An efficient multi-scale method for non-linear analysis of composite structures

Abstract

The use of multi-scale procedures is encouraged by the continuous increase of computational capacity, but it is still a challenge performing a non-linear analysis of a real composite structure without the aid of large computers. This work proposes a strategy to conduct non-linear two-scale analysis in an efficient way. The proposed method considers that in a large structure, in general, material non-linear processes only take place in a localized region (or in a reduced number of finite elements, if a FE method is used). The strategy determines the elements that require a non-linear analysis defining of a non-linear activation function that accounts for the failure of the most critical point in the microstructure. The procedure conserves the dissipated energy through the scales, being mesh independent as the mesh objectivity concept is extended to the microstructure. The validity of the strategy proposed is proved with the analysis of academic examples showing not only the mesh independency but also the reduction of computational cost. Finally, an industrial composite component is solved using a standard computer, showing that the proposed strategy is capable of reducing the computational cost from 32 days and 14 hours (required by a classical multi-scale method) to less than 12 hours.

Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method

“…In general, these strategies introduced in the formulation a characteristic length as a numerical parameter which is coming from the RVE domain size e.g. the finite element size [94], the bandwidth of crack [126] or the bandwidth of cohesive zone [89]. In addition, computational homogenization schemes using a gradient-enhanced to connect the scales were developed [60,114,62,66,67,51], in these kind of approaches it is not necessary to introduce artificially a length-scale parameter because it arrives naturally.…”

“…In addition, several recent contributions have been presented aiming at improving the robustness and reducing the computational cost e.g. adaptive strategies to solve the micro-scale problem only the minimum number of times necessary [126,94], adaptive sub-incremental strategies to ensure the convergence of the multiscale solution in the presence of several sources of non-linearity [112,100], modelorder reduction techniques [129,80,65,42] which use the Proper Orthogonal Decomposition (POD), or proper generalized decomposition, to obtain the reduced set of empirical shape functions.…”

“…The proposed EFOCH has been implemented in PLCd [99,93], a parallel FE code that works with 3D solid geometries. The PLCd program has already implemented the FOCH described previously [95,94]. The microscopic displacement field obtained from the solution of the microscopic BVP must satisfy the boundary conditions defined previously, in Section 4.2.1.…”

“…Therefore, it does not require any composite constitutive assumption or compatibility equation to address the composite response [95]. And, there are not restriction on the constitutive model used in the component materials, even non-linear materials and time-dependency models can be taken into account [110,90,94].…”

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

“…Although this method is known to be computationally expensive, it is trivially parallelizable as the computations at the microscale are completely independent of each other [367][368][369][370]. Also, a number of methods have been recently developed aiming at reducing the computational cost and increasing the accuracy of multiscale analysis [371][372][373][374][375]. These methods are typically based on decomposing the macroscale problem and selective usage of computational techniques discussed in Refs.…”