Finite Deformation Behavior Of Elastomeric Materials: Constitutive Model And Numerical Implementation

Design engineers and material mechanics researchers are constantly challenged to formulate mathematical models with meticulous descriptions of the complex mechanical behavior of elastomeric materials.With accurate constitutive relations,virtual experiments via computerbased simulations can accelerate the design process by providing a detailed analysis of the expected mechanical response under varying loading conditions.Consequently,the formulation of new or improved constitutive models is an important research problem.This dissertation presents a series of research projects aimed at achieving constitutive models with a better description of the large nonlinear elastic mechanical behavior of elastomer-based components under different loading conditions.The models were formulated via the phenomenological approach,thus,the material parameters were obtained by utilizing the nonlinear least-squares technique,the Levenberg-Marquardt Algorithm,to fit the models’ strain energy density expressions to the strain energy density data calculated from the experimental data.The accuracy of the predicted data was determined based on the coefficient of determination and the relative errors.The models’ predictions were obtained by numerical implementation of their stress-strain expressions in Python codes.Furthermore,the computerbased simulations were achieved by implementing the model equations in Abaqus CAE 2016 via subroutines written in FORTRAN language.The main highlight of the results in this dissertation is a new model whose strain energy density expression has a linear and logarithmic dependence on the first and the second invariants of the Cauchy-Green deformation tensor respectively.The model was demonstrated to describe both the moderate and large deformation behavior of elastomeric materials with relatively higher accuracy.The model was extended to capture the effect of strain rates on the stress-strain response by incorporating a rate-dependent term on the strain energy density expression.The proposed term was found to be consistently accurate in describing the strain rate-dependent behavior of elastomeric materials.The strain energy density function of the Carroll model was modified to comply with the mathematical restriction that it should vanish at the undeformed state and to include a term that captures the volume changes during deformation.The resulting improved model exhibited numerous advantages such as having material parameters that are obtained in a single fitting in contrast to the three-step fitting process of the original model,requiring only the uniaxial tension experimental data,and the capability to be implemented in a finite element program.The strain energy density function of the well-known Yeoh model was modified by adding a term with dependence on the second invariant of the Cauchy-Green deformation tensor to improve its predictive behavior in the equibiaxial loading.The modified version exhibited significant improvements in accuracy whilst describing the equibiaxial loading behavior.The model was further modified by incorporating a damage criterion to capture the damage behaviors of elastomer-based components.Its finite element implementation accurately simulated the damage response of rubber panels under impact loading.The research presented in this dissertation accomplished advancements in the constitutive modeling of elastomeric materials.The proposed models can be utilized in designing elastomerbased components for engineering applications.Moreover,the mathematical formulations provide a basis for further developments to capture more complex phenomena such as stress softening,temperature-dependent response,and visco-hyperelasticity.