Abaqus has always been first choice of analysts for modeling any form of non-linearity in the model: geometric non-linearity, material non-linearity, or boundary condition non-linearity which is large sliding contact. Within material non-linearity, the most popular model is piecewise linear plasticity used to model plastic deformations in alloys or metals beyond their yield point. This blog post primarily discusses another powerful but somewhat less known non-linear material model of Abaqus used to model elastomers or rubbers.
Before getting into Abaqus’ functionalities for rubbers, let’s see what types of rubbers primarily exist, along with their mechanical characteristics:
They exist almost everywhere: tires, weather seals, oil seals, civil engineering equipment, etc. Their main mechanical characteristics are
- Nearly incompressible: While it is easy to stretch these materials, it is very difficult to compress them volumetrically. It’s a common observation that a rubber band can be stretched easily but a piece of pencil eraser cannot be compressed so easily. This behavior is particularly important in elastomer modeling.
- Progressive loading and unloading cycles show hysteresis as well as damage. As cycles continue, damage progresses.
They are a physical combination of rubber materials and thermal plastics. They can be easily molded or extruded. They are not physically as strong as solid rubbers, neither resistant to heat and chemicals. They are more prone to creep and permanent set.
Commercially, they are referred to as porous rubbers or just foams.
- They can undergo very large strain, as large as 500% that is still recoverable. Their counterparts, crushable foams, can exhibit inelastic strains.
- They exhibit cellular structure that may be open or closed type. Typical examples are cushions, paddings, etc.
- The compressive stress strain curve is as follows:
Foams exhibit a linear behavior in a compressive strain range of 0% to 5%. Subsequently, there is a plateau of severe deformation at almost constant stress. In this region, the walls and plates of cells buckle under compression thereby forming a denser structure. Post buckling, the cellular walls and plates start interacting with each other, causing a gradual increase in compressive stress.
- Due to high porosity, foams exhibit very large axial compressive strain without any lateral strain. Due to this, the Poisson’s ratio of foams is nearly zero. This behavior is critical for material modeling of foams in Abaqus.
Material models in Abaqus for rubbers
Abaqus uses the “hyperelastic materials” terminology for its material libraries that support rubbers. This is primarily because rubbers are elastic in nature even at very high strains. The basic assumptions in modeling solid rubbers are: elastic, isotropic and nearly incompressible. Foam material libraries in Abaqus are referred as “hyperfoam” and are highly incompressible. None of the rubber material models can be represented by a single coefficient such as modulus. It rather requires a strain energy density function that can have an infinite number of terms. Therefore, in Abaqus, strain energy functions have specific forms with certain numbers of parameters to be determined. Each of these function is associated with a separate material model, as shown below.
If you wish to learn the mathematical aspects of each of these material models and how they are applied in Abaqus input decks, along with demonstrations, you can always contact us for a dedicated training session that can be offered either at our office or on-site.