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Elasto‐plastic models based on critical state formulations have been successful in describing many of the most important features of the mechanical behaviour of soils. This review paper deals with the applications of this class of models to the numerical analysis of geotechnical problems. After a brief overview of the development of the models, the basic critical state formulation is presented together with the main modifications which have actually been used in computational applications. The problems associated with the numerical implementation of this type of models are then discussed. Finally, a summary of reported computational applications and some specific examples of analyses of geotechnical problems using critical state models are presented.

The present paper aims to explore a computational homogenisation procedure to investigate the full geometric representation of yield surfaces for isotropic porous ductile media. The effects of cell morphology and imposed boundary conditions are assessed. The sensitivity of the yield surfaces to the Lode angle is also investigated in detail.

The microscale of the material is modelled by the concept of Representative Volume Element (RVE) or unit cell, which is numerically simulated through three-dimensional finite element analyses. Numerous loading conditions are considered to create complete yield surfaces encompassing high, intermediate and low triaxialities. The influence of cell morphology on the yield surfaces is assessed considering a spherical cell with spherical void and a cubic RVE with spherical void, both under uniform strain boundary condition. The use of spherical cell is interesting as preferential directions in the effective behaviour are avoided. The periodic boundary condition, which favours strain localization, is imposed on the cubic RVE to compare the results. Small strains are assumed and the cell matrix is considered as a perfect elasto-plastic material following the von Mises yield criterion.

Different morphologies for the cell imply in different yield conditions for the same load situations. The yield surfaces in correspondence to periodic boundary condition show significant differences compared to those obtained by imposing uniform strain boundary condition. The stress Lode angle has a strong influence on the geometry of the yield surfaces considering low and intermediate triaxialities.

The exhaustive computational study of the effects of cell morphologies and imposed boundary conditions fills a gap in the full representation of the flow surfaces. The homogenisation-based strategy allows us to further investigate the influence of the Lode angle on the yield surfaces.

The purpose of this study is to investigate the effects of stud height, stud diameter, ultimate stress of stud and concrete strength on the static behaviour of studs in push-off tests based on the ductile fracture theory.

Push-off tests of headed stud shear connectors with different heights and diameters used in concrete of various strengths were designed and implemented. A finite element model was established based on a ductile fracture criterion of ML15 cold-heading steel with stress triaxiality and Lode angle parameter. Based on the results of the parametric study of the numerical model, equations were proposed to evaluate the effect of stud height h_s, stud area A_s, concrete strength f_c and stud ultimate strength f_su used in concrete of various strengths on the static behaviour of studs.

The typical failure phenomenon observed among the test specimens was the fracture of the shank of studs. The microscopic images of the stud fracture surfaces and the verified finite element model indicate that the studs were fractured as a result of the combined action of tension and shear.

A new method for calculating ultimate load P_u and ultimate slip S_u is proposed in this paper. In the method, P_u is linearly related to f_su^0.2143, A_s^0.7790, h_s^0.0974, f_c^0.2065. S_u is linearly related to f_su^1.078, A_s^0.4681, h_s^(−0.3135), f_c^(−0.3480).

In this paper, we examine the influence of the third invariant in computational plasticity. For this purpose we consider the extended Leon model, an elasto‐plastic model for concrete materials which accounts for the difference of shear strength in triaxial compression and triaxial extension. Consequently, the deviatoric trace of the loading surface is no longer circular like in von Mises and Drucker‐Prager plasticity. In the limit it approaches the triangular shape of the Rankine condition of maximum direct stress. Thereby, elliptic functions describe the out‐of‐roundness of the circular trace in terms of C¹‐continuous functions of the Lode angle. The algorithmic aspects of the third invariant considerably complicate the computational implementation since the radial return method of J₂‐plasticity does no longer maintain normality leading to loss of deviatoric associativity. The paper will focus on the computational issues near the three regions with high curvature at the compressive meridians with special attention on the lack of convergence of the plastic return algorithm and its slow rate of convergence in these regions. The algorithmic discussion at the constitutive level will be augmented by the axial plane‐strain compression test in order to illustrate the effect of the third invariant at the structural level of finite element analysis.

The fracture mechanism of S-07 steel was investigated by observing the fracture surface of the specimens with scanning electron microscope (SEM). Furthermore, the overall elastic–plastic behaviors and the stress state evolution during the loading procedure of all specimens were simulated by FE analysis to obtain the local strain at crack nucleated location and the average triaxiality of each type of specimen.

Three types of tests under various stress states were performed to study the ductile fracture characteristics of S-07 high strength steel in quasi-static condition.

Under tensile and torsion loading conditions, S-07 steel exhibits two distinctive rupture mechanisms: the growth and internal necking of voids governs the rupture mechanism in tension dominated loading mode, while the change of void shape and internal shearing in the ligaments between voids dominants for shear conditions.

The failure criterion for S-07 steel considering the influence of the triaxial stress state was established.

The purpose of this paper is to perform a numerical assessment of two recently proposed extensions of the Gurson‐Tveegard‐Needleman ductile damage constitutive model under low stress triaxiality.

One of the most widely used ductile damage models is the so‐called Gurson‐Tveegard‐Needleman model, commonly known as GTN model. The GTN model has embedded into its damage formulation the effects of nucleation, growth and coalescence of micro‐voids. However, the GTN model does not include void distortion and inter‐void linking in the damage evolution. To overcome this limitation, some authors have proposed the introduction of different shear mechanisms based on micromechanical grounds or phenomenological assumptions. Two of these constitutive formulations are reviewed in this contribution, numerically implemented within a quasi‐static finite element framework and their results critically appraised.

Through the analysis of the evolution of internal variables, such as damage and effective plastic strain, obtained by performing a set of numerical tests using a Butterfly specimen, it is possible to conclude that the extended GTN models are in close agreement with experimental evidence.

Even though the results obtained with the modified GTN models have shown improvements, it can also be observed that both shear mechanisms have inherent limitations in the prediction of the location of fracture onset for some specific stress states.

From the results reported, it is possible to identify some shortcomings in the recently proposed extensions of the GTN model and point out the direction of further improvements.

The purpose of this work is to apply a recently proposed constitutive model for mechanically induced martensitic transformations to the prediction of transformation loci. Additionally, this study aims to elucidate if a stress-assisted criterion can account for transformations in the so-called strain-induced regime.

The model is derived by generalising the stress-based criterion of Patel and Cohen (1953), relying on lattice information obtained using the Phenomenological Theory of Martensite Crystallography. Transformation multipliers (cf. plastic multipliers) are introduced, from which the martensite volume fraction evolution ensues. The associated transformation functions provide a variant selection mechanism. Austenite plasticity follows a classical single crystal formulation, to account for transformations in the strain-induced regime. The resulting model is incorporated into a fully implicit RVE-based computational homogenisation finite element code.

Results show good agreement with experimental data for a meta-stable austenitic stainless steel. In particular, the transformation locus is well reproduced, even in a material with considerable slip plasticity at the martensite onset, corroborating the hypothesis that an energy-based criterion can account for transformations in both stress-assisted and strain-induced regimes.

A recently developed constitutive model for mechanically induced martensitic transformations is further assessed and validated. Its formulation is fundamentally based on a physical metallurgical mechanism and derived in a thermodynamically consistent way, inheriting a consistent mechanical dissipation. This model draws on a reduced number of phenomenological elements and is a step towards the fully predictive modelling of materials that exhibit such phenomena.

The purpose of this paper is to present several methods on how to deal with yield surface discontinuities. The explicit formulations, first presented by Koiter (1953), result in multisingular constitutive matrices which can cause numerical problems in elasto-plastic finite element calculations. These problems, however, are not documented in previous literature. In this paper an amendment to the Koiter formulation of the constitutive matrices for stress points located on discontinuities is proposed.

First, a review of existing methods of handling yield surface discontinuities is given. Examples of the numerical problems of the methods are presented. Next, an augmentation of the existing methods is proposed and its robustness is demonstrated through footing bearing capacity calculations that are usually considered “hard”.

Previous studies documented in the literature all present “easy” calculation examples, e.g. low friction angles and few elements. The amendments presented in this paper result in robust elasto-plastic computations, making the solution of “hard” problems possible without introducing approximations in the yield surfaces. Examples of “hard” problems are highly frictional soils and/or three-dimensional geometries.

The proposed method makes finite element calculations using yield criteria with corners and apices, e.g. Mohr-Coulomb and Hoek-Brown, much more robust and stable.

Abutment damage in liquefied ground is an important form of seismic damage of bridge structure. This paper aims to further research the effect of beam restriction on seismic damage mode of abutment in liquefied ground.

Based on the investigation of the seismic damage of Shengli Bridge in Tangshan earthquake, the finite element software dynamic effective stress analysis for ground (UWLC) is used to simulate the seismic damage of Shengli Bridge, and the results were compared with the actual seismic damage results. Then, the influences of the horizontal binding force of the beam, the liquefaction layer thickness, the top weight of the abutment, the peak acceleration, the liquefaction layer buried depth and the type of the foundation soil on the abutment seismic damage model are studied.

The results show that numerical simulation results are consistent with the actual seismic damage, and it is feasible to use UWLC software to simulate seismic damage. The results show that the seismic failure mode of the gravity abutment in liquefied ground is slip–rotation coupling type, not single slip type or rotation type. The large deformation of abutment bottom layer, horizontal binding force of the beam and post-stage soil pressure are the main reasons for abutment rotation or even destruction.

A series of basic assumptions are used in the calculation process in this paper. The gravity abutment is defined as the elastic body and neglects its local deformation. The soil layer is a homogeneous isotropic. The consolidation process and the drainage boundary problem are not considered in the calculation process. Therefore, the paper may have some limitations.

To further research the seismic damage mode and influencing factors of abutment in liquefied ground, in this paper, based on the investigation of the seismic damage of Shengli Bridge in Tangshan earthquake, the finite element software UWLC is used to simulate the seismic damage of Shengli Bridge, and the results were compared with the actual seismic damage results. The seismic damage mode and influencing factors of gravity abutment in liquefied ground have been studied.

Presents a computational algorithm for the numerical integration of triaxial concrete plasticity formulations. The specific material formulation at hand is the so‐called extended leon model for concrete. It is based on the flow theory of plasticity which entails isotropic hardening as well as fracture energy‐based softening in addition to non‐associated plastic flow. The numerical algorithm resorts to implicit integration according to the backward Euler strategy that enforces plastic consistency according to the closes‐point‐projection method (generalized radial‐return strategy). Numerical simulations illustrate the overall performance of the proposed algorithm and the significant increase of the convergence rate when the algorithmic tangent is used in place of the continuum operator.