Abstract

This paper studies the phenomenon of strain bifurcation and localization in J2plasticity under plane stress and plane strain conditions. Necessary conditions for the outcome of bifurcation, localization, stress boundedness and decohesion are analytically established. It is shown that the explicit consideration of these conditions allows for the determination of localization angles in certain situations of interest that can be used to conduct benchmark tests on finite element formulations. The relative merits of irreducible, (stabilized) mixed and (displacement and/or strain) enhanced formulations are discussed. Numerical examples show that the mixed displacement/pressure formulation is to be preferred to the standard irreducible schemes in order to predict correct failure mechanisms with localized patterns of plastic deformation. Mixed elements are shown to be practically free from mesh directional bias dependence.

Abstract

This paper studies the phenomenon of structural size effect and strain localization in J2 plasticity. Size effect is here understood as the change in the response of a given structure when the spatial dimensions are scaled up or down while the geometry and other relevant properties of the structure are preserved. The work exploits the advantages of the mixed displacement–pressure formulation in incompressible or quasi-incompressible situations. Elasto-J2-plastic constitutive behaviour with regularized softening is considered. Stability issues are discussed to ensure existence and uniqueness of the solution of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is able to solve a wide range of structural scales, including real life engineering applications. The results obtained do not suffer from spurious mesh dependence. Furthermore, the formulation includes the classical theories of perfect plasticity and linear fracture mechanics as limit cases.

Abstract

In this article we present the approximation of the coupled model of the equations of motion of a fluid in shallow waters with the convection-diffusion-reaction (CDR) equation of pollutant transport. This approximation is carried out using high order finite elements and using stabilised variational sub-scale methods. We write the coupled system of equations, previously discretised in time and linearised, as a transient vector equation of CDR. The stabilised finite element methods used are the known ASGS and OSS sub-scale methods, the same ones that allow us to use the same interpolation for all unknowns, as well as to deal with dominant convection and reaction flows. We consider the possibility of non-linearity in both the convective and reaction terms. We will not consider the possible development of shocks in the solution. In order to examine the accuracy and robustness of the ASGS and OSS methods, we present four test cases: mesh convergence, transport of a pollutant in a square cavity, transport of a pollutant in the Gulf of Roses and at the river Guadalquivir mouth, and the predator-prey model, which can be written as a transient CDR vector equation with non-linearity in the reaction term.

Abstract

This paper studies the phenomenon of structural size effect and strain localization in J2 plasticity. Size effect is here understood as the change in the response of a given structure when the spatial dimensions are scaled up or down while the geometry and other relevant properties of the structure are preserved. The work exploits the advantages of the mixed displacement–pressure formulation in incompressible or quasi-incompressible situations. Elasto-J2-plastic constitutive behaviour with regularized softening is considered. Stability issues are discussed to ensure existence and uniqueness of the solution of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is able to solve a wide range of structural scales, including real life engineering applications. The results obtained do not suffer from spurious mesh dependence. Furthermore, the formulation includes the classical theories of perfect plasticity and linear fracture mechanics as limit cases.