Multiscale Degenerated Kinematics (MDK) Approach for the Design of Next Generation Laminated Composite Materials
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A novel multiscale computational methodology based on degenerated kinematics is presented in this study for the analysis of laminated composite materials. A hierarchical link is outlined based on a generalized Hill-Mandel energetic equivalence between macro and mesoscales represented by 2D plates and 1D RVE filaments, respectively. The approach employs the minimum essential kinematics and discretization at both scales and proves to capture the relevant phenomena at a lower cost compared to full 3D simulations and with higher accuracy when compared to the approaches based on Esquivalent Single Layer (ESL) theories. The approach overcomes the main drawback of First Order Shear Deformation Theory (FSDT), i.e. the consideration of a constant distribution of the transverse shear strains throughout the plate thickness, by inserting 3D equilibrium equations in a weak format within the RVE Boundary Value Problem (BVP). Such novelty has proven to provide highly accurate stress distributions with minimal kinematics at the mesoscale when compared to full 3D reference simulations. The multiscale methodology is able to outperform computational homogenization schemes based on full 3D macro and mesoscopic samples. This renders the proposed methodology as an attractive alternative to improve virtual modelling of next generation laminate composite materials in order to accelerate its costly qualification and certification campaigns within aerospace and aeronautical industries.
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