Crushable Foam Material Model
Crushable Foam Material: Theoretical Foundations
Mechanics of Foam Materials
Professor, how does the mechanics of foam materials differ from metals?
Foam materials (EPS, PU foam, metal foam) exhibit significant volume reduction under compression. Metals are incompressible plastic ($\Delta V = 0$), but foams are compressible plastic ($\Delta V \neq 0$). They absorb energy through buckling and crushing of cell walls.
Compressive Stress-Strain Curve
Typical compression curve for foam:
1. Elastic Region — Elastic deformation of cell walls
2. Plateau Region — Buckling/crushing of cell walls. Nearly constant stress with large deformation
3. Densification Region — Cell walls compact. Stress rises sharply
Modeling in FEM
Summary
Motivation Behind the Foam Model's Creation
The paper "Isotropic constitutive models for metallic foams" published by Deshpande & Fleck (University of Cambridge) in 2000 was developed to quantify the impact absorption of aluminum foam metals (Alporas, Cymat). Prior von Mises models could not represent the large deformation due to isotropic compression in foams at all, necessitating a new yield surface that allowed volumetric plastic strain. This paper became the theoretical foundation for the Abaqus "Crushable Foam" model.
Computational Methods for Crushable Foam Material
FEM Settings for Foam
```
*MAT_LOW_DENSITY_FOAM
$ Compressive stress-strain table
*DEFINE_CURVE
0., 0.
0.1, 0.5
0.5, 0.6
0.8, 5.0
```
Abaqus: *CRUSHABLE FOAM + table input.
Summary
Experimental Measurement Method for Stress Ratio Parameter k₀
The parameter k₀ (initial hydrostatic yield stress ratio) that determines the yield surface shape of Crushable Foam is determined from two types of experiments: uniaxial compression tests and hydrostatic compression tests. For Alporas (Sumitomo Electric's aluminum foam, density 0.25 g/cm³), Deshpande's own experiments report that from a uniaxial compressive yield stress ≈1.6 MPa and a hydrostatic yield ≈1.9 MPa, k₀≈1.19 is obtained. In practice, it is customary to first try k₀=1.1~1.3 when k₀ is unknown.
Crushable Foam Material in Practice
Practical Foam Applications
Packaging (cushioning for electronic devices), automotive bumper foam, EPS liners for helmets.
Practical Checklist
Automotive Seat Cushion Impact Absorption
Polypropylene (PP) foam (density 30-60 kg/m³) is used in occupant protection components like headrests and knee pads. Since the 2010s, Toyota, Honda, and Volkswagen have utilized Abaqus's Crushable Foam model for virtual testing to comply with FMVSS201U (passenger car interior impact standards). Manufacturers report that by inputting only the compression-densification curve (stress ~100% strain) of resin foam, impact acceleration-time histories can be reproduced within ±10%.
Crushable Foam Material: Software & Solver Comparison
Tools for Foam
Differences in Foam Implementation Between LS-DYNA and Abaqus
LS-DYNA's representative foam model is MAT_LOW_DENSITY_FOAM (#57), a semi-physical model where strain-rate dependent loading-unloading curves can be input directly. On the other hand, Abaqus's Crushable Foam is based on mathematical formulation of the yield surface, requiring inverse analysis to identify parameters like k₀ and α from experimental curves. In practice, there is industry consensus on usage: LS-DYNA MAT57 for high-speed phenomena like drop impact or explosion, and Abaqus CDP series for creep deformation or long-term fatigue.