New developments in multiscale formulations for material failure

S. TORO; P.J. SÁNCHEZ; P.J. BLANCO; A.E. HUESPE; R.A. FEIJÓO

Eindhoven

Simposio; EuroMech 559: Multi-scale computational methods for bridging scales in materials and structures; 2015

Eindhoven University of Technology

This contribution presents a two-scale (macro-micro) formulation addressed to simulate fracture in materials having heterogeneous micro-structures. The methodology adopted by this formulation can be categorized as a semi-concurrent model which uses the Representative Volume Element (RVE) concept. The computational aspects and numerical implementation of the formulation are also shown. The mechanical model which takes into account the fracture phenomenon, assumes cohesive cracks at both scales of analysis. Initiation and posterior propagation of cohesive micro-cracks leads to material instability at the macro-scale. Once detected instability at the macro-scale, a cohesive surface is activated, and the cohesive tractions are obtained by a convenient homogenization procedure drawn from the evolution of the fracturing process at the micro-scale. A variational multiscale formulation based on a similar methodology has previously been presented by the authors, [1], [2], [3]. It has been shown that the procedure provides objective results with respect to the micro-cell size, even after the onset of strain localization process, observed at the macroscopic scale. Subsequently, the formulation has been generalized and improved in two aspects: i) cohesive surfaces are introduced at both scales of analysis; they are modeled with strong discontinuity kinematics. New equations describing the insertion of the macro-scale strains, into the micro-scale and the posterior homogenization procedure are considered; ii) the computational procedure and numerical implementation are adapted to the improved formulation. The first point has been presented and developed in [4], The second point has been developed in [5]. Here, we describe a summarized version of this improved technique. The correct capturing of the crack pattern tortuosity at smaller scales is a decisive topic for modeling material degradation in multiscale frameworks. Following our multiscale modeling approach, the tortuosity effect is introduced in the scale-bridging equations, through a kinematical concept, when the macro-kinematics is injected into the micro-scale. Therefore, it has a direct consequence in the homogenized mechanical response, particularly in reference to the overall fracture energy described at larger scale. In this contribution we present adequate nite element techniques for modeling the cohesive surfaces at both scales of analysis: finite elements with embedded strong discontinuities (EFEM) are used for the macro-scale simulation, and continuum-type finite elements with high aspect ratios, mimicking cohesive surfaces, are adopted for simulating the failure mechanisms at the micro-scale. The methodology is numerically assessed through the simulation of several quasi-brittle concrete fracture problems, typically, a four point beam bending test. Numerical simulations adequately captures the material degradation phenomenon at the mesostructural level, which induces the activation of cohesive surfaces at the structural scale. In the numerical test, it is emphasized the role played by the micro-crack path tortuosity and its effect on the overall fracture energy observed at the macro-scale. Validation of the model is performed by means of a comparative analysis of solutions, in problems involving crack propagation phenomenon, obtained via Direct Numerical Simulations (DNS).