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An implicit integration algorithm based on invariants for isotropic elasto-plastic models of the Cosserat continuum
No full textA Finite Element (FE) procedure based on a fully implicit backward Euler predictor/corrector scheme for the Cosserat continuum is here presented. The integration algorithm is suitable for yield and plastic potential surfaces with general shape in the deviatoric plane. The key element of the integration scheme is the spectral decomposition of the stress tensor, which is achieved, despite the lack of symmetry, because of the mathematical structure of the yield function and the set of invariants chosen as independent variables. It is also shown that the choice of invariants enables considerable mathematical simplifications, which result in the reduction of the system of equations and unknowns of the elasto-plastic problem from 19 to 1, and to rigorously handle the discontinuity at the apex of the surfaces. The algorithm has been implemented in a proprietary FE programme, and used for the constitutive model recently proposed by the same authors in this journal for the Cosserat continuum, which allows to set various classical failure criteria as yield and plastic potential surfaces. Numerical analyses have been conducted to simulate a biaxial compression test and a shallow strip footing resting on a Tresca, Mohr–Coulomb, Matsuoka–Nakai and Lade–Duncan soil. The benefits of the Cosserat continuum over the Cauchy/Maxwell medium are discussed considering mesh refinement, non-associated flow and softening behaviour
The difficult challenge of modelling the non‐linear elastic behaviour of soils within a theoretically sound framework
No full textHypo‐elastic relations are often adopted to simulate the recoverable non‐linear behaviour of soils within elasto‐plastic constitutive models. In reality, they are unable to reproduce the elastic, ie, recoverable, response of materials; hence, they introduce severe inconsistencies in models based on the decomposition of the total strain tensor into its recoverable and permanent parts. Hyper‐elasticity should then be used. However, existing models developed within this framework do not satisfy a number of fundamental theoretical requirements. A new hyper‐elastic model is proposed, which is rigourously formulated by integrating some of the main relations which emerge from experimental results. The model satisfies all theoretical requirements and also possesses features that are fundamental for its numerical integration. The model can be considered as the correct hyper‐elastic version of the classical hypo‐elastic constitutive relation adopted in models based on the Critical State framework, such as the Modified Cam‐Clay, with a constant Poisson's ratio
An extended modified Cam-Clay yield surface for arbitrary meridional and deviatoric shapes retaining full convexity and double homothety
No full textThis paper presents a new yield function, defined in terms of stress invariants and suitable for isotropic geomaterials. It is a generalisation of that of the modified Cam-Clay (MCC) model and as such it retains all the mathematical advantages of the original formulation, which are particularly convenient for the numerical integration of the constitutive law. In addition the proposed function is capable of providing a wide range of shapes and it is therefore suitable for defining both the yield and the plastic potential surfaces. As compared to the original MCC ellipse, one additional parameter is introduced for defining the shape of the meridional section, which conveniently controls also the relative position of the normal compression and critical state lines. In the deviatoric plane the function not only provides the exact shape of classical failure criteria, such as von Mises, Drucker–Prager, Matsuoka–Nakai, Lade–Duncan, Tresca and Mohr–Coulomb, but it is also capable of rounding the hexagons of the last two criteria with a continuity of class at least C2 required for achieving a quadratic convergence of the integration scheme. The new function has an unrestricted domain of definition, expands/shrinks homothetically with respect both to the origin of the stress space and to its centre and is characterised by convexity for any level set. The last two important features were obtained by applying a convexification technique proposed by the authors elsewhere
Transient myocardial ischemia in patients with chronic angina: relation to heart rate changes and variability in exercise threshold. BAY r 1999 in Chronic Angina Study Group.
No full textValore prognostico della velocità del flusso ematico nelle vene polmonari in pazienti con cardiomiopatia dilatativa. Studio condotto mediante ecocardiografia transesofagea
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