In materials engineering, one of the key challenges is to model materials that exhibit both hyperelastic and creep characteristics, that is, materials that exhibit both large elastic deformations and time-dependent deformations under long-term loading. Examples of such materials are:
Rubbers and elastomers
These materials are characterized by high elasticity, meaning that they can undergo large deformations and return to their original shape when the load is removed. However, under prolonged loading, rubber can also exhibit creep (e.g., in car tires, gaskets, or vibrating components).
Biological tissues
Soft tissues, such as skin, muscles, and tendons, exhibit both hyperelastic behavior and creep. Modeling this phenomenon is important in biomechanics, such as in the design of prostheses or the analysis of the behavior of human organs under load, such as during surgical procedures.
Polymers
Many plastics and polymeric materials, such as polyethylene and polypropylene, exhibit hyperelasticity under short-term loading and creep under long-term loading. These properties are important in many industries: automotive (vehicle components), consumer products, and packaging.
For Abaqus software, which is used to simulate the mechanics of solids, the question is often how to combine these two behaviors in a single material definition.
Can hyperelasticity and creep be combined in Abaqus?
At the level of direct material definition using keywords, the answer is no. The keyword *HYPERELASTIC cannot be directly combined with *CREEP, because creep (*CREEP) requires the use of the classical definition of elasticity (*ELASTIC), not hyperelasticity. Nevertheless, there are alternative approaches that allow both behaviors to be modeled simultaneously.
PRF (parallel rheological framework) constitutive model
One of the advanced approaches in Abaqus is the use of the PRF model. This model allows combining hyperelasticity with creep and other nonlinear material behaviors. The following keywords can be used within this approach:- *HYPERELASTIC - used to model the nonlinear elasticity of materials, such as rubber or biological tissues.
- *VISCOELASTIC, NONLINEAR, NETWORKID, LAW, SRATIO - describes visco-elastic properties that allow time to be taken into account in material deformation.
Additional capabilities within the PRF
Additional elements can also be included in the PRF model to further represent the actual behavior of the material:
- *PLASTIC - for materials that exhibit permanent deformation after exceeding a certain yield point.
- *MULLINS EFFECT - this effect describes the phenomenon of reduction of stiffness of a material after it has been previously loaded and partially unloaded, typical of rubber materials.
- *TRS - thermal expansion of a material, i.e., changes in mechanical properties depending on temperature.
How does PRF work?
The parallel rheological approach is based on a parallel combination of several nonlinear viscoelastic models, with the possibility of adding a nonlinear elasto-plastic model. Nonlinear elasticity in this model is described using hyperelasticity, while viscous behavior is modeled using creep potential. Importantly, to correctly represent large elastic deformations, it is assumed that the strain gradient is divided into elastic and creep-related components.
Alternative approaches for combining hyperelasticity with time-dependent behavior
There are other options in Abaqus for combining hyperelasticity with time-dependent plastic behavior:
- *HYPERELASTIC combined with *PLASTIC, RATE - allows plasticity to be modeled with deformation rates.
- *HYPERELASTIC in combination with *PLASTIC and *RATE DEPENDENT - allows for more complete control of deformation rate dependent material behavior.
- *HYPERELASTIC in combination with *HYSTERESIS - models materials that exhibit hysteresis, the difference between the loading and unloading of a material.
Summary
Although hyperelasticity and creep cannot be directly linked in Abaqus using basic keywords, PRF (parallel rheological framework) and other advanced features allow such phenomena to be modeled. With the combination of nonlinear elasticity and creep models, it is possible to accurately represent the complex behavior of materials in response to different loads.
If you would like to learn more about material modeling in Abaqus, we invite you to take a look at our training courses.
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