Testing for Foam Material Models for CAE
Foams are widely used in industries ranging from packaging to automotive safety and seating due to their unique ability to absorb energy, provide cushioning, or act as structural fillers. Their performance is heavily influenced by their internal structure, material properties, and how they are processed.
Foam materials vary significantly in mechanical behavior, largely due to their morphology — which includes factors like whether they are open-cell or closed-cell, pore size, and whether the matrix is rigid or flexible. These structural details impact their deformation response, recovery behavior, and overall function.
To learn more regarding material testing and characterization in support of material models for CAE, see our TestPaks or contact us to talk with our materials testing experts.
Foam Morphology
Foams are formed from a matrix material (often polymeric, but also metallic or rubber-based) and contain a gaseous phase trapped in pores. Two general types of cellular structures exist:
- Open-cell foams: Pores are interconnected, allowing air or gas to flow out easily under compression.
- Closed-cell foams: Pores are sealed, trapping gas and resisting compression differently.
The pore size, open/closed cell ratio, and type of matrix material greatly influence the mechanical properties. For instance:
- Rigid foams (e.g., metallic or polyurethane) deform plastically or fracture under stress and typically do not recover.
- Flexible foams (e.g., polyurethane, rubber-based) often exhibit full or partial recovery after deformation and may be hyperelastic in behavior.
Bead foams are another category made by fusing unfoamed beads into a shape. These are often used in packaging and modeled as crushable foams.
Foamed components often have outer skins formed during processing. These skins are typically denser and stronger than the core, adding complexity to characterization. Sometimes, skins are removed to isolate core behavior in testing.
Manufacturers now blend characteristics across traditional categories — for example, designing foams that are crushable but with slow or partial recovery — by tuning matrix composition and pore structure.
Foam Behavior
The primary mode of loading for most foams is compression. Though tension and shear do occur, especially due to geometry, foams are weakest in those modes and are rarely intentionally tested under them.
In compression, foams typically exhibit three regions on a stress-strain curve:
- Initial (Zone 1): Some stiffness is present due to the material’s matrix.
- Plateau (Zone 2): The foam “yields,” and cells collapse or rupture. For open-cell foams, gas escapes; for closed-cell foams, gas compresses and may cause cell rupture if pressure builds too much.
- Densification (Zone 3): Once cells are collapsed or burst, the material behaves more like the solid matrix.
During unloading, responses vary:
- Crushable foams show no recovery, with permanent damage.
- Elastomeric foams may fully recover, often with time-dependent effects.
- Viscoelastic modeling may be required to simulate time-based recovery behaviors.
Assumptions in Foam Testing
Most foam tests are performed on samples cut from larger pieces, assuming that the specimen is representative of the whole part. However, this assumption can be flawed because foam density is often non-uniform, particularly near surfaces where the skin may be stiffer than the core.
Due to batch-to-batch and intra-part variability, engineers must use judgement to select the most representative data. In some cases, different regions (skin vs. core) may be modeled separately.
Zero Poisson’s Ratio Assumption
Foams are often assumed to have very low or zero Poisson’s ratio, meaning that they do not expand laterally when compressed. This is valid for most open-cell and crushable foams, where volume is reduced primarily through cell collapse, not material flow.
Typical Poisson’s ratios for these foams are near 0.01 and remain negligible until densification begins. This simplification allows many simulations to ignore lateral strain until high compression is reached.
However, closed-cell elastomeric foams may exhibit increasing lateral expansion under strain because trapped gas cannot escape. Their Poisson’s ratio can increase with strain and approach that of solid rubber, requiring more detailed modeling.
Implementation Strategies
Since foam applications usually involve compressive loading, most testing and modeling efforts focus on compression tests. Biaxial tests may be useful for thin foam sheets. Some FEA codes also require tensile cut-off stress values, representing the maximum tensile stress the foam can withstand.
Testing Methods
Compression specimens are typically cylindrical or square prisms. The specimen size must be large enough relative to the pore size to avoid localized or inconsistent data. Small specimens can cause error due to surface effects (cut cells, skin layers, etc.).
Testing complications include:
- Load measurement sensitivity: Small load cells are required for soft foams to detect the onset of contact and early deformation. However, these load cells may max out before reaching densification, requiring test restarts with larger cells or extrapolation for high-stress data.
- Extensometry: In foams where the zero Poisson’s ratio assumption applies, strain can be derived from platen displacement (no lateral strain is assumed). This simplification works well in Zones 1 and 2, enabling faster, less complex testing.
For closed-cell foams and materials with significant lateral strain, biaxial video extensometry is used to measure both axial and transverse strain. Lateral strain calculations may be based on diameter changes, but this requires caution due to:
- Friction at platens, which can cause bulging or uneven lateral expansion
- Non-uniformity due to skins, leading to inconsistent cross-section behavior
In tension testing, non-contact extensometers are again recommended, and samples must be large enough to avoid stress concentrations or edge failures. Tabbing (reinforcing the ends) may be used. ASTM C297 offers guidance on tensile testing, and ASTM C273 covers shear testing.
Foam Modeling Approaches
Many FEA codes use hyperfoam material models, which treat foam as a hyperelastic material based on compressive test data.
- Ogden-type models are common, using uniaxial compression data for the main fit.
- Poisson’s ratio can be submitted either as a constant or as a function of strain, depending on test data availability.
- If lateral strain data are not measured, a constant Poisson’s ratio may be assumed for low to moderate strains, but this introduces error in Zone 3 (densification) where significant lateral strain occurs.
For applications involving high compression levels — such as crash simulations or impact testing — foam may be compressed beyond what is practical to test. In these cases, extrapolation of stress-strain curves is needed. A hyperbolic sine function can extend the curve to simulate very high compressive forces beyond the test range.
Additional test data, such as tensile or shear curves, can be included in the model to improve stability and accuracy under multi-axial stress states.
Conclusion
Foam testing and modeling involve significant complexity due to the high variability in material behavior, foam morphology, and application needs. Critical factors include:
- Matrix material (rigid, plastic, or elastomeric)
- Cell structure (open vs. closed)
- Skin vs. core differences
- Compression vs. tension/shear behavior
- Recovery characteristics (elastic, plastic, or time-based)
- Poisson’s ratio assumptions
For reliable simulations, engineers must match test data and model selection to the specific strain modes and deformation levels encountered in the application. A thoughtful balance between testing effort, model complexity, and simulation objectives is key to building accurate foam material models in FEA.
To explore the topics discussed on this page further, see Hubert Lobo (Founder, DatapointLabs) and Brian Croop (CEO, DatapointLabs), Determination and Use of Material Properties for Finite Element Analysis (NAFEMS, 2016), Ch.7.
