To mathematically explain the nonlinear large deformation and rate dependent behavior of soft materials, viscohyperelastic models are usually used for modeling and finite element (FE) simulation purposes. The nonlinear elastic part in such formalisms is expressed in terms of either hyperelastic energy functions which incorporate higher order strains, or nonlinear elastic constants which are functions of deformation. The viscous part, on the other hand, is formulated based on either the time-dependent relaxation behavior or by incorporating nonlinear dashpot constants which are functions of deformation rate. It is, however, important to note that use of hyperelastic energy functions implies incorporating a certain definition for the strain field during large deformation. On the other hand, explaining the rate dependent part of the deformation in terms of relaxation functions may not take into account the same definition for the strain field. Such a formalism, hence, results in a physically inconsistent constitutive model for the overall behavior of a material with viscoelastic behavior. The model proposed in this study is based on a novel methodology which formulates the large deformation of ultra-soft materials at different strain rates with incorporating a unified strain field for elastic and viscous behaviors which relies on replacing the classical strain rate with the rate of the nonlinear Seth-Hill strain. This approach is basically different from the classical approaches for defining a nonlinear dashpot element in which the stress is related to the strain rate with higher order polynomial functions (such as ) or a nonlinear dashpot constant. The proposed model can be calibrated with the information of monotonic loading at different rates and does not require information from different loading conditions such as creep or relaxation. Accordingly, a generalized Maxwell model is developed which includes fully nonlinear springs and dashpots. The generalized closed-form equations of stress-stretch of individual Maxwell elements and the overall viscoelastic solid model for a monotonic constant rate deformation is presented. The appropriateness and accuracy of the model is studied *via* implementing it for formulating the compressive behavior of the brain tissue (as an ultra-soft material) at rates pertinent to impact loading as compared with the experiments. To be applicable to the full-scale mechanical investigation of the ultra-soft materials, the model needs to be used in FE simulations. Nevertheless, the equations for such a constitutive model do not exist in the library of commercial FE packages. Hence, the future development of this model includes developing subroutines that can be incorporated in FE software for large-scale modeling of the soft materials at high rates.


A Nonlinear Viscoelastic Model Applicable to Soft Materials at Large Deformation

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

IMECE2020 - Virtual Conference

Supporting the need among researchers worldwide for additional online and multimedia content, ASME now offers the ASME Conference Video Collection. This platform will collect and provide long-term access to conference presentation videos, encompassing all technology areas within ASME's technical conference and events program. About 30,000-40,000 engineers across all mechanical engineering and related disciplines participate in ASME conferences each year. This includes authors of approximately 6,000 to 8,000 technical papers published by ASME, the majority of whom also submit video presentations for our virtual conferences. The video collection will be available as an add-on to existing product packages or as a separate subscription.