The influence of crumb-rubber on the mechanical properties of Portland cement concrete (PCC) is studied by experimental tests and numerical simulations. The main hypothesis of the study is that replacing part of the stone aggregate with crumb-rubber in the mix modifies the energy dissipation during the cracking process and affects the concrete behaviour under monotonically increasing loads. The experimental research program characterizes the mechanical properties of PCC for three different types of concrete with a variable content of crumb-rubber. The experimental results showed that fracture energy and other properties are directly related to the rubber fineness used in the mixture. The material properties derived for these laboratory tests are used to study, by numerical models, its response through its damage evolution. The numerical model used to simulate the damage evolution of the concrete is the Embedded Discontinuity Method (EDM). One characteristic of the EDM is that it does not need to modify the mesh topology to propagate the damage through the continuum solid. For this study, the Disk-Shaped Compact Tension specimen geometry, normed by the D7313-13 of the ASTM, is used. Results showed that the numerical methods provide good approximation of the experimental curve in the elastic and softening branches.

This paper investigates the variational finite element formulation and its numerical implementation of the damage evolution in solids, using a new discrete embedded discontinuity approach. For this purpose, the kinematically optimal symmetric (KOS) formulation, which guarantees kinematics, is consistently derived. In this formulation, rigid body motion of the parts in which the element is divided is obtained. To guarantee equilibrium at the discontinuity surfaces, the length of the discontinuity is introduced in the numerical implementation at elemental level. To illustrate and validate this approach, two examples, involving mode-I failure, are presented. Numerical results are compared with those reported from experimental tests. The presented discontinuity formulation shows a robust finite element method to simulate the damage evolution processes in quasi-brittle materials, without modifying the mesh topology when cohesive cracks propagate.

The theory of the fractal structure characterizing propagation of a crack through identification of its generator is presented. It's generating fractal, the peculiarities of its construction and the way to measure its segments are defined, and a theorem on the inverse scale property of such and other of the axial symmetry property of the fractal generator are presented and demonstrated. The theory is applied on 6061-T6 aluminum samples, using SENB probes. Direction of crack propagation and its fractal dimension are calculated numerically. Results obtained from modeling the direction of crack propagation through mechanics of elastic linear fracture and the one proposed here, called geometrical fractal fracture, are compared, thus developing the mirror case.

In this work, the flexibility properties of variable cross section beams are derived, through the application of the second theorem of Castigliano; considering the complementary energy by bending and share forces. To perform the integration of the flexibility coefficients, a numerical method, which considers the discretization of the beam domain with first order rectangular finite elements, in conjunction with the Gauss rule, is proposed. At the end of the work, the proposed method is applied to a tapered beam that has been discretized with a maximum of five finite elements. It is shown that the method is general, and that it can be applied to beams of variable section in which the cross section can be complex. The results shown that no more than 3 finite elements are needed to discretize the domain of beams in which, the ratio height-length is of the order of ten.

En este trabajo se reportan resultados parciales derivados de una serie de experimentos de laboratorio, con los que se estudia el  empleo de caucho de llantas de desecho como agregado en concreto de cemento Portland, reemplazando el 10% en peso del agregado pétreo. Se estudiaron tres mezclas de concreto: simple, con caucho grueso y con caucho fino. Los tamaños de las  partículas del caucho grueso variaron de 6.32 - 9.53 mm, mientras que para el fino iban de 2.35 - 2.80 mm. La influencia de este material en la resistencia mecánica del concreto se evaluó mediante cilindros y vigas, a los 28 días de edad, bajo condiciones de carga uniaxial de compresión, tracción indirecta y flexión. Para las tres condiciones de carga estudiadas, los resultados  experimentales mostraron una reducción de la resistencia del concreto, cuando se sustituye parte del agregado pétreo con caucho. La mezcla de concreto con partículas finas de caucho presentó un mejor comportamiento mecánico que la mezcla con partículas gruesas; incluso en condiciones de flexión, la resistencia era casi igual a la del concreto simple.