Enhanced transformation field analysis for reduced-order modeling of problems with cohesive interfaces

We propose a novel transformation field analysis (TFA) technique designed to solve problems with cohesive interfaces. The TFA approach, originally proposed for homogenization purposes, is (i) extended to account for arbitrary boundary conditions (i.e. not only those suitable for homogenization), (ii) endowed with an iterative Newton–Raphson solution scheme involving the consistent tangent matrix and (iii) provided with an arc-length strategy to follow possible snap-back branches. The extension to arbitrary boundary conditions leads to an efficient reduced-order modeling approach for solving complex non-linear problems. Numerical tests demonstrate that the approach performs well in challenging scenarios with several interfaces, and that sharp and multiple snap-back branches can be followed. The comparison with finite element results shows that the proposed technique yields fast yet accurate solutions.