2016/12/06 by Leszek Bartczak, Bartczak, Leszek, Sebastian Owczarek +1
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Composite Material Mechanics #Elasticity and Material Modeling #FOS: Mathematics #Gas Dynamics and Kinetic Theory #math.AP
paper · pdf · doi:10.48550/arxiv.1612.01886
arxiv created 2016/12/06 · openalex publication_date 2016/12/06 · arxiv updated 2016/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the quasi-static evolution of the thermo-plasticity model in which the evolution equation law for the inelastic strain is given by the Prandtl-Reuss flow rule. The thermal part of the Cauchy stress tensor is not linearised in the neighbourhood of a references temperature. This nonlinear thermal part imposed to add a damping term to the balance of the momentum, which can be interpreted as external forces acting on the material. In general the dissipation term occurring in the heat equation is integrable function only and the standard methods can not be applied. Combining truncation techniques and Boccardo-Gallouët approach with monotone methods we prove an existence of renormalised solutions.