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

This paper exploits the concept of stabilization techniques to improve the behaviour of mixed linear/linear simplicial elements (triangles and tetrahedra) in incompressible or nearly incompressible situations. Elasto‐J2‐plastic constitutive behaviour has been considered with linear and exponential softening. Two different stabilization methods are used to attain global stability of the corresponding discrete finite element formulation. Implementation and computational aspects are also discussed, showing that a robust application of the proposed formulation is feasible. Numerical examples show that the formulation derived is free of volumetric locking and spurious oscillations of the pressure. The results obtained do not suffer from spurious mesh‐size or mesh‐bias dependence, comparing very favourably with those obtained with the standard, non‐stabilized, approaches.

Abstract

Coupling between fluid fingering and strain localization during the imbibition of a partially saturated soil is investigated in this paper. The fluid mixture saturating the granular skeleton is regarded as a non-uniform fluid characterized via a double well Helmoltz free energy endowed with a gradient regularizing contribution. The porous medium is assumed deformable and the associated elasto-plastic constitutive law is described by the 'Sinfonietta Classica' plastic model. Because of the higher differential order of the hydraulic problem a mixed finite element method is employed.

Abstract

We develop a fully coupled finite element solution for elastoplastic indentations of unsaturated granular soils by a rigid cylinder by using a mortar-type contact algorithm. In the presented solution, we have employed an advanced constitutive model that allows the inclusion of the effect of matric suction and induced anisotropy in the problem. Several numerical examples in both static and dynamic scenarios are provided for validation and demonstrating the capabilities of the presented framework.

Abstract

Abstract

Abstract

This paper exploits the concept of orthogonal sub-grid scales to stabilize the behaviour of mixed linear/linear simplicial elements (triangles and tetrahedra) in incompressible or nearly incompressible situations. Both incompressible elastic and J2-plastic constitutive behaviours have been considered. The different assumptions and approximations used to derive the method are exposed. Implementation and computational aspects are also discussed, showing that a robust application of the proposed formulation is feasible. Numerical examples show that the elements derived are free of volumetric locking and spurious oscillations of the pressure, and that the results obtained compare favourably with those obtained with the Q1P0 quadrilateral.