Generalized thermo-mechanical framework for heterogeneous materials through asymptotic homogenization

Analysis and optimization of heterogeneous materials using the variational asymptotic method for unit cell homogenization

The variational asymptotic method for unit cell homogenization is used to find the sensitivity of the effective properties of periodically heterogeneous materials, within a periodic base-cell. The sensitivities are found by the direct differentiation of the variational asymptotic method for unit cell homogenization (VAMUCH) and by the method of adjoint variables. This sensitivity theory is impl...

A Review of Homogenization Techniques for Heterogeneous Materials

A dynamic lattice model for heterogeneous materials

In this paper, the mechanical behavior of three-phase inhomogeneous materials is modeled using the meso-scale model with lattice beams for static and dynamic analyses. The Timoshenko beam theory is applied instead of the classical Euler-Bernoulli beam theory and the mechanical properties of lattice beam connection are derived based on the continuum medium using the non-local continuum theory. T...

Homogenization of heterogeneous tissue scaffold: A comparison of mechanics, asymptotic homogenization, and finite element approach

Actual prediction of the effective mechanical properties of tissue scaffolds is very important for tissue engineering applications. Currently common homogenization methods are based on three available approaches: standard mechanics modeling, homogenization theory, and finite element methods. Each of these methods has advantages and limitations. This paper presents comparisons and applications o...

Numerical Homogenization of Heterogeneous Anisotropic Linear Elastic Materials

Abstract. The numerical homogenization of anisotropic linear elastic materials with strongly heterogeneous microstructure is studied. The developed algorithm is applied to the case of trabecular bone tissue. In our previous work [1], the orthotropic case was considered. The homogenized anisotropic tensor is transformed according to the principle directions of anisotropy (PDA). This provides opp...