A one‐dimensional implementation of a coupled elasto‐plastic model for ductile damage

Abstract

A one-dimensional numerical implementation of the Lemaitre damage model is presented. The implementation is close to classical finite element schemes but can be realised by simple codes or by the application of commercial computer algebra systems. Based on the presented theory and computational algorithm, the elasto-plastic deformation of a one-dimensional bar is simulated. The damage evolution is evaluated for different isotropic hardening behaviour and stated as a function of the plastic strain. The described algorithm allows a simple investigation of the influence of different parameters on the damage evolution.Keywords: damage / Lemaitre model / plasticity / numerical mechanics / finite element method / Eine eindimensional numerische Implementierung des Schädigungsmodells nach Lemaitre wird vorgestellt. Die Implementierung orientiert sich an den klassischen Finite-Elemente-Formulierungen und kann durch ein einfaches Programm oder durch die Anwendung kommerzieller Computeralgebrasysteme realisiert werden. Basierend auf der vorgestellten Theorie und des numerischen Algorithmus wird die elastisch-plastische Verformung eines eindimensionalen Stabes simuliert. Die Schädigungsentwicklung wird für verschiedene isotrope Verfestigungsverläufe ausgewertet und als Funktion der plastischen Dehnung angegeben. Der beschriebene Algorithmus erlaubt eine einfache Untersuchung des Einflusses verschiedener Parameter auf die Schädigungs-entwicklung.

Modelling of Steel Creep at High Temperatures Using an Implicit Creep Model

“…The presented implicit creep model is used to modify the initial elasto-plastic steel material model [21] and creates a new visco-plastic material model by modifying stationary stress-strain curves. Results of the deflections obtained by the numerical model show good agreement with the experiment when using the proposed implicit creep model, and therefore, indicate the validity of the applied implicit creep model.…”

A return mapping algorithm for elastoplastic and ductile damage constitutive equations using the subloading surface method

“…The conventional numerical scheme for the solution of the elastoplastic/damage problem , , is defined by 5 equations. The first equation defines the stress state at the n + 1 as where is the trial elastic input strain increment for the n + 1 step freezing the plastic variables, Δ λ n + 1 is the plastic multiplier, and E is the elastic constant matrix.…”

“…Moreover, a return mapping scheme is adopted here for integrating the constitutive equations to obtain an accurate solution even for large prescribed displacement input conditions. The algorithm is based on the work of de Sousa Neto, de Sousa Neto et al, Esmaeili and Öchsner, and Gate and is adapted to preserve the features of the unconventional plasticity model.…”