Theory of residual stresses with application to an arterial geometry
Theory of residual stresses with application to an arterial geometry
复制标题
残余应力理论及其在动脉几何形状中的应用
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
Jonas Stålhand
中科院分区：
文献类型：
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作者：
A. Klarbring;T. Olsson;Jonas Stålhand
本文介绍了残余应力理论，并将其应用于生物力学，特别是动脉。对于超弹性材料，我们使用初始局部变形张量K作为残余应变的描述符。这个张量，一般来说，不是一个整体变形的梯度，和一个无应力的参考配置，表示为B -，因此，变得不兼容。任何兼容的参考配置B 0通常都将受到残余应力。然而，当一定的曲率张量消失，实际上存在一个兼容的和无应力的配置，我们表明，传统的治疗动脉中的残余应力，使用开角的方法，涉及到这样的情况。非线性弹性力学的边值问题最好在固定的积分区域上进行表述。对于残余应力体，自然会出现三种这样的公式：（i）与具有非欧几里德度量结构的B 0有关的公式;（ii）与具有欧几里德度量结构的B 0有关的公式;和（iii）与不相容构型B -有关的公式。我们陈述了这些公式，表明（i）和（ii）在不可压缩的情况下是一致的，并且由于不相容性，在B -上的公式中出现了一个额外的项。
This paper presents a theory of residual stresses, with applications to biomechanics, especially to arteries. For a hyperelastic material, we use an initial local deformation tensor K as a descriptor of residual strain. This tensor, in general, is not the gradient of a global deformation, and a stress-free reference configuration, denoted B - , therefore, becomes incompatible. Any compatible reference configuration B 0 will, in general, be residually stressed. However, when a certain curvature tensor vanishes, there actually exists a compatible and stress-free configuration, and we show that the traditional treatment of residual stresses in arteries, using the opening–angle method, relates to such a situation. Boundary value problems of nonlinear elasticity are preferably formulated on a fixed integration domain. For residually stressed bodies, three such formulations naturally appear: (i) a formulation relating to B 0 with a non-Euclidean metric structure; (ii) a formulation relating to B 0 with a Euclidean metric structure; and (iii) a formulation relating to the incompatible configuration B - . We state these formulations, show that (i) and (ii) coincide in the incompressible case, and that an extra term appears in a formulation on B - , due to the incompatibility.
影响因子：
2.4
作者：
RODRIGUEZ, EK;HOGER, A;MCCULLOCH, AD
通讯作者：
MCCULLOCH, AD