Forced Vibrations in One-Dimensional Nonlinear Viscoelasticity

Phase Transitions in One-Dimensional Nonlinear Viscoelasticity: Admissibility and Stability

For the motion of a one-dimensional viscoelastic material of rate type with a non-monotonic stress-strain relation, a mixed initial boundary value problem is considered. A simple existence theory is outlined, based on a novel transformation of the equation into the form of a degenerate reaction-diffusion system. This leads to new results characterizing the regularity of weak solutions. It is sh...

Forced Vibrations for a Nonlinear Wave Equation

One dimensional infinite-horizon variational problems arising in viscoelasticity

Low-dimensional intrinsic material functions for nonlinear viscoelasticity

Rheological material functions are used to form our conceptual understanding of a material response. For a nonlinear rheological response, the possible deformation protocols and material measures span a high-dimensional space. Here we use asymptotic expansions to outline lowdimensional measures for describing leading-order nonlinear responses in large-amplitude oscillatory shear (LAOS). These i...

Quasilinear Hyperbolic{parabolic Equations of One{dimensional Viscoelasticity

We study the global existence of solutions of initial-boundary-value problems for a quasilinear hyperbolic-parabolic equation describing the longitudinal motion of a one-dimensional viscoelastic rod. We treat a variety of nonhomogeneous boundary conditions, requiring separate analyses, because they lead to distinctive physical eeects. We employ a constitutive equation giving the stress as a gen...