2007/04/23 by Gianni Dal Maso, Antonio DeSimone, Maso, Gianni Dal +5
Engineering · Materials Science · Mathematics · #28A33 #35Q72 #49J45 #74C05 #74G65 #Analysis of PDEs (math.AP) #Composite material #Elasticity and Material Modeling #Elasticity and Wave Propagation #FOS: Mathematics #Functional Analysis (math.FA) #Materials science #Mechanics #Nonlocal and gradient elasticity in micro/nano structures #Physics #Plasticity #Quasistatic process #Softening #Thermodynamics #math.AP #math.FA #msc:28A33 #msc:35Q72 #msc:49J45 #msc:74C05 #msc:74G65
paper · pdf · doi:10.48550/arxiv.0704.2984
published in arXiv (Cornell University) (Cornell University) · 43 pages
arxiv created 2007/04/23 · openalex publication_date 2007/04/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each time interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response.