: Soft materials, such as polymers and biological tissues, have several engineering and biomechanical applications. Characterizing of mechanical behavior of soft materials has been faced with a tremendous challenge, due to strain-rate- and time-dependent nature. The former is known as short-term, while the latter is termed as long-term behaviors. While different properties of tissues have already been extensively examined, some behavioral aspects, such as dependence of the stress relaxation behavior on the strain levels, have not been studied yet. In this thesis, a new 3D non-linear hyperviscoelastic constitutive model is proposed for an isotropic homogeneous compressible material. The model consists of two parts; hyperelastic and viscous parts. The well-known neo-Hookean strain energy functions is used to represent the hyperelastic part, and the short-term viscous part is described using a differential-type theory. In order to achieve the latter, a new strain energy function is suggested, which depends on both the right Cauchy-Green deformation tensor and its material derivative. Therefore, unlike most of the existing differential-type models, the model is able to account for stress reduction in a stress relaxation test. Moreover, the long-term viscous function, which represents the history of deformation, is formulated using an integral framework which depends on the strain level. The material constants of the model are determined by fitting the constitutive relation to experimental data. For this purpose, uniaxial compression and stress relaxation tests were carried out on bovine liver tissue. To demonstrate the capabilities of the proposed constitutive model, a UMAT subroutine has been developed to implement the model into ABAQUS software. In order to validate the model, experimental data for a polymeric, published in the literature, been used to compare with the model prediction. The results show that the model can well predict the nonlinear, strain-rate-dependent behavior, during loading and relaxation phases, at different strain levels. Keywords: Liver tissue, Long-term viscous function, Non-linear hyperviscoelastic model, Soft material, Subroutine UMAT.
