Search

A novel nonlinear coupled finite-strain electro-magneto-thermo-hyperelasticity (EMTHE) model is developed for the first- and second-sound wave propagation and reflection investigations in media that are exposed to electromagnetic fields and mechanical shocks. In contrast to the previous studies which studied behaviors of the finite-strain elastic or incompressible materials with small deformations, the current research proposes a much more complicated but much more accurate novel practical model for wave propagation and reflection analyses in near-incompressible finite-strain materials. Furthermore, to evaluate the effects of the electro-magneto-thermomechanical coupling, the strain energy density function of the hyperelastic material is expanded in a new way. The governing equations are obtained according to a nonlinear version of the Helmholtz free energy. The energy equations comprise the first- and second-order time rates of the temperature to enable the modeling of the finite-speed heat transfer; i.e., the establishment of a second-sound model. A nonlinear iterative finite element solution algorithm is proposed and implemented for the resulting coupled time-dependent generalized electro-magneto-thermo-hyperelasticity equations. The results show significant differences between the predicted wave propagation and reflection characteristics and behaviors of the near-incompressible and incompressible finite-strain models. [ABSTRACT FROM AUTHOR]

Introduction: Nano-indentation has recently been employed as a powerful tool for determining the mechanical properties of biological tissues on nano and micro scales. A majority of soft biological tissues such as ligaments and tendons exhibit viscoelastic or time-dependent behaviors. The constitutive characterization of soft tissues is among very important subjects in clinical medicine and especially, biomechanics fields. Periodontal ligament plays an important role in initiating tooth movement when loads are applied to teeth with orthodontic appliances. It is also the most accessible ligament in human body as it can be directly manipulated without any surgical intervention. From a mechanical point of view, this ligament can be considered as a thin interface made by a solid phase, consisting mainly of collagen fibers, which is immersed into a so-called ground substance. However, the viscoelastic constitutive effects of biological tissues are seldom considered rigorous during Nano-indentation tests. Methods: In the present paper, a mathematical contact approach is developed to enable determining creep compliance and relaxation modulus of distinct periodontal ligaments, using constant–rate indentation and loading time histories, respectively. An adequate curve-fitting method is presented to determine these characteristics based on the Nano-indentation of rigid Berkovich tips. Generalized Voigt-Kelvin and Wiechert models are used to model constitutive equations of periodontal ligaments, in which the relaxation and creep functions are represented by series of decaying exponential functions of time. Results: Time-dependent creep compliance and relaxation function have been obtained for tissue specimens of periodontal ligaments. Conclusion: To improve accuracy, relaxation and creep moduli are measured from two tests separately. Stress relaxation effects appear more rapidly than creep in the periodontal ligaments.