𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On a System of Nonlinear PDEs with Temperature-Dependent Hysteresis in One-Dimensional Thermoplasticity

✍ Scribed by Pavel Krejčı́; Jürgen Sprekels

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
316 KB
Volume
209
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we develop a thermodynamically consistent description of the uniaxial behaviour of thermoelastoplastic materials that are characterized by a Ž . w Ž .xŽ . constitutive law of the form x, t s P P , x, t x,t , where , , denote the fields of strain, stress, and absolute temperature, respectively, and where Ä w x4 Ž . P P и , denotes a family of rate-independent hysteresis operators of

Prandtl᎐Ishlinskii type, parametrized by the absolute temperature. The system of state equations governing the space-time evolution of the material are derived. It turns out that the resulting system of two nonlinearly coupled partial differential equations involves partial derivatives of hysteretic nonlinearities at different places.

It is shown that an initial-boundary value problem for this system admits a global weak solution. The paper can be regarded as a first step towards a thermodynamic theory of rate-independent hysteresis operators depending on temperature.

📜 SIMILAR VOLUMES

On a class of PDEs with nonlinear distri
On a class of PDEs with nonlinear distributed in space and time state-dependent delay terms
✍ Alexander V. Rezounenko 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 157 KB

## Abstract A new class of nonlinear partial differential equations with distributed in space and time state‐dependent delay is investigated. We find appropriate assumptions on the kernel function which represents the state‐dependent delay and discuss advantages of this class. Local and long‐time a

Effect of daily water treatment on hatch
Effect of daily water treatment on hatchling sex ratios in a turtle with temperature-dependent sex determination
✍ Anne Marie LeBlanc; Thane Wibbels 📂 Article 📅 2009 🏛 Wiley (John Wiley & Sons) 🌐 English ⚖ 66 KB

## Abstract Some previous studies indicate that the local hydric environment may influence sex determination in turtles with temperature‐dependent sex determination. In this study, the effect of a daily application of 0.77 mL of ddH~2~0 per egg using an incubation temperature of 29.1°C was examined

Independent effects of incubation temper
Independent effects of incubation temperature and gonadal sex on the volume and metabolic capacity of brain nuclei in the leopard gecko (Eublepharis macularius), a lizard with temperature-dependent sex determination
✍ Coomber, Patricia; Crews, David; Gonzalez-Lima, Francisco 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 317 KB 👁 2 views

The extent to which variation within and between the sexes can be assigned to genes vs. environment is problematic, because, in most vertebrates, males and females differ genetically. However, factors other than sex chromosomes and the consequent sex-typical gonadal hormone secretions may play impor