This technical report contains some additional calculations supplementing Example 6 in the paper Normcontrollability of nonlinear systems by M. A. Müller, D. Liberzon, and F. Allgöwer, IEEE Transactions on Automatic Control, 2015. References and labels in this technical report (in particular Equation labels (1)–(59) and all theorem numbers etc.) refer to those in that paper. In the following, c...

We present an interactive rendering system for realistic lighting and material design under complex illumination with arbitrary BRDFs. Our system smoothly integrates accurate all-frequency relighting of shadows and reflections with dynamic per-pixel shading effects such as bump mapping and spatially varying BRDFs. This combination of capabilities is typically missing in current systems. We buil...

In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purpo...

Driven by the wide range of new material properties offered by multi-material 3D printing, there is emerging need to create predictive material models for these materials. A data driven process for estimating nonlinear material model is presented in this paper. In contrast with classical methods which derive the engineering stress-strain relationship assuming constant cross-section area and fix...

A new phenomenon of self-induced hysteresis has been observed in the interaction of bulk acoustic waves with a cracked solid. It consists in a hysteretic behavior of material nonlinearity as a function of the incident pump wave amplitude. Hysteresis manifests itself in the self-action of the monochromatic pump wave and in the excitation of its superharmonics and of its subharmonics. The propose...

A constitutive equation for nonlinear viscoelasticity is used to model the mechanical response of solid polymers such as polycarbonate. The nonlinearity arises from a reduced time which causes stress relaxation to accelerate with increasing strain. The constitutive equation can account for the occurrence of yield in a homogeneous uniaxial constant strain rate test. The constitutive equation is ...

In this paper we study a non-homogeneous elliptic Kirchhoff equation with nonlinear reaction term. We analyze the existence and uniqueness of positive solution. The main novelty is the inclusion of non-homogeneous term making the problem without a variational structure. We use mainly bifurcation arguments to get the results.