Keywords: gradient dependent plasticity, wavelets, hybrid-mixed formulations, finite elements.

In recent years, hybrid-mixed finite element formulations based on the use of systems of wavelets defined on the interval have been used for the elastic and elastoplastic analysis of plate bending and plate stretching problems [1]. The numerical models proved to be effective and the stress estimates quite accurate. This communication presents a hybrid-mixed stress model for gradient plasticity analysis. The new feature presented here consists in the use of wavelets to build the approximation basis. The main advantage of these functions is that they are hierarchical by nature and well suited for the application of effective adaptive algorithms.

In the hybrid-mixed stress model, the stress and the displacement fields are directly approximated in the domain of each element [1]. The displacements along the static boundary are also independently approximated. None of the fundamental equations has to be satisfied a priori. All field equations are imposed in a weighted residual form. To model the evolution of plastic straining, a mesh of critical cells is defined and the plastic multiplier field increments are independently approximated in the domain. The stress radiation is also independently approximated along the boundary of the active critical cells [2].

A complete series of wavelets defined on the interval [1] are used to approximate both the stress and the displacement fields. The properties of such functions are used to obtain analytical expressions for the computation of most of the structural operators. Complete sets of non-negative polynomials are used to define the approximations for the plastic multiplier increments [2].

The classical example of a softening bar subject to a displacement controlled loading is used to illustrate the use of the hybrid-mixed gradient dependent model described above and to assess its accuracy and efficiency.

1

L.M.S. Castro and A.R. Barbosa, "Implementation of an hybrid-mixed stress model based on the use of wavelets", Computers & Structures, 84, 718-731, 2006. doi:10.1016/j.compstruc.2005.11.012

2

J.A.T. Freitas and Z.M. Wang, "Hybrid-Trefftz stress elements for elastoplasticity", Int. J. Num. Meth. Eng., 43, 655-683, 1998. doi:10.1002/(SICI)1097-0207(19981030)43:4<655::AID-NME416>3.3.CO;2-T

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £120 +P&P)