Poroelastic Materials (Biot theory)

Poroelastic materials can be used to model coupled fluid-structure systems where the fluid exists within the interstitial spaces of a porous solid.

The mechanical response of a porous material varies, depending on the amount of fluid present within the pores, the type of fluid, the pressure of the interstitial fluid, and the structure of the porous material. In OptiStruct, a poroelastic material based on the Biot theory of poroelasticity can be modeled for use in relevant applications.

Motivation

A porous material containing fluid within interstitial spaces cannot be accurately modeled without accounting for the influence of the fluid on the mechanical response of the structure. There are various physical applications for poroelastic material models; for example, trimmings of an automobile are porous and the cabin cavity is filled with air. The fluid (air) enters the interstitial spaces within these trimmings and the dynamic behavior of the system is altered. This difference in dynamic behavior should be accurately accounted for in Noise Vibration and Harshness (NVH) studies of the automobile.


Figure 1. Difference in Mechanical Response between Porous and Non-porous Materials

For a possible application, the Biot poroelastic material implementation in OptiStruct can be used to model automobile trim components in frequency response analyses to generate a more accurate solution. Trim materials, carpets, foam pads, and other porous materials can be modeled.

Implementation

Poroelastic materials in OptiStruct are implemented using the Biot poroelastic theory. They can be modeled using CTETRA, CHEXA, or CPENTA solid elements. The Biot u-p (displacement-pressure) formulation is used wherein each grid consists of three displacement degrees of freedom (DOF) and one pressure component. The required material properties are listed in detail on the MATPE1 entry in the Reference Guide. The MATPE1 entry can be selected on the PSOLID property entry with FCTN=PORO.

Supported Solution Sequences

The Biot poroelastic material is frequency-dependent. The frequency-dependent element matrices are calculated at each frequency for each element. Direct and Modal Frequency Response Analyses are supported. The frequency-dependent matrices are reduced to modal spaces for modal frequency response analysis. Panel participation calculation for the Biot material is available similar to that of other panels. The fluid-structural grid participation is also available for detailed interpretation of panel contributions.
Note:
  1. Coupling between the acoustic cavity (FLUID) and trim component (BIOT):
    1. A GRID to GRID match or Multi-point constraints (MPCs) are required to connect the acoustic cavity to fluid dof of the BIOT material.
    2. The ACMODL entry will be used to couple the fluid dof and the structural dof of the BIOT material.
    3. If a GRID to GRID match is used to couple the acoustic cavity to the BIOT material, the grids on the fluid that are shared with the BIOT material should not have their CD fields set to -1. However, if Multi-point constraints (MPCs) are used, the CD fields should be set equal to -1.
    4. When MPC's are used, the dependent grid of the MPC should belong to the BIOT material.
  2. Coupling between the trim component (BIOT) and the body structure:
    1. Coincident nodes (GRID to GRID match) can be used to achieve displacement continuity. However, if the nodes between the trim component and the body structure are not shared, TIE and CONTACT entries with the FREEZE option, rigids, MPC's, or other structural elements can be used to ensure continuity.

Limitations

The pressure output for the trim component (poroelastic Biot material) is not currently supported. However, the pressure of the closest acoustic domain is available.