Methodologies for constitutive model parameter identification for strain locking materials

Strain locking materials exhibit a pronounced stiffening above an apparent critical strain. In practice, both natural materials, such as biological tissues, and human-made composites with flexible or undulating microstructures, can exhibit this type of response. This paper describes several methodologies for identifying the material constants required for a thermodynamically consistent constitutive model, that appropriately simulates the strain-locking behavior. Attempts to fit the material constants by minimizing an RMS error function between model behavior and experimental stress-strain curves reveal a non-smooth surface of the stress-based error function, which lead to difficulties in convergence to a material constant set that has a minimum error. An analysis of the constitutive model based on the relationships between the parameters of the constitutive model and physical behavior they govern lead to the construction of a smoother error function and minimization of an objective function with reduced dimensionality. This technique yielded parameters values that accurately represented the experimental data for several material systems. Two optimization methods (both gradient-based and direct) were investigated and their effectiveness in converging to the global minimum solution of the error function was compared. Selected composites and biological materials with strain-locking behaviors were analyzed, and the material constants required for the constitutive model were successfully determined.