
| N company_P_a t m   | N Company P_at m |
| N company_P_a t m   | N Company P_at m |
| N company_P_a t m   (Time of detonation) | N Company P_at m |
| N company_P_a t m   | N Company P_at m |
| N company_P_a t m   | N company P_at m |
| N company_P_a t m   | N company P_at m |
| N company_P_a t m   | N company P_at m |
| N company_P_a t m   | N company P_at m |
| N company_P_a t m   | N company P_at m |
| N company_P_a t m   | N company P_at m |
| N company_P_a t m   | N company P_at m |
| N company_P_a     | N Company P_at m |
| N company_P_a     | N Company P_at m |
| N company_P_a     | N company P_at m |
| N company_P_a     | N company P_at m |
| N company_P_a     | N company P_at m |
| N company_P_a     | N company P_at m |
| N company_P_a     | N company P_at m |
| N company_P_a     | N company P_at m |
| N company_P_a     | N company P_at m |
| N company_P_a     | N company P_at m |
| N company_P       | N Company P_at m |
| N company_P       | N Company P_at m |
| N company_P       | N company P_at m |
| N company_P       | N company P_at m |
| N company_P       | N company P_at m |
| N company_P       | N company P_at m |
| N company_P       | N company P_at m |
| N company_P       | N company P_at m |
| N company_P       | N company P_at m |
| N company_P       | N company P_at m |
| N company_P       | N company P_at m |
</details>

Figure 34.4.6–3 Pressure history of a blast wave.

The total pressure, $P ( t )$ , on a surface due to the blast wave is a function of the incident pressure, $P _ { i n c i d e n t } ( t )$ , the reflected pressure, $P _ { r e f l e c t } ( t )$ , and the angle of incidence, , which is defined as the angle between the normal of the loading surface and the vector that points from the surface to the explosion source. The total pressure is defined as

$$
P (t) = P _ {i n c i d e n t} (t) [ 1 + \cos \theta - 2 \cos^ {2} \theta ] + P _ {r e f l e c t} (t) \cos^ {2} \theta \quad f o r \cos \theta \geq 0;
$$

$$
P (t) = P _ {i n c i d e n t} (t) \quad f o r \cos \theta <   0.
$$

The air blast loading due to the total pressure can be scaled using a magnitude scale factor.

A detonation time can be specified if the explosion does not occur at the start of the analysis. The detonation time needs to be given in total time; see “Conventions,” Section 1.2.2, for a description of the time convention. The arrival time at a location is defined as the elapsed time for the wave to arrive at that location after detonation.

The CONWEP empirical data are given in a specific set of units, which must be converted to the units used in the analysis. You will need to specify multiplying factors for conversion of these units to SI units. For the specification of the mass of the explosive in TNT equivalence, you can choose any convenient mass unit, which can be different from the mass unit used in the analysis. For computation of the pressure loading, you will need to specify multiplying factors for conversion of length, time, and

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pressure units used in the analysis to SI units. Some typical conversion multiplier values are given in Table 34.4.6–3.

Table 34.4.6–3 Multipliers used in conjunction with the CONWEP model for conversion to SI units. 

<table><tr><td>Quantity</td><td>Unit</td><td>SI Unit</td><td>Multiplier for conversion to SI</td></tr><tr><td>Mass</td><td>ton</td><td>kg</td><td>1000</td></tr><tr><td>Mass</td><td>lb</td><td>kg</td><td>0.45359</td></tr><tr><td>Length</td><td>mm</td><td>m</td><td>0.001</td></tr><tr><td>Length</td><td>ft</td><td>m</td><td>0.3048</td></tr><tr><td>Time</td><td>msec</td><td>sec</td><td>0.001</td></tr><tr><td>Pressure</td><td>MPa</td><td>Pa</td><td> $10^{-6}$ </td></tr><tr><td>Pressure</td><td>psi</td><td>Pa</td><td>6894.8</td></tr><tr><td>Pressure</td><td>psf</td><td>Pa</td><td>47.88</td></tr></table>

For any given amount of explosive, the CONWEP empirical data are valid only within a range of distances from the source. The minimum distance at which the data are valid corresponds to the charge radius. Thus, the analysis terminates if the distance of any part of the loading surface from the source is less than the charge radius. For distances that are larger than the maximum valid range, linear extrapolation is used up to an extended maximum range where the reflected pressure decreases to zero. No loading is applied beyond the extended maximum range.

The CONWEP empirical data do not account for shadowing by intervening objects or for any effects due to confinement. In the definition of incident wave interaction using the CONWEP model, you cannot use incident wave reflection.

The CONWEP pressure load can be requested as element face variable output to the output database file (see “Abaqus/Explicit output variable identifiers,” Section 4.2.2).

# Input File Usage:

Use the following options to specify loading effects due to explosion in air using the CONWEP charge property definition:

\*INCIDENT WAVE INTERACTION PROPERTY, NAME=wave property name, TYPE=AIR BLAST or SURFACE BLAST \*CONWEP CHARGE PROPERTY data defining the CONWEP charge \*INCIDENT WAVE INTERACTION, PROPERTY=wave property name, CONWEP loading surface name, source node, detonation time, magnitude scale factor

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Abaqus/CAE Usage: Use the following options to specify loading effects due to explosion in air using the CONWEP charge property definition:

Interaction module: Create Interaction Property: Name: wave property name and Incident wave: Definition: Air blast or Surface blast: enter data defining the CONWEP charge

Interaction module: Create Interaction: Name: incident wave name and Incident wave: select the source point: CONWEP (Air/Surface blast): select the region: CONWEP Data: enter data defining the time of detonation and magnitude scale factor

# Modifying or removing incident wave loads

Only the incident wave loads that are specified in a particular step are applied in that step; previous definitions are removed automatically. Consequently, incident wave loads that are active during two subsequent steps should be specified in each step. This is akin to the behavior that can be specified for other types of loads by releasing any load of that type in a step (see “Applying loads: overview,” Section 34.4.1).

# Alternative incident wave loading interface

In general, the concepts of the alternative incident wave loading interface are the same as the preferred interface; however, the syntax for specifying the incident wave loading is different. The preferred incident wave loading interface is supported in Abaqus/CAE. The alternative interface is not supported in Abaqus/CAE. For conceptual information, see “Incident wave loading due to external sources.”

Prescribing the geometric properties and the speed of the incident wave (alternative interface)

Conceptually, the alternative interface is the same as the preferred interface; however, the usages are different. For conceptual information, see “Prescribing geometric properties and the speed of the incident wave.”

<table><tr><td>Input File Usage:</td><td>*INCIDENT WAVE PROPERTY, NAME=wave property name,TYPE=PLANE or SPHERedata lines to specify the location of the acoustic source and the standoff point*INCIDENT WAVE FLUID PROPERTYbulk modulus, mass density*INCIDENT WAVE, PROPERTY=wave property name</td></tr></table>

Abaqus/CAE Usage: The alternative incident wave loading interface is not supported in Abaqus/CAE.

Defining the time history of the source pulse (alternative interface)

Conceptually, the alternative interface is the same as the preferred interface; however, the usages are different. For conceptual information, see “Defining the amplitude of the source pulse.”

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<table><tr><td>Input File Usage:</td><td>Use the following option to define the time history in terms of fluid pressure values:*INCIDENT WAVE, PRESSURE AMPLITUDE=amplitude data table name solid or fluid surface name, reference magnitudeUse the following option to define the time history in terms of fluid particle acceleration values:*INCIDENT WAVE, ACCELERATION AMPLITUDE=amplitude data table namefluid surface name, reference magnitude</td></tr></table>

<table><tr><td>Abaqus/CAE Usage:</td><td>The alternative incident wave loading interface is not supported in Abaqus/CAE.</td></tr></table>

Defining bubble loading for spherical incident wave loading (alternative interface)

Conceptually, the alternative interface is the same as the preferred interface; however, the usages are different. For conceptual information, see “Defining bubble loading for spherical incident wave loading.”

To define the bubble dynamics using a model internal to Abaqus, you can specify a bubble amplitude. Use of the bubble loading amplitude is generally similar to the use of any other amplitude in Abaqus.

<table><tr><td>Input File Usage:</td><td>Use the following options:*AMPLITUDE, DEFINITION=BUBBLE, NAME=name*INCIDENT WAVE PROPERTY, TYPE=SPHERE, NAME=wave property name*INCIDENT WAVE, PRESSURE AMPLITUDE=name solid or fluid surface name, reference magnitude</td></tr></table>

<table><tr><td>Abaqus/CAE Usage:</td><td>The alternative incident wave loading interface is not supported in Abaqus/CAE.</td></tr></table>

Specifying the reflection effects (alternative interface)

Conceptually, the alternative interface is the same as the preferred interface; however, the usages are different. For conceptual information, see “Specifying the reflection effects.”

<table><tr><td>Input File Usage:</td><td>Use the following option in conjunction with the *INCIDENT WAVE option to define an incident wave reflection plane:</td></tr><tr><td></td><td>*INCIDENT WAVE REFLECTION</td></tr></table>

<table><tr><td>Abaqus/CAE Usage:</td><td>The alternative incident wave loading interface is not supported in Abaqus/CAE.</td></tr></table>

Modeling incident wave loading on a moving structure (alternative interface)

To model the effect of rigid motion of a structure such as a ship during the incident wave loading history, the standoff point can have a specified velocity. It is assumed that the entire fluid-solid model is moving

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at this velocity with respect to the source point during the loading and that the speed of the model’s motion is low compared to the speed of propagation of the incident wave.

Input File Usage: \*INCIDENT WAVE PROPERTY, NAME=wave property name data line to specify the velocity of the standoff point

Abaqus/CAE Usage: The alternative incident wave loading interface is not supported in Abaqus/CAE.

# Example: submarine close to the free surface

The problem shown in Figure 34.4.6–4 has the following features: a free surface $A _ { 0 }$ , seabed $A _ { s b }$ as a reflection plane, a wet solid surface $A _ { s w }$ , the fluid surface $A _ { f w }$ that is tied to the solid surface $A _ { s w }$ , and the boundary $A _ { \mathrm { i n f } }$ of the finite modeled domain separating the infinite acoustic medium. The source S of the underwater explosion loading is also shown.

![](images/page-199_ed5fe6348da5ea7980a2720d68613854d05c35404635422fb475b0d5ec8b9950.jpg)

<details>
<summary>text_image</summary>

Free surface A₀
Acoustic medium
Solid surface Aₛw
Fluid surface Afw
A
B
Ainf model boundary
S
Source
Seabed Asb
</details>

Figure 34.4.6–4 Incident wave loading on a submarine lying near a free surface.

# Scattered wave solution

Here the scattered wave response in the acoustic medium is of interest along with that of the structure to the incident wave loading. Cavitation in the fluid is not considered in a scattered wave formulation. Similarly, the initial hydrostatic pressure in the fluid is not modeled.

The zero dynamic acoustic pressure boundary condition on the free surface requires both a “soft” reflection plane coinciding with the free surface $A _ { 0 }$ and a zero scattered pressure boundary condition at the nodes on this free surface. The incident wave loading is applied on the fluid surface, $A _ { f w ; }$ , and on

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the wet solid surface, $A _ { s w }$ . The incident wave loading can be only of pressure amplitude type since the loading includes a solid surface.

A good location for the standoff node is marked as A in Figure 34.4.6–4. This node is in the fluid, close to the structure, and closer to incident wave source S than any portion of the seabed or the free surface. The standoff node’s offset from the loaded surfaces is exaggerated for emphasis in the figure.

The radiation condition is specified on the acoustic surface $A _ { \mathrm { i n f } }$ such that the scattered wave impinging on this boundary with the infinite medium does not reflect back into the computational domain. The seabed is modeled with an incident wave reflection plane on surface $A _ { s b }$ . The reflection loss at this seabed surface is modeled using an impedance property.

If the response of the structure in the nonlinear regime is of interest, the initial stress state in the structure should be established using Abaqus/Standard in a static analysis. The stress state in the structure is then imported into Abaqus/Explicit, and the loading on the solid surfaces causing the initial stress state is respecified in the acoustic analysis.

The following template schematically shows some of the Abaqus input file options that are used to solve this problem using the scattered wave formulation:

*HEADING
...
*SURFACE, NAME= $A_{fw}$ Data lines to define the acoustic surface that is wetting the solid
*SURFACE, NAME= $A_{sw}$ Data lines to define the solid surface that is wetted by the fluid
*SURFACE, NAME= $A_{inf}$ Data lines to define the acoustic surface separating the modeled region from the infinite mean
*INCIDENT WAVE INTERACTION PROPERTY, NAME=IWPROP
*AMPLITUDE, DEFINITION=TABULAR, NAME=PRESSUREVTIME
*TIE, NAME=COUPLING $A_{fw}$ , $A_{sw}$ *STEP
** For an Abaqus/Standard analysis:
*DYNAMIC
** For an Abaqus/Explicit analysis:
*DYNAMIC, EXPLICIT
** Load the acoustic surface
*INCIDENT WAVE INTERACTION, PRESSURE AMPLITUDE=PRESSUREVTIME, PROPERTY=IWPROP $A_{fw}$ , source node, standoff node, reference magnitude
*INCIDENT WAVE REFLECTION
Data lines for the reflection plane over the seabed $A_{sb}$ , seabed_Q
*INCIDENT WAVE REFLECTION
Data lines for a "soft" reflection plane over the free surface $A_{0}$ .
** Load the solid surface
*INCIDENT WAVE INTERACTION, PRESSURE AMPLITUDE=PRESSUREVTIME,
Quantity	Unit	SI Unit	Multiplier for conversion to SI
Mass	ton	kg	1000
Mass	lb	kg	0.45359
Length	mm	m	0.001
Length	ft	m	0.3048
Time	msec	sec	0.001
Pressure	MPa	Pa	$10^{-6}$
Pressure	psi	Pa	6894.8
Pressure	psf	Pa	47.88
Input File Usage:	Use the following option in conjunction with the *INCIDENT WAVE option to define an incident wave reflection plane:
	*INCIDENT WAVE REFLECTION