Performing RVE calculations under constant stress triaxiality for monotonous and cyclic loading

• Published in: International journal for numerical methods in engineering Vol. 66; no. 8; pp. 1331 - 1360
• Main Authors: Lin, R. C., Steglich, D., Brocks, W., Betten, J.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 21.05.2006; Wiley
• Subjects: Axisymmetric; Computational techniques; elastoplastic material; Exact sciences and technology; Fatigue (materials); finite elements; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Mathematical analysis; Mathematical methods in physics; Mathematical models; Physics; RVE; Solid mechanics; Strain; Strategy; stress triaxiality; Stresses; Structural and continuum mechanics; Triaxiality; void growth; Axial stress; RVE; Representative volume element; stress triaxiality; Cavitation; Modeling; Axial symmetry; Triaxial stress; Finite element method; Mesoscale; Elastoplasticity; Cyclic load; elastoplastic material; Porosity; void growth; finite elements; Strain rate
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.1600

In the present work the mesoscopic stress, strain rate and strain states of axisymmetric cells under two types of boundary loadings are formulated. Then, the stress triaxiality of axisymmetric cells is expressed in terms of the axial and radial mesoscopic stress components. Based on the formulations of the mesoscopic stress, three strategies for numerical realization of constant stress triaxiality are presented. The advantages and disadvantages of these strategies are discussed. These numerical strategies are implemented on the platform of the general‐purpose finite element programme ABAQUS. They can be applied for representative volume element (RVE) calculations under constant triaxiality, monotonous and cyclic loading controlled by displacement, force, traction and the mesoscopic equivalent strain of the RVE. Several numerical examples are shown to prove the effectivity of these strategies and programme. Copyright © 2005 John Wiley & Sons, Ltd.