Many traditional materials used in construction and engineering are considered to be linear materials: the relation between how much force is applied to the material and how much it deforms is a direct proportion. Materials such as metals, steel, concrete, may be considered to be linear.
On the other hand, many modern materials (rubbers, elastomers, plastics, biological, composites) are nonlinear in nature. These materials find wide applications in automotive, aerospace, engineering, biomedical and consumer applications.
Linear materials are described by a traditional material model known as Hooke's Law. Different classes of nonlinear materials have different material models. Famous material models include Arruda-Boyce, Mooney-Rivlin and Ogden material models. Each of these material models specifies the use of a certain number of constants — to be experimentally evaluated — known as material model parameters. The theory and practice of evaluating material model parameters is underdeveloped. Having such theory and practice would improve material formulation, material testing, engineering design, accuracy of simulations, and quality control processes.
In this ongoing project, we have suggested a theory for evaluating material parameters for the Mooney-Rivlin model. The theory has been verified by COMSOL simulations, and given rise to a plethora of methods for model parameter evaluation. Current and future work includes extending the theory to various material classes, and adding analyses for phenomena such as hysteresis, frequency dependence, anisotropy, etc.
This project showcases the following expertise of Noumenon Multiphysics: