3D-2D降维中的空间异质性
Spatial heterogeneity in 3D-2D dimensional reduction
摘要：
根据Le Dret & Raoult的思想，提出了非均质薄膜模型作为圆柱形三维非均质非线性超弹性体的零厚度极限的合理性。产生了二维弹性能的具体表征。作为Bouchitté、Fonseca和Mascarenhas的推广，还研究了外载荷引起弯矩密度产生Cosserat向量场的情况。在整个过程中，3D-2D降维被视为弹性能量的$Γ$收敛问题，因为厚度趋于零。
英文摘要：
A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret & Raoult. Specific characterizations of the 2D elastic energy are produced. As a generalization of Bouchitté, Fonseca & Mascarenhas, the case where external loads induce a density of bending moment that produces a Cosserat vector field is also investigated. Throughout, the 3D-2D dimensional reduction is viewed as a problem of $Γ$-convergence of the elastic energy, as the thickness tends to zero.
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