engleski

On Two-Scale Modelling of Softening Material Responses

The paper deals with the two-scale approaches for modelling of quasi-brittle and ductile softening responses of heterogeneous materials. The damage is induced at the microstructural level and after the homogenization procedure it is mapped via the constitutive stiffness at the macrolevel material point. In the case of quasi-brittle softening the nonlocal continuum theory employed in the𝐶1 continuous finite element formulation is applied at both micro- and macrolevel, and a second-order computational homogenization has been performed. The ductile damage is modelled by means of the first- and the second-order computational homogenization. At the first order homogenization the macrostructure is discretized by the regular displacement finite element formulation, while the mixed finite elements employing elastoplastic algorithm are used at microlevel, where the three microstructural volume elements are considered. On the contrary, only one microstructural volume element discretized by the mixed finite element is used at the second-order homogenization, while the discretization at macrolevel has been performed by the 𝐶1 continuous finite element formulation. All approaches proposed are verified in the standard benchmark examples.

Heterogeneous material, two-scale approach, computational homogenization, quasi-brittle damage, ductile damage, data-clustering

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