论文标题
从非线性到线性格里菲斯骨折的通过
Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture
论文作者
论文摘要
我们表征了从非线性到线性化的格里菲斯 - 骨折理论的段落，这是在非互相构造约束下的。特别是，在SBV^2中满足ciarlet-Nečas条件的变形序列，并确保能量的收敛性，被证明可以在GSBD^2中接受渐近表示，满足合适的接触条件。通过明确的反例，我们证明，如果能量的收敛性不存在，则该结果会失败。我们进一步证明，满足接触条件的每个限制位移都可以通过满足Ciarlet-Nečas条件的变形序列来近似。证明依赖于GSBD2中的分段korn-poincaré不平等，仔细爆破了跳跃点，以及精制的GSBD^2密度结果，可确保近似值的增强接触条件。
We characterize the passage from nonlinear to linearized Griffith-fracture theories under non-interpenetration constraints. In particular, sequences of deformations satisfying a Ciarlet-Nečas condition in SBV^2 and for which a convergence of the energies is ensured, are shown to admit asymptotic representations in GSBD^2 satisfying a suitable contact condition. With an explicit counterexample, we prove that this result fails if convergence of the energies does not hold. We further prove that each limiting displacement satisfying the contact condition can be approximated by an energy-convergent sequence of deformations fulfilling a Ciarlet-Nečas condition. The proof relies on a piecewise Korn-Poincaré inequality in GSBD2, on a careful blow-up analysis around jump points, as well as on a refined GSBD^2-density result guaranteeing enhanced contact conditions for the approximants.
