We consider a quasistatic nonlinear model in thermoviscoelasticity at finite-strain setting the Kelvin–Voigt rheology, where both elastic and viscous stress tensors comply with principle of frame indifference under rotations. The force balance is formulated reference configuration by resorting to concept nonsimple materials, whereas heat transfer equation governed Fourier law deformed configura...

This paper addresses that class of complex problems where there is little or no underlying theory upon which to build a model and the situation dictates the use of an adaptive approach based on the observed data. The field of study is known as adaptive nonlinear models (ANMs), and its goal is to quantify interaction terms without imposing assumptions on the solution. The purpose of this paper i...

In mechanics, linear models have been well developed and received wide acceptance. They are based on linear elasticity, incompressibility of fluids and ideal gas properties. At the present stage of scientific and technical advances very exacting requirements are imposed upon materials and structures. The necessity to take into account their properties in nonlinear area of the mechanical behavio...

The paper studies regularity properties of set-valued mappings between metric spaces. In the context of metric regularity, nonlinear models correspond to nonlinear dependencies of estimates of error bounds in terms of residuals. Among the questions addressed in the paper are equivalence of the corresponding concepts of openness and “pseudo-Hölder” behavior, general and local regularity criteria...