INTEC   05402
INSTITUTO DE DESARROLLO TECNOLOGICO PARA LA INDUSTRIA QUIMICA
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
A variational multiscale model for fracture
Autor/es:
P.J. SÁNCHEZ; S TORO; PJ. BLANCO; A.. HUESPE; RA. FEIJÓO
Lugar:
Viena
Reunión:
Congreso; ECCOMAS 2012, 6th European Congress on Computational Methods in Applied Sciences and Engineering; 2012
Institución organizadora:
ECCOMAS
Resumen:
A two-scale variational formulation for modeling fracture problem of heterogeneous materials withsoftening, induced by strain localization and failure phenomena at micro scales, is here summarized.Also, some issues related with the numerical implementation of the model are addressed.The model follows the recent proposal of Sanchez et al. [1]. It considers two coupled mechanical problemsat different physical length scales, denoted as macro and micro scales, respectively. Every point,at the macro scale, is linked to a Representative Volume Element (RVE), and its constitutive responseemerges from a consistent homogenization of the micro-mechanical problem.Figure 1 depicts schematically the model. At the macroscopic level, the initially continuum body isallowed to develop a strong discontinuity kinematics, a cohesive crack, after the macroscopic pointfulfills a given failure criterion. The micro RVE model is used to drawn the homogenized stress inthe complete loading process: i.e., during the evolution of the continuum as well as during the strongdiscontinuity kinematics regimes.The homogenization model to describe the heterogeneous material during the continuous regime is astandard variational multiscale procedure, such as that described in [2]. However, when a macro-crackis activated, the classical homogenization model is modified in two key aspects: (i) a change in the rulethat defines how the increments of generalized macro-strains are inserted into the microscale and (ii)the Kinematical Admissibility concept, from where specific Strain homogenization Procedures are obtained.Then, as a consequence of the Hill-Mandel Variational Principle, this variational model providesan adequate homogenization formula for the traction acting on the macro-discontinuity surface.The consistent kinematical scale bridging demands the definition of new kinematical boundary conditionsin the RVE model that guarantee the existence of an objective stress homogenization responsewith the RVE-size. These RVE boundary conditions are imposed on the micro-displacement fluctuationfield.Both scales, the macro and micro, are discretized with the Finite Element Method. Then, a unifiedand systematic algorithmic treatment, for imposing the above mentioned generic kinematical boundaryconditions on the RVE model, is provided. As specific cases of boundary conditions that can be handledwith this numerical implementation are the: i) linear, ii) periodic or iii) minimal kinematical constraintsfor the standard homogenization procedure, as well as, the new kinematical constraints required by themultiscale cohesive model formulation.An adequate identification and characterization of all the possible boundary conditions are first specified.As a result, generic mixed kinematical constraints are defined that are imposed, in the RVE numericalmodel, through additional equations. The total d.o.f’s of the model are partitioned in free anddependent ones. The dependent ones are statically condensed. Particularly, we mention that the presentapproach allows for a flexible implementation of the periodic-aligned with the discontinuity boundaryconditions that is described in [3].Numerical examples shown the objectivity of the formulation, the capabilities of the new multi-scaleapproach to model material failure problems, as well as, the flexibility to impose different kind ofkinematical boundary conditions on the RVE.