Question: Dynamic Stiffness of Rubber Considering Geometric and Material Nonlinearities
I am planning to perform a simulation on the Dynamic Stiffness of Rubber.
Before introducing the model, let me define a few terms for clarity. The Static stiffness of rubber is referred to as the Static Spring Constant, which is the load corresponding to axial displacement, with units of N/mm.
On the other hand, the Dynamic Stiffness of rubber is referred to as the Dynamic Spring Constant. Typically, this is calculated by compressing the rubber with a certain preload (e.g., 100 N or 10 mm displacement as applied in the uploaded file) and then applying a specific excitation frequency and displacement (e.g., ±0.5 mm at 200 Hz). The Dynamic Stiffness is then calculated based on the reaction force (SPCF) corresponding to the displacement, with the unit again being N/mm.
Model Description:
The top and bottom plates of the rubber are assumed to be rigidly bonded with steel .
In the uploaded model, the steel plates connected to the top and bottom of the rubber are replaced with RBE2 elements, which simulate the plates.
Static Spring Constant
Assuming the exact material properties of the rubber are known, the Static Spring Constant was analyzed through a nonlinear-static analysis.
Dynamic Stiffness
This is where I am encountering difficulties.
The Dynamic Stiffness of rubber varies depending on the preload, excitation frequency, and excitation displacement. Initially, I conducted a nonlinear static analysis (SUBCASE1, Enforced Disps) to apply the preload. Afterward, I attempted to compute the Dynamic Stiffness by performing a Frequency Response Analysis (SUBCASE2) with an excitation frequency of 200 Hz(RLOAD2 and FREQi card) and a displacement of ±0.5 mm(SPCD). Reaction forces from the excitation were used to calculate the Dynamic Spring Constant.
A key step in my method was transferring the results from SUBCASE1 to SUBCASE2 using STATSUB(PRELOAD) to incorporate both the Geometric Stiffness Matrix (Geometric Nonlinearity) and Material Nonlinearity into the analysis. However, it seems that these two factors are not being properly reflected in the results.
Question:
I am seeking advice on how to compute the Dynamic Stiffness (reaction forces due to harmonic excitation) of rubber under axial preload while considering Geometric Nonlinearity and Material Nonlinearity.
I have attached the h3d and hm files for reference. Please take a look(v.2022.3).
Reference Studies:
- A related study is "Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators", link:
- A simulation methodology is discussed in the paper "On the dynamic stiffness of preloaded vibration isolators in the audible frequency range: Modeling and experiments", but this study was conducted using FORTRAN code and not commercial simulation software.