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arXiv 0711.4664cond-mat.soft
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弹性体和软组织的不稳定性

Instabilities in elastomers and soft tissues

Alain Goriely, Michel Destrade, Martine Ben Amar

摘要:

生物软组织表现出与橡胶类材料(弹性体)截然不同的弹性特性。为了更好地了解本构关系在确定材料的负载下的响应的作用,我们比较了三种不同类型的不稳定性(两个在压缩,一个在扩展)在超弹性的各种形式的应变能函数通常用于弹性体和软组织。令人惊讶的是,我们发现软组织的应变硬化特性并不总是稳定的材料。特别是,我们表明,压缩半空间和压缩球形厚壳的稳定性分析可以导致相反的结论:软组织材料是更稳定的弹性体在前一种情况下,在后一种情况下不太稳定。

英文摘要:

Biological soft tissues exhibit elastic properties which can be dramatically different from rubber-type materials (elastomers). To gain a better understanding of the role of constitutive relationships in determining material responses under loads we compare three different types of instabilities (two in compression, one in extension) in hyperelasticity for various forms of strain energy functions typically used for elastomers and for soft tissues. Surprisingly, we find that the strain-hardening property of soft tissues does not always stabilize the material. In particular we show that the stability analyses for a compressed half-space and for a compressed spherical thick shell can lead to opposite conclusions: a soft tissue material is more stable than an elastomer in the former case and less stable in the latter case.

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