The work focuses on the numerical resolution of the discontinuous material bifurcation problem as a relevant ingredient in computational material failure mechanics. The problem consists of finding the\ud conditions for the strain localization onset in terms of the so-called bifurcation time, localization directions and localization modes. A numerical algorithm, based on the iterative resolution of a coupled eigenvalue\ud problem in terms of the localization tensor, is proposed for such purpose. The algorithm is shown to be always convergent to the exact solution for the symmetric case (major and minor symmetries of the tangent constitutive operator). In the unsymmetric case (only minor symmetries), the solution is no longer exact, although it is shown that using the symmetric part of the localization tensor in the proposed\ud algorithms provides enough accurate solutions for most of cases. Numerical examples illustrate the benefits of the proposed methodology in terms of accuracy and savings in the computational cost associated with the problem.Peer ReviewedPostprint (published version

SUMMARYA new phenomenological macroscopic constitutive model for the numerical simulation of quasi-brittle fracture and ductile concrete behavior, under general triaxial stress conditions, is presented. The model is particularly addressed to simulate a wide range of confinement stress states, as also, to capture the strong influence of the mean stress value in the concrete failure mechanisms.The model is based on a two-surface damage-plastic formulation. The mechanical behavior in different domains of the stress space is separately described by means of a quasi-brittle or ductile material response:(i) For positive values of the mean stress (tensile states), an isotropic continuum damage model with strain softening is considered. In this context, and in order to avoid the Boundary Value Problem ill-posedness induced by the softening law, a regularization technique based on the Continuum Strong Discontinuity Approach (CSDA) is adopted, which results equivalent to a damage model with embedded cohesive cracks providing anisotropic responses.(ii) A plastic model governs the material behavior when the mean stress is negative (confinement states). It is based on the classical plastic flow theory. In particular, a yield criterion similar to that of Willam and coauthors, which depends on the three stress invariants, is used. Additional features defining the plastic response are: an isotropic strain hardening law and a non-associative flow rule.The paper presents the numerical implementation of the model using an efficient integration algorithm, namely, the Impl-Ex scheme. Several widely known experimental tests (such as uniaxial, biaxial and triaxial tests) carried out on concrete specimens are used to calibrate and validate the performance of the proposed formulation. Finally, a classical 2D reinforced concrete beam example is analyzed in order to show the predictive capability of the model in structural analysis applications.

The paper presents a methodology to model three-dimensional reinforced concrete members by means of embedded discontinuity elements based on the Continuum Strong Discontinuous Approach (CSDA). Mixture theory concepts are used to model reinforced concrete as a 3D composite material constituted of concrete with long fibers (rebars) bundles oriented in different directions embedded in it. The effects of the rebars are modeled by phenomenological constitutive models devised to reproduce the axial non-linear behavior, as well as the bond-slip and dowel action. The paper presents the constitutive models assumed for the components and the compatibility conditions chosen to constitute the composite. Numerical analyses of existing experimental reinforced concrete members are presented, illustrating the applicability of the proposed methodology.

This paper deals with two different approaches suitable for the description of plasticity in single crystals. The first one is the standard approach that is based on a continuous deformation mapping. Plasticity is driven by a classic Schmid-type relation connecting the shear stresses to the shear strains at a certain slip system. By way of contrast, the second approach is nonstandard. In this novel model, localized plastic deformation at certain slip planes is approximated by a strong discontinuity (discontinuous deformation mapping). Accordingly, a modified Schmid-type model relating the shear stresses to the shear displacements (displacement jump) is considered in this model. Although both models are indeed different, it is shown that they can be characterized by almost the same set of equations, eg, by a multiplicative decomposition of the deformation gradient into an elastic part and a plastic part. This striking analogy eventually leads to a unifying algorithmic formulation covering both models. Since the set of active slip systems is not known in advance, its determination is of utmost importance. This problem is solved here by using the nonlinear complementarity problem (NCP) as advocated by Fischer and Burmeister. While this idea is not new, it is shown that the NCP problem is well posed, independent of the number of active slip systems. To be more explicit, the tangent matrix in the return-mapping scheme is regular even for more than five simultaneously active slip systems.Based on this algorithm, texture evolution in a polycrystal is analyzed by means of both models and the results are compared in detail.

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