A new multiscale computational method is developed for the elasto-plastic analysis of heterogeneous continuum materials with both periodic and random microstructures. In the method, the multiscale base functions which can efficiently capture the small-scale features of elements are constructed numerically and employed to establish the relationship between the macroscopic and microscopic variables. Thus, the detailed microscopic stress fields within the elements can be obtained easily. For the construction of the numerical base functions, several different kinds of boundary conditions are introduced and their influences are investigated. In this context, a two-scale computational modeling with successive iteration scheme is proposed. The new method could be implemented conveniently and adopted to the general problems without scale separation and periodicity assumptions. Extensive numerical experiments are carried out and the results are compared with the direct FEM. It is shown that the method developed provides excellent precision of the nonlinear response for the heterogeneous materials. Moreover, the computational cost is reduced dramatically.
An extended multiscale finite element method is developed for small-deformation elasto-plastic analysis of periodic truss materials. The base functions constructed numerically are employed to establish the relationship between the macroscopic displacement and the microscopic stress and strain. The unbalanced nodal forces in the microscale of unit cells are treated as the combined effects of macroscopic equivalent forces and microscopic perturbed forces, in which macroscopic equivalent forces are used to solve the macroscopic displacement field and microscopic perturbed forces are used to obtain the stress and strain in the microscale to make sure the correctness of the results obtained by the downscale computation in the elastic-plastic problems. Numerical examples are carried out and the results verify the validity and efficiency of the developed method by comparing it with the conventional finite element method.
A spatial and temporal multiscale asymptotic homogenization method used to simulate thermo-dynamic wave propagation in periodic multiphase materials is systematically studied. A general field governing equation of thermo-dynamic wave propagation is expressed in a unified form with both inertia and velocity terms. Amplified spatial and reduced temporal scales are, respectively, introduced to account for spatial and temporal fluctuations and non-local effects in the homogenized solution due to material heterogeneity and diverse time scales. The model is derived from the higher-order homogenization theory with multiple spatial and temporal scales. It is also shown that the modified higher-order terms bring in a non-local dispersion effect of the microstructure of multiphase materials. One-dimensional non-Fourier heat conduction and dynamic problems under a thermal shock are computed to demonstrate the efficiency and validity of the developed procedure. The results indicate the disadvantages of classical spatial homogenization. Copyright (c) 2006 John Wiley & Sons, Lt
3D elastoplastic frictional contact problems with orthotropic friction law belong to the unspecified boundary problems with nonlinearities in both material and geometric forms. One of the difficulties in solving the problem lies in the determination of the tangential slip states at the contact points. A great amount of computational efforts is needed so as to obtain high accuracy numerical results. Based on a combination of the well known mathematical programming method and iterative method, a finite element model is put forward in this paper. The problems are finally reduced to linear complementarity problems. A specially designed smoothing algorithm based on NCP-function is then applied for solving the problems. Numerical results are given to demonstrate the validity of the model and the algorithm proposed.
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