Una formulazione agli sforzi per modelli elastoplastici con variabili interne: formulazione variazionale ed implementazione numerica basate sul metodo del lagrangiano aumentato

Dottorato di ricerca in ingegneria delle strutture. 8. ciclo. A.a. 1993-95Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

A framework of elastic-plastic damaging model for concrete under multiaxial stress states

International audienceThe paper concerns the description and the validation of a constitutive model for concrete characterized by a combined plastic-hardening-damage-fracture dissipative criterion developed within the framework of the simple material model, so that its numerical implementation is easy and robust. Two different damage isotropic mechanisms associated with tensile and compressive strain processes are introduced and two hardening variables are used; the first rules the plastic hardening while the second controls the compaction of the material. The limit domain is defined through the envelope of three yield criteria presenting a strong and original coupling between plastic and damage dissipative mechanisms. It is demonstrated that the proposed framework allows the reproduction of some distinctive features of the behavior of concrete under multiaxial stress states, such as volumetric hardening in triaxial compression load processes, the increment of strength under confined compression, post-peak dilatancy, varying degradation of the elastic stiffness in tensile or compressive stress states, the increase of the limit strain in cyclic processes. A comparison of the numerical predictions with the literature experimental tests is presented. The limits of the proposed model are also discussed in the paper

Stress rate formulation for elastoplastic models with internal variables based on augmented Lagrangian regularisation

International audienceThe constitutive laws of elasto-plasticity with internal variables are described through the definition of suitable dual potentials, which include various hardening models. A family of variational principles for inelastic problems is obtained using convex analysis tools. The structural problem is analysed using the complementary energy (Prager-Hodge) functional. The functional is regularised introducing an Augmented Lagrangian Regularisation for the indicator function of the elastic domain so that a smooth optimisation problem is obtained. In the numerical solution the discretised problem is reformulated in a finite step form using a fully implicit integration scheme and the functional is redefined in the space of the self-equilibrated nodal stresses, after enforcing satisfaction of the equilibrium equations in a weak form. Numerical tests have shown good performance on the part of the algorithm, which approaches the converged solution for a considerably smaller number of elements as compared with other algorithms. The method is equally available for perfect or hardening plasticity

A globally convergent numerical algorithm for damaging elasto-plasticity based on the Multiplier method

International audienceIn the paper it is proposed a new method for the solution of equilibrium problems based on a F.E. displacement formulation, that, at least in principle, is globally convergent as opposed to the classical Lagrangian method that presents only local convergence. The method, which appears to be particularly useful for plasticity models characterized by yield surfaces with regions of sharp curvature or corner points, is based on the Multiplier method. The structure of the procedure is presented and the consequent constrained optimization scheme is implemented for the case of associated plasticity coupled with damage. The main aspect of originality of the proposal is that it is not applied to the 'return algorithm', but to entire equilibrium iteration. At first, the local convergence properties of the constitutive equations are examined at the Gauss point level. It is proved that, also for involved constitutive models (a generalized Ottosen yield surface including isotropic hardening and damage is used in the applications), the convergence of a classical Newton's scheme is always reached with few iterations, ensuring a quadratic rate of convergence in the solution, provided a conversion of the inequality plastic constraint into an equality one is introduced, using an augmented Lagrangian functional for exactly evaluating the slack constraints. However, it is observed that the converged stresses are often attracted far from the initial trial point, towards regions with sharper curvature, and the main reason for the lack of convergence of the procedure is found in a divergence of the solution of the non-linear equilibrium equations. It is shown that the Multiplier method allows to enlarge the radius of convergence with respect to classical iterations based on the Lagrangian method. The price for the enlargement of the convergence radius is a higher number of iterations, since the Multiplier method presents only a linear rate of convergence. Indeed, the exact fulfilment of the compatibility and admissibility equations is not attained simultaneously, once an equilibrated solution is reached, but it is iterative. In the closure of the paper a convergence analysis of an elastic-plastic problem characterized by a yield criterion resulting from the convex hull of crises surfaces, and as a consequence, presenting regions of non-differentiability, is presented. It is shown how the ability of the Multiplier method in finding the solution of the structural problem for large loading step with respect to the classical Lagrangian technique compensate its slower convergence rate

Comparison of two forms of strain decomposition in an elastic-plastic damaging model for concrete

International audienceIn the paper a new modified form of the constitutive equations for concrete in the general framework for elastic-plastic damaging models proposed by the authors in (Contrafatto and Cuomo 2006 J. Plast. 22 2273-300) is presented. The modification concerns the definition of the internal energy potential. In the original paper the expression of the elastic energy potential depends on the sign of the trace of the elastic strain tensor. In the new formulation a decomposition of the strain tensor in its positive and negative component by means of a basis-free representation in terms of eigenprojections is used. As a consequence a different evolution of damage, affecting in a different way the tensile and compressive component of the strain tensor, is obtained. The two models belong to the class of continuum scalar damage models and are developed within the context of simple materials. The new model, first formulated in an arbitrary cartesian coordinate system, is presented in a principal axes representation, in order to reduce the algebraic complexity of the expressions and to make easier the analysis of simple load processes, while the treatment of the constitutive equations for the general case will be an object of future developments. A comparison between the predictions of the two models is performed by means of the analysis of some loading processes. The new formulation is able to overcome some drawbacks of the original model, especially in the tensile regime. In contrast, in the compressive regime, for which already the original formulation yielded satisfactory results, no change was detected

A new thermodynamically consistent continuum model for hardening plasticity coupled with damage

International audienceA phenomenological model for hardening-softening elasto-plasticity coupled with damage is presented. Specific kinematic internal variables are used to describe the mechanical state of the system. These, in the hypothesis of infinitesimal changes of configuration, are partitioned in the sum of a reversible and an irreversible part. The constitutive equations, developed in the framework of the Generalised Standard Material Model, are derived for reversible processes from an internal energy functional, postulated as the sum of the deformation energy and of the hardening energy both coupled with damage, while for irreversible phenomena from a dissipation functional. Performing duality transformations, the conjugated potentials of the complementary elastic energy and of the complementary dissipation are obtained. From the latter a generalised elastic domain in the extended space of stresses and thermodynamic forces is derived. The model, which is completely formulated in the space of actual stresses, is compared with other formulations based on the concept of effective stresses in the case of isotropic damage. It is observed that such models are consistent only for particular choices of the damage coupling. Finally, the predictions of the proposed model for some simple processes are analysed

An enriched finite element for crack opening and rebar slip in reinforced concrete members

Object of the paper is the simulation of reinforced concrete bars behaviour, accounting for crack opening and concrete-rebar slippage. A macro beam element with a single uniform reinforcement is studied in details in the uniaxial case. Distinct constitutive hypotheses are formulated for the materials. The CEB-FIP Model Code 90 rules the behaviour of the materials interface that is assumed to be fully dissipative. Steel is supposed to behave elastoplastically with hardening. Crack opening in the concrete matrix is introduced by means of a strong discontinuity approach (SDA). All the relevant equations of the problem are variationally derived from a mixed energy functional. Two enhancements of the enriched kinematics, based on polynomial or exponential shape functions, respectively, are compared with the usual SDA enhancement. As an alternative approach, high-order interpolation of the displacement field based on B-splines, both for steel and concrete, is proposed. These functions appear to be adequate in reproducing rapidly varying fields, like the stress gradients occurring in the shear lag problem near the boundaries or where slips and/or cracks occur. Their use allow to use few macro-element instead of the very dense meshing required in those areas by the traditional FE interpolations

Use of recycled aggregates in road sub-base construction and concrete manufacturing

This paper investigates the use of construction and demolition waste in road embankment and concrete manufacturing. The aggregates are recycled from the demolition waste of a building and in particular from basalt, sandstone, structural concrete and vibrated concrete blocks. The main physical characteristics of recycled aggregates for road applications and the performance of road sub-base layers containing recycled components are determined and validated on the basis of the latest Italian specifications. The study demonstrates that recycled mixes have sufficient mechanical characteristics and are hence suitable in road sub-base construction, even if only limited to minor technical importance works. Moreover, the mechanical properties of concrete mixtures that use recycled aggregates as replacement for natural aggregates are evaluated and compared to those of standard concrete mixtures. Three types of recycled aggregates are considered (structural concrete, basalt, vibrated concrete blocks) at different replacement ratios. A higher percentage of recycled aggregates than the one prescribed by the current legislations can be effectively used in concrete preparation, especially in the case of aggregates derived from crushed basalt waste or from structural concrete manufactured using basaltic fine and coarse aggregates. The effect of natural fine aggregate replacement with recycled fine fractions on concrete is investigated. The results of the experimental program are significant and encourage the use of 100% recycled basalt aggregate in concrete. Therefore, in areas where the use of basalt stone as primary masonry building material is widespread, the reuse of demolition waste is highly recommended.