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A concrete material model is presented. The model is based on non‐associated plasticity for the pre‐failure and ductile post‐failure regimes and fracture (smeared crack approach) for the brittle post‐failure regime. The implementation of the constitutive model in the 2‐D elements of a general purpose non‐linear incremental finite element code is discussed. Some important numerical features of the implementation are the implicit integration of the stress/strain relation and the use of an efficient symmetric stiffness formulation for the equilibrium iterations.

This paper aims to develop a finite element analysis strategy, which is suitable for the analysis of progressive failure that occurs in pressure-dependent materials in practical engineering problems.

The numerical difficulties stemming from the strain-softening behaviour of the frictional material, which is represented by a non-associated Drucker–Prager material model, is tackled using the Cosserat continuum theory, while the mixed finite element formulation based on Hu–Washizu variational principle is adopted to allow the utilization of low-order finite elements.

The effectiveness and robustness of the low-order finite element are verified, and the simulation for a real-world landslide which occurred at the upstream side of Carsington embankment in Derbyshire reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved.

The permit of using low-order finite elements is of great importance to enhance computational efficiency for analysing large-scale engineering problems. The case study reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved.

The initial stiffness method has been extensively adopted for elasto‐plastic finite element analysis. The main problem associated with the initial stiffness method, however, is its slow convergence, even when it is used in conjunction with acceleration techniques. The Newton‐Raphson method has a rapid convergence rate, but its implementation resorts to non‐symmetric linear solvers, and hence the memory requirement may be high. The purpose of this paper is to develop more advanced solution techniques which may overcome the above problems associated with the initial stiffness method and the Newton‐Raphson method.

In this work, the accelerated symmetric stiffness matrix methods, which cover the accelerated initial stiffness methods as special cases, are proposed for non‐associated plasticity. Within the computational framework for the accelerated symmetric stiffness matrix techniques, some symmetric stiffness matrix candidates are investigated and evaluated.

Numerical results indicate that for the accelerated symmetric stiffness methods, the elasto‐plastic constitutive matrix, which is constructed by mapping the yield surface of the equivalent material to the plastic potential surface, appears to be appealing. Even when combined with the Krylov iterative solver using a loose convergence criterion, they may still provide good nonlinear convergence rates.

Compared to the work by Sloan et al., the novelty of this study is that a symmetric stiffness matrix is proposed to be used in conjunction with acceleration schemes and it is shown to be more appealing; it is assembled from the elasto‐plastic constitutive matrix by mapping the yield surface of the equivalent material to the plastic potential surface. The advantage of combining the proposed accelerated symmetric stiffness techniques with the Krylov subspace iterative methods for large‐scale applications is also emphasized.

Numerical solutions in computational plasticity are severely challenged when concrete and geomaterials are considered with non‐regular yield surfaces, strain‐softening and non‐associated flow. There are two aspects that are of immediate concern within load steps which are truly finite: first, the iterative corrector must assure that the equilibrium stress state and the plastic process variables do satisfy multiple yield conditions with corners, Fi(σ, q) = 0, at discrete stages of the solution process. To this end, a reliable return mapping algorithm is required which minimizes the error of the plastic return step. Second, the solution of non‐linear equations of motion on the global structural level must account for limit points and premature bifurcation of the equilibrium path. The current paper is mainly concerned with the implicit integration of elasto‐plastic hardening/softening relations considering non‐associated flow and the presence of composite yield conditions with corners.

Implicit solutions in viscoplastic analysis of structures are very often avoided due to the fact that they lead to non‐symmetric systems of equations. On the other hand, structures such as soils have a marked non‐associate behaviour that has to be taken into consideration. Here the implicit solutions are formulated in a way that, even for non‐associate models, the system of equations is kept as symmetric. Apart from an ‘exact’ formulation of the algorithm other possibilities are considered and tested in the numerical examples given.

A constitutive model based on classical plasticity theory for non‐linear analysis of concrete structures using finite elements is presented. The model uses the typical parameters of non‐associated plasticity theory for frictional materials and a modified Mohr‐Coulomb yield surface is suggested. Onset and amount of cracking at a point are controlled by the values of the effective plastic strain and thus it can be studied by a posteriori postprocessing of numerical results. The accuracy and objectivity of the model is checked out with some examples of application.

Purpose – The aim of this work is to provide a global 3D finite element (FE) model devoted to the modelling of superficial soil ploughing in the large deformation range and for a vast class of soil treatment tools. Design/methodology/approach – We introduced soil constitutive equation in a FE software initially designed for the metal forming. We performed the numerical integration of the non‐linear ploughing problem. Non‐linearities encountered by the problem can be summed up: as soil constitutive equation (idealized with non‐associated compressible plastic law), unilateral frictional contact conditions (with a rigid body), geometrical non‐linearities (the ploughing tool) and large deformation range. To handle such difficulties we performed several numerical methods as implicit temporal scheme, Newton‐Raphson, non‐symmetric iterative solver, as well as proper approximation on stress and strain measures. Findings – Main results deal with the validation of the integration of the non‐linear constitutive equation in the code and a parametric study of the ploughing process. The influence of tool geometric parameters on the soil deformation modes and on the force experienced on the tools had been point out. As well, the influence of soil characteristics as compressibility had been analyzed. Research limitations/implications – This research is devoted to perform a numerical model applicable for a large range of soil treatment tools and for a large class of soil. However, taking into account all kind of soil is utopist. So limitations met are essentially related to the limit of the accuracy of the elasto‐plastic idealization for the soil. Practical implications – In practice the numerical model exposed in the paper can clearly help to improve and optimize any process involving superficial soil submitted to the mechanical action of a rigid body. Originality/value – The original value of the paper is to provide a global and an applicable numerical model able to take into account the main topics related to the ploughing of superficial soils. Industrials in geotechnics, in agriculture or in military purposes can benefit in using such numerical model.

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.

A new model for handling non‐orthogonal cracks within the smeared crack concept is described. It is based on a decomposition of the total strain increment into a concrete and into a crack strain increment. This decomposition also permits a proper combination of crack formation with other non‐linear phenomena such as plasticity and creep and with thermal effects and shrinkage. Relations are elaborated with some other crack models that are currently used for the analysis of concrete structures. The model is applied to some problems involving shear failures of reinforced concrete structures such as a moderately deep beam and an axisymmetric slab. The latter example is also of interest in that it confirms statements that ‘reduced integration’ is not reliable for problems involving crack formation and in that it supports the assertion that identifying numerical divergence with structural failure may be highly misleading.

Liquefaction phenomenon and its catastrophic nature can be analysed as a particular material behaviour of granular media under certain loading paths. Proposes a definition of liquefaction and its modelling by constitutive relations. Discusses this modelling in relation to the questions of stability and uniqueness. Considers the signs of three scalar quantities: the work of second order, the determinant of the symmetric part of the tangent constitutive tensor and the determinant of the tensor itself. Concludes that the liquefaction path is situated inside a potentially unstable domain and that in some cases this path reaches some states of loss of uniqueness, which are essentially bifurcation points.