Thermal and wear analysis of an elastic beam in sliding contact

Existence for a thermoviscoelastic beam model of brakes

“…Next, we denote by = (t) the shortening of the beam as a result of the wear; it measures the averaged length (over the beam's cross-section A b ) of the removed material (see [8,9] for further details). The beam is assumed viscoelastic with constitutive relation…”

“…The device's temperature is assumed to be  dev =  dev (t), and the end has the device temperature, thus Â(1; t) =  dev (t). The wheel is held in place and a simple argument (see, e.g., [8,9]) shows that the contact pressure caused by the horizontal thermal expansion, the wear and the applied force is given by…”

“…Finally, the wear of the beam's end is given by the di erential form of the Archard law (see, e.g., [4,8,9,14,17] and references therein),…”

“…Related results for various geometries and simple settings in engineering literature can be found in [6,11] and references therein, as well as in [4]. One-dimensional thermoviscoelastic contact problems can be found in [8,9].…”

Existence and uniqueness for a quasistatic frictional bilateral contact problem in thermoviscoelasticity

“…A one-dimensional thermoviscoelastic problem for a beam was investigated in [15] where the existence of the weak solution was established and numerical simulations of the solutions conducted. A quasistatic thermoviscoelastic problem for a beam can be found in [12,11] where the wear of the contacting end is included. A frictionless one-dimensional thermoelastic contact problem for a rod was thoroughly analyzed in [3].…”