Nonlinear viscoelasticity of strain rate type: an overview

A variational approach to frame-indifferent quasistatic viscoelasticity of rate type

The three-dimensional dynamical model for nonlinear viscoelasticity of strain-rate type is investigated in a quasistatic setting under the assumption of higher-order regularity of the deformation, which in the literature is referred to as the case of non-simple materials. The existence of weak solutions is proven using a time-discretization technique while respecting the condition of dynamical frame indifference. Some observations on frame indifference for strain-rate-type stresses are made, and corrections are proposed for some related work in the literature. Finally, a counterexample is given to show that the assumed higher-order regularity is necessary in order to obtain the required compactness.This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

Viscoelasticity Acts as a Marker for Tumor Extracellular Matrix Characteristics

Biological materials such as extracellular matrix scaffolds, cancer cells, and tissues are often assumed to respond elastically for simplicity; the viscoelastic response is quite commonly ignored. Extracellular matrix mechanics including the viscoelasticity has turned out to be a key feature of cellular behavior and the entire shape and function of healthy and diseased tissues, such as cancer. The interference of cells with their local microenvironment and the interaction among different cell types relies both on the mechanical phenotype of each involved element. However, there is still not yet clearly understood how viscoelasticity alters the functional phenotype of the tumor extracellular matrix environment. Especially the biophysical technologies are still under ongoing improvement and further development. In addition, the effect of matrix mechanics in the progression of cancer is the subject of discussion. Hence, the topic of this review is especially attractive to collect the existing endeavors to characterize the viscoelastic features of tumor extracellular matrices and to briefly highlight the present frontiers in cancer progression and escape of cancers from therapy. Finally, this review article illustrates the importance of the tumor extracellular matrix mechano-phenotype, including the phenomenon viscoelasticity in identifying, characterizing, and treating specific cancer types.