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a b s t r a c tA new technique for modeling cracks in quasi-brittle materials based on the use of interface solid finite elements is presented. This strategy named mesh fragmentation technique consists in introducing sets of standard low-order solid finite elements with a high aspect ratio in between regular (or bulk) elements of the mesh to fill the very thin gaps left by the mesh fragmentation procedure. The conception of this strategy is supported by the fact that, as the aspect ratio of a standard low-order solid finite element increases, the element strains also increase, approaching the same kinematics as the Continuum Strong Discontinuity Approach. As a consequence, the analyses can be performed integrally in the context of the continuum mechanics, and complex crack patterns can be simulated without the need of tracking algorithms. A tension damage constitutive relation between stresses and strains is proposed to describe crack formation and propagation. This constitutive model is integrated using an implicit-explicit integration scheme to avoid convergence drawbacks, commonly found in problems involving discontinuities. 2D and 3D numerical analyses are performed to show the applicability of the presented technique. Relevant aspects such as the influence of the thickness of the interface elements and mesh objectivity are investigated. The results show that the technique is able to predict satisfactorily the behavior of structural members involving different crack patterns, including multiple cracks, without significant mesh dependency provided that unstructured meshes are used.

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A new adaptive concurrent multiscale approach for modeling concrete that contemplates two well separated scales (represented by two different meshes) is proposed in this paper. The macroscale stress distribution is used as an indicator to identify critical regions (where the material is prone to degrade) with the explicit aim to enrich these zones with detailed mesoscale material information comprising three basic phases: coarse aggregates, mortar matrix and interfacial transition zone. Thus, the concrete initially idealized as a homogeneous material is gradually replaced and enhanced by a heterogeneous multiphase one. This technique is particularly powerful to handle cases where the region with nonlinear behavior is not easy to anticipate. Furthermore, the proposed approach does not require the definition of a periodic cell (or a RVE), and the meshes from distinct scales are totally independent. The new adaptive mesh technique is based on the use of coupling finite elements to enforce the continuity of displacements between the non-matching meshes associated with the two different scales of analysis. Besides that, mesh fragmentation concepts are incorporated to simulate the crack formation and propagation at the mesoscopic scale, without the need of defining complex and CPU-time demanding crack-tracking algorithms. The strategy is developed integrally within the framework of continuum mechanics, which represents an advantage with respect to other approaches based on discrete traction/separation-law. Numerical examples with complex crack patterns are conducted to validate the proposed multiscale approach. Furthermore, the efficiency and accuracy of the novel technique are compared against full mesoscale and standard concurrent multiscale models, showing excellent results.

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