HIGH-PERFORMANCE MODEL ORDER REDUCTION IN NON-LINEAR MULTISCALE MODELLING OF CEMENTITIOUS MATERIALS

J. OLIVER; M. CAICEDO; A. HUESPE; J.L. MROGINSKI

Valencia

Congreso; Congress on Numerical Methods in Engineering - CMN 2017; 2017

Sociedad Española de Métodos Numéricos en Ingeniería (SEMNI) y Associação Portuguesa de Mecânica Teórica, Aplicada e Computacional (APMTAC).

Multi-scale computational homogenization methods (FE2) offer a huge potential to incorporate, to macroscopic non-linear modelling in concrete-like materials, the complexity of the material meso/micro-structure morphology, through simple and physically realistic models. However, they presently suffer the burden of their enormous computational cost, since the computational complexity (number of the involved operations) has a multiplicative character in terms of the involved sampling points at every scale. In this context, a powerful, and conceptually simple but efficient, multiscale computational model for fracture of cementitious materials has been recently presented by the authors in [1] and successfully applied to a number of 2D benchmarks. In this work, two combined techniques are explored and applied to that model: 1) low-dimension-space projection of the solution (reduced order modeling, ROM) and 2) reduced optimal quadrature (ROQ). They lead to a high performance reduced order model (HPROM) of the original high fidelity (HF) multiscale fracture problem [2], which dramatically diminish the computational demand, at the cost of a very small additional error. A number of representative simulations in 2D problems show high resulting speedups and linear scalability in terms of the problem complexity, which make think of the HPROM techniques as a possible way to make computational multi-scale computational fracture available for daily-life engineering problems.