2021/02/19 by Alexandros Stathas, Ioannis Stefanou
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Cauchy distribution #Classical mechanics #Computer science #Constitutive equation #Continuum mechanics #Elasticity and Material Modeling #Engineering #Finite element method #Geology #Geomechanics #High-Velocity Impact and Material Behavior #Mathematical analysis #Mathematics #Mechanics #Physics #Plane stress #Regularization (linguistics) #Solid mechanics #Strain hardening exponent #Strain rate #Structural Response to Dynamic Loads #Structural engineering #Thermodynamics #Viscoplasticity #math.AP #physics.app-ph
paper · pdf · doi:10.1016/j.cma.2021.114185
29 pages, 18 figures
openalex publication_date 2021/02/19 · arxiv created 2021/05/03 · openalex created_date 2021/10/25 · arxiv updated 2021/11/03 · openalex updated_date 2026/08/05
Strain localization is responsible for mesh dependence in numerical analyses concerning a vast variety of fields such as solid mechanics, dynamics, biomechanics and geomechanics. Therefore, numerical methods that regularize strain localization are paramount in the analysis and design of engineering products and systems. In this paper we revisit the elasto-viscoplastic, strain-softening, strain-rate hardening model as a means to avoid strain localization on a mathematical plane in the case of a Cauchy continuum. Going beyond previous works (de Borst and Duretz (2020); Needleman (1988); Sluys and de Borst (1992); Wang et al. (1997)), we assume that both the frequency ω and the wave number k belong to the complex plane. Therefore, a different expression for the dispersion relation is derived. We prove then that under these conditions strain localization on a mathematical plane is possible. The above theoretical results are corroborated by extensive numerical analyses, where the total strain and plastic strain rate profiles exhibit mesh dependent behavior.