从非线性模型推导线性化Griffith能量
A derivation of linearized Griffith energies from nonlinear models
摘要：
我们推导出格里菲斯泛函的框架内的线性弹性非线性和框架无关能量脆性断裂通过伽玛收敛。的收敛性给出了在重新缩放的位移场测量的距离变形分段刚性运动。极限模型的结构由材料的分区、相应的分段刚性变形和位移场组成，它们分别定义在裂纹体的每个分量上。除了线性化的Griffith能量之外，极限泛函还包括断开样本的部分所必需的分割能量。
英文摘要：
We derive Griffith functionals in the framework of linearized elasticity from nonlinear and frame indifferent energies in brittle fracture via Gamma-convergence. The convergence is given in terms of rescaled displacement fields measuring the distance of deformations from piecewise rigid motions. The configurations of the limiting model consist of partitions of the material, corresponding piecewise rigid deformations and displacement fields which are defined separately on each component of the cracked body. Apart from the linearized Griffith energy the limiting functional comprises also the segmentation energy which is necessary to disconnect the parts of the specimen.
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