Yilin Zhu

Viscoelastic–Viscoplastic Cyclic Deformation of Polycarbonate Polymer: Experiment and Constitutive Model

A series of uniaxial tests (including multilevel loading–unloading recovery, creep-recovery, and cyclic tension–compression/tension ones) were performed to investigate the monotonic and cyclic viscoelastic–viscoplastic deformations of polycarbonate (PC) polymer at room temperature. The results show that the PC exhibits strong nonlinearity and rate-dependence, and obvious ratchetting occurs during the stress-controlled cyclic tension–compression/tension tests with nonzero mean stress, which comes from both the viscoelasticity and viscoplasticity of the PC. Based on the experimental observation, a nonlinear viscoelastic–viscoplastic cyclic constitutive model is then constructed. The viscoelastic part of the proposed model is constructed by extending the Schaperys nonlinear viscoelastic model, and the viscoplastic one is established by adopting the Ohno–Abdel-Karims nonlinear kinematic hardening rule to describe the accumulation of irrecoverable viscoplastic strain produced during cyclic loading. Furthermore, the dependence of elastic compliance of the PC on the accumulated viscoplastic strain is considered. Finally, the capability of the proposed model is verified by comparing the predicted results with the corresponding experimental ones of the PC. It is shown that the proposed model provides reasonable predictions to the various deformation characteristics of the PC presented in the multilevel loading–unloading recovery, creep-recovery, and cyclic tension–compression/tension tests.

A finite viscoelastic–plastic model for describing the uniaxial ratchetting of soft biological tissues

In this paper, a phenomenological constitutive model is constructed to describe the uniaxial ratchetting (i.e., the cyclic accumulation of inelastic deformation) of soft biological tissues in the framework of finite viscoelastic-plasticity. The model is derived from a polyconvex elastic free energy function and addresses the anisotropy of cyclic deformation of the tissues by means of structural tensors. Ratchetting is considered by the evolution of internal variables, and its time-dependence is described by introducing a pseudo-potential function. Accordingly, all the evolution equations are formulated from the dissipation inequality. In numerical examples, the uniaxial monotonic stress-strain responses and ratchetting of some soft biological tissues, such as porcine skin, coronary artery layers and human knee ligaments and tendons, are predicted by the proposed model in the range of finite deformation. It is seen that the predicted monotonic stress-strain responses and uniaxial ratchetting obtained at various loading rates and in various loading directions are in good agreement with the corresponding experimental results.

A New Kinematic Hardening Rule Describing Different Plastic Moduli in Monotonic and Cyclic Deformations

To describe the different plastic moduli of the metal materials presented in the monotonic and cyclic deformations, a new nonlinear kinematic hardening rule is proposed by modifying the Chaboche’s one (Chaboche 1989). In the proposed rule, the back stress is assumed to be decomposed into three components as done by Chaboche (1989), but the linear hardening and dynamic recovery terms of each back stress component are further divided into two parts, respectively, and a part in each of them is only activated when the reverse loading occurs so that the cyclic stress-strain hysteresis loops can be predicted more accurately; moreover, a rachetting coefficient is introduced into one part of dynamic recovery term to describe the ratchetting. The proposed rule can be reduced to the Chaboche’s one under the monotonic loading conditions, or by setting some material parameters as zero. Finally, the proposed model is verified by comparing the predicted results with corresponding experimental ones. It is seen that the predicted results are in good agreement with the corresponding experimental ones.

Logarithmic rate based elasto-viscoplastic cyclic constitutive model for soft biological tissues.

Based on the logarithmic rate and piecewise linearization theory, a thermodynamically consistent elasto-viscoplastic constitutive model is developed in the framework of finite deformations to describe the nonlinear time-dependent biomechanical performances of soft biological tissues, such as nonlinear anisotropic monotonic stress-strain responses, stress relaxation, creep and ratchetting. In the proposed model, the soft biological tissue is assumed as a typical composites consisting of an isotropic matrix and anisotropic fiber aggregation. Accordingly, the free energy function and stress tensor are divided into two parts related to the matrix and fiber aggregation, respectively. The nonlinear biomechanical responses of the tissues are described by the piecewise linearization theory with hypo-elastic relations of fiber aggregation. The evolution equations of viscoplasticity are formulated from the dissipation inequalities by the co-directionality hypotheses. The anisotropy is considered in the hypo-elastic relations and viscoplastic flow rules by introducing some material parameters dependent on the loading direction. Then the capability of the proposed model to describe the nonlinear time-dependent deformation of soft biological tissues is verified by comparing the predictions with the corresponding experimental results of three tissues. It is seen that the predicted monotonic stress-strain responses, stress relaxation, creep and ratchetting of soft biological tissues are in good agreement with the corresponding experimental ones.

Ratchetting of Snake Skin: Experiments and Viscoelastic-Plastic Constitutive Model

In this paper, the cyclic deformation of snake skin is experimentally observed by the in vitro tests under uniaxial cyclic loading conditions and at room temperature for the first time. The effect of loading level on the cyclic deformation and the anisotropic deformation of snake skin are investigated, respectively. The results show that ratchetting (i.e., a cyclic accumulation of strain) occurs during the cyclic tension-tension tests of snake skin, and depends greatly on the loading orientations and levels. Based on the experimental results of uniaxial ratchetting, a simplified version of the finite viscoelastic-plastic model (Zhu et al. in J Biomech 47:996–1003, 2014) for soft biological tissues is obtained. The comparison shows that the simulated results are in qualitative agreement with the experimental ones.