论文标题
线性弹性中的能量与表面不连续性的积分表示
Integral representation for energies in linear elasticity with surface discontinuities
论文作者
论文摘要
在本文中，我们证明了在任意空间维度中有界变形（$ GSBD^p $）的通用特殊功能（$ GSBD^p $）的一般能量类别的整体表示公式。这种类型的功能自然出现在线性弹性固体与表面不连续性（包括骨折，损伤，不同弹性相之间的表面张力或材料空隙之间的现象）的建模。我们的方法基于Bouchittè等人在Bouchittè等人中设计的全球放松方法。 '98和$ GSBD^p $（Cagnetti-Chambolle-Scardia '20）的最近的Korn型不平等现象。我们的一般策略还允许将积分表示形式概括为$ SBD^p $，以二维为2（conti-forcardi-iurlano '16）获得，以更高的维度，并重新审视有界变化的通用特殊功能的框架（$ gsbv^p $）。
In this paper we prove an integral representation formula for a general class of energies defined on the space of generalized special functions of bounded deformation ($GSBD^p$) in arbitrary space dimensions. Functionals of this type naturally arise in the modeling of linear elastic solids with surface discontinuities including phenomena as fracture, damage, surface tension between different elastic phases, or material voids. Our approach is based on the global method for relaxation devised in Bouchittè et al. '98 and a recent Korn-type inequality in $GSBD^p$ (Cagnetti-Chambolle-Scardia '20). Our general strategy also allows to generalize integral representation results in $SBD^p$, obtained in dimension two (Conti-Focardi-Iurlano '16), to higher dimensions, and to revisit results in the framework of generalized special functions of bounded variation ($GSBV^p$).
