A Research On Computational Homogenization For Composite Structures

In complex working conditions,the coexisting of geometrical nonlinearity and material nonlinearity,the coupling between multi-physics and the interaction between macro and micro scales can be frequently found in composite structures,which make it difficult to accurately predict the behavior of structures.Up till now,micro material and macro structure integrated numerical methods for composite structures are still to be improved.Thus,developing macro-micro computational homogenization scheme and investigating the interaction between material and structure are of importance for predicting the multi-scale behavior of composite structures and further aiding their design and applications.There are some difficulties in the macro-micro integrated analysis for composite structures:(1)In macro-micro integrated geometrical nonlinear problems,such as buckling and wrinkling,there are too many instability modes and dense bifurcations to be followed;(2)In multi-scale and multi-physics problems,the micro geometry and material properties are complicated,which makes it difficult to create geometrical model and formulate the constitutive relationship;(3)In the commonly used concurrent computational homogenization scheme,a large number of repeated micro problems are required to be solved for each macro integration point,resulting in low computational efficiency.Based on computational homogenization methods,this thesis developed efficient material-structure integrated methods,and studied the multi-scale mechanical behavior of composite structures.Firstly,a concurrent multi-scale finite element model was constructed for the compression instability of long fiber reinforced composite structures,by introducing the Fourier reduction model and asymptotic numerical method in the framework of concurrent computational homogenization method.With this model,the multi-scale instability of long fiber reinforced composite structures was revealed.Secondly,by introducing the computational homogenization framework and the constitutive law of shape memory alloy in ABAQUS,a general multi-scale tool was developed to accurately simulate the multi-scale superelastic response and shape memory effect of composite structures with shape memory alloy inclusions.Thirdly,by decoupling the macro and micro scales which interact with each other,a material-genome-driven computational homogenization method was developed.In this method,the micro problems were solved offline,while the macro problems were solved online.Thus,the computational efficiency of the online macro analysis was significantly improved.Finally,in the framework of data-driven computational homogenization,a structure-genomedriven method with fewer integration points and lower database dimension than those of material-genome-driven method was proposed.In this method,the control functional of data-driven algorithm was reconstructed by structure model reduction techniques,and the structure genome database was collected by computational homogenization method.