A non-iterative approach for the modelling of quasi-brittle materials
- 488 Downloads
Due to the softening behaviour of quasi-brittle materials, in particular the localisation of initially diffused cracking, convergence problems are often found using an iterative procedure, such as the Newton–Raphson method. This is why a new non-iterative procedure is adopted in this paper, which is inspired by the sequentially linear approach(SLA) (Rots et al. in Eng Fract Mech 75(3–4):590–614, 2008). However, several important differences between the present approach and the SLA are presented. In the present model, multi-linear material laws are adopted such that non-linearities occur only due to changes in loading/unloading states. An incremental solution is obtained until non-convergence occurs, upon which a secant approach is used in a corresponding step. The update of the stiffness in the secant approach is based on information obtained from the previous incremental solution. This method is applied to: (i) softening materials, within the scope of the discrete crack approach, and to (ii) hardening materials. As a consequence, conversely to the smeared crack approach adopted in the SLA, no mesh size sensitivity problems are obtained and there is no need to adjust material parameters. Several numerical examples are shown in order to illustrate the proposed formulation.
KeywordsNIEM Fracture Non-iterative procedure Sequentially linear analysis
Unable to display preview. Download preview PDF.
- Alfaiate J, Sluys LJ (2002) Analysis of a compression test on concrete using strong embedded discontinuities. In: Mang HA, Rammerstorfer FG, Eberhardsteiner J (eds) WCCM V, fifth world congress on computational mechanics. Wien, AustriaGoogle Scholar
- Billington SL (2009) Nonlinear and sequentially linear analysis of tensile strain hardening cement-based composite beams in flexure. In: Hendriks M, Billington SL (eds) Computational modeling workshop on concrete, masonry and on fiber-reinforced composites, pp 7–10, Delf, The NetherlandsGoogle Scholar
- Burns NH, Seiss CP (1962) Load-deformation characteristics of beam-column connections in reinforced concrete. Report technical report, Engineering Studies SRS 234. Department of Civil Engineering, University of California, BerkeleyGoogle Scholar
- CEB: (1991) CEB-FIP Model Code 1990. Thomas Telford, LondonGoogle Scholar
- Crisfield MA (1984) Difficulties with current numerical models for reinforced-concrete and some tentative solutions. Comput Aided Anal Des Concr Struct (1):331–358Google Scholar
- Gago A, Milosevic J, Lopes M, Bento R (2011, submitted) Shear strength of rubble stone masonry walls. Bull Earthq EngGoogle Scholar
- Graça-e-Costa R (2005) Modelação de vigas de betão armado reforçadas com chapas metálicas. MSc thesis, Instituto Superior Técnico, Universidade Técnica de Lisboa, PortugalGoogle Scholar
- Lowes LN (1999) Finite element modeling of reinforced concrete beam-column bridge connections. PhD thesis, University of California, BerkeleyGoogle Scholar
- Milosevic J, Bento R, Gago A, Lopes M (2010) Seismic vulnerability of old masonry buildings—SEVERES project. Report 1. Instituto Superior Técnico, Lisbon. www.severes.org
- Rots JG (2001) The role of structural modelling in preserving Amsterdam architectural city heritage. In: Lourenço PB, Roca P (eds) Historical constructions. Guimarães, Portugal, pp 685–696Google Scholar
- Schlangen E (1993) Experimental and numerical analysis of fracture process in concrete. PhD thesis, Delft University of Technology, The NetherlandsGoogle Scholar