The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials
The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials
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不可压缩弹性材料有限平面应变裂纹尖端附近的平衡场
DOI：
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发表时间：
1982
期刊：
影响因子：
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通讯作者：
R. A. Stephenson
中科院分区：
文献类型：
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作者：
R. A. Stephenson
本文研究了平面应变条件下含无牵引力平面裂纹的无限长板的变形和应力。分析是在均质各向同性不可压缩弹性固体的完全非线性平衡理论框架内进行的。对于相当广泛的一类这类材料和无限大的一般载荷条件，推导了适合于裂纹尖端附近各种场量的渐近估计。对于所考虑的一个子类材料，这些结果--与线性化理论的类似预测相反--导致了裂纹在其尖端附近张开的结论，即使所施加的载荷相对于裂纹平面是反对称的(例如，II型载荷)。进一步证明了与这种载荷相对应的非线性整体裂纹问题一般不允许有反对称解。
This investigation is concerned with the deformations and stresses in a slab of all-around infinite extent containing a traction-free plane crack, under conditions of plane strain. The analysis is carried out within the framework of the fully nonlinear equilibrium theory of homogeneous and isotropic incompressible elastic solids. For a fairly wide class of such materials and general loading conditions at infinity, assymptotic estimates appropriate to the various field quantities near the crack-tips are deduced. For a subclass of the materials considered, these results — in contrast to the analogous predictions of the linearized theory — lead to the conclusion that the crack opens up in the neighborhood of its tips even if the applied loading is antisymmetric about the plane of the crack, (e.g., Mode II loading). It is shown further that the non-linear global crack problem corresponding to such a loading in general cannot admit an antisymmetric solution.