论文标题
通过渐近扩展对离散扩散模型的均质化
Homogenization of discrete diffusion models by asymptotic expansion
论文作者
论文摘要
在许多工程问题中，异质材料的扩散行为至关重要。考虑到此类材料的内部结构的数值模型是可靠的，但在计算上非常昂贵。通过使用离散模型可以部分减轻这种负担，但是即使这样，实际应用也仅限于相对较小的材料量。 本文为离散扩散模型制定了均质化方案。应用渐近膨胀均质化用于区分（i）通过标准有限元法近似的连续宏观描述和（ii）材料的局部代表体积元素（RVE）中完全分辨的离散中尺度描述。讨论了具有非线性本构关系的瞬态和稳态变体。在所有情况下，由此产生的离散RVE问题成为一个简单的线性稳态问题，很容易预先计算。量表分离可显着减少计算时间，允许解决实际问题的解决方案，主要由宏观上有限元离散化引入的误差可忽略不计。
Diffusion behaviors of heterogeneous materials are of paramount importance in many engineering problems. Numerical models that take into account the internal structure of such materials are robust but computationally very expensive. This burden can be partially decreased by using discrete models, however even then the practical application is limited to relatively small material volumes. This paper formulates a homogenization scheme for discrete diffusion models. Asymptotic expansion homogenization is applied to distinguish between (i) the continuous macroscale description approximated by the standard finite element method and (ii) the fully resolved discrete mesoscale description in a local representative volume element (RVE) of material. Both transient and steady-state variants with nonlinear constitutive relations are discussed. In all the cases, the resulting discrete RVE problem becomes a simple linear steady-state problem that can be easily pre-computed. The scale separation provides a significant reduction of computational time allowing the solution of practical problems with a negligible error introduced mainly by the finite element discretization at the macroscale.
