Mechanics of soft polymeric materials using a fractal viscoelastic model

Abstract

Soft materials are known for their plethora of biomedical applications, intricate structure-property correlation and nonlinear mechanical response. Multiple length-time scale phenomena and hierarchical structure results in their nonlinearity. Phenomenological and continuum mechanical models have been developed to predict their mechanics, which have mostly been very material-specific with inability to predict the mechanics of different types of soft materials simultaneously. This shortcoming has been addressed in the present work, wherein a generic nonlinear viscoelastic model has been proposed to predict the mechanical response of hydrogels, sponges, and xerogels. A fractal derivative viscoelastic model is proposed considering a fractal Maxwell model in parallel with a nonlinear spring. In particular, this model is chosen to qualitatively mimic the material nonlinearity inherent in soft materials. The fractal dashpot in combination with the nonlinear spring accounts for the power law time-dependent rheology of generic soft materials. These two different aspects in the form of nonlinear stiffness and non-Newtonian rheology account for mechanics of most soft materials. The present model is shown to fit well the existing literature results for mechanical response of a multitude of soft material classes with different test conditions and loading rates, which is one of the salient features of the model, apart from its simplistic mathematical framework. Further, a parametric study is reported on the mechanics of nanocellulose loaded poly(vinyl alcohol) xerogel. The model predictions are observed to be in conjunction with the experimental observations.

From fundamental concepts to recent developments in the adhesive bonding technology: a general view

“…Despite its accuracy, its use is limited due to the large number of constants required to mathematically define the model. Several models using springs and dashpots have been developed for large deformations, chain networks, damage accumulation, cyclic loadings, and strain-softening conditions [168,169]. It has been shown that a combination of linear and nonlinear springs with a nonlinear dashpot can appropriately consider the effects of strain rate and relaxation [168].…”

Simulating mechanical properties of human tissues or organs based on magnetorheological fluid for tactile display

“…However, they cannot accurately characterize the material nonlinearity and time-dependent behaviors that is often seen in biomedical materials. Therefore, in this section, inspired by [44], the classical Maxwell model is modified as the nonlinear fractal order Maxwell model to characterize the nonlinear and timedependent behaviors caused by the interaction of MR fluid and the PU sponge. This model includes two parts: normal force model and shear force model.…”

Vision-Based Contact Adhesion Measurement Method on Soft Matter Surfaces

“…At present, it is worth noting the relevant research on the adhesion of soft matters. From the perspective of adhesion mechanics, researchers have carried out in-depth exploration of the behavior characteristics, theoretical analysis and test methods of soft matters, and have achieved fruitful results in the fields of biomechanics, interface and contact mechanics and colloid mechanics . However, the research on the adhesion of soft matter surfaces is still weak, and the combination of theory and experiment is more urgent.…”

“…From the perspective of adhesion mechanics, researchers have carried out in-depth exploration of the behavior characteristics, theoretical analysis and test methods of soft matters, and have achieved fruitful results in the fields of biomechanics, 4 interface and contact mechanics 5 and colloid mechanics. 6 However, the research on the adhesion of soft matter surfaces is still weak, and the combination of theory and experiment is more urgent. In addition, current instrument is commonly photographed from the bottom 7 or side 8 of indentation, which requests the research object must be a thinner transparent soft matter to obtain the adhesion deformation of the contact surface.…”