The Quadtree-scaled Boundary Finite Element Method For Estimation Of Effective Parameters Of Heterogeneous Viscoelastic Materials

Many heterogeneous materials(such as concrete/polymer matrix composites)have viscoelastic properties and are widely used in engineering,which shows good mechanical properties in macroscopic via designing physical properties of the composite materials,internal microstructure and so on.Therefore,viscoelastic composite materials are increasingly used in construction,aviation,aerospace and other fields.Due to the complex microstructure of the heterogeneous viscoelastic material,the macroscopic viscoelastic behavior of the composite becomes more complicated.Therefore,the macroscopic equivalent properties of heterogeneous viscoelastic materials(such as equivalent creep/relaxation properties)are important indicators for describing their material properties and macroscopic performance evaluation,and are also important parameters for their performance optimization design.The design and application of heterogeneous viscoelastic materials are closely integrated with materials science and engineering technology,which makes the research on the macroscopic equivalent performance of materials have a solid engineering background and urgent needs,and thus the research on the equivalent parameters of heterogeneous viscoelastic materials has important theoretical exploration value and guiding significance for material design.The study of equivalent parameters of heterogeneous viscoelastic materials can start from two Strategies: "frequency domain" and "time domain".In this paper,a new numerical calculation model is proposed based on the combination of quad-tree method,the scaled boundary element method(SBFEM)and a piecewise adaptive algorithm from a “time domain” perspective.The main advantages are:(1)The quad-tree method provides a convenient image-based mesh generation technique by adopting regular structured mesh,and only fine is used in the area around the interfaces of inclusions;(2)The difficulties caused by hanging nodes in the traditional quad-tree technology are naturally avoid by the use of SBFEM;(3)In the time domain,a piecewise adaptive algorithm can adaptively ensure the accuracy of calculation at different time steps.The proposed method is verified by numerical examples,and the influence of the properties of heterogeneous material inclusions(shape,proportion,distribution,etc.)on mechanical behavior of materials is studied,and the parameters of viscoelastic equivalent material are predicted based on the proposed model,the numerical results are well agreed with analytical solutions or reference solutions.The main research in this paper is:(1)Quadtree/octree tree directly reads images of heterogeneous materials to achieve mesh segmentation(2)Based on SBFEM and time domain adaptive algorithm,a finite element recursive scheme for solving viscoelastic mechanics of heterogeneous materials is established.Compared with ABAQUS,the proposed method gives satisfactory estimates and is highly efficient under the same precision.(3)Based on viscoelastic numerical simulation results based on large sample of heterogeneous materials,the Gauss-Newton iterative algorithm is adopted to inverse the viscoelastic overall equivalent modulus of heterogeneous materials.The work of this paper mainly analyzes the viscoelastic mechanical behavior of heterogeneous materials without periodic structure and predict equivalent parameters from the numerical simulation approach,which provides a reference solution for improving the design of material properties.