Auxetic behaviour , the unphysical transverse expansion during uniaxial tension, is a common and undesirable feature of classical anisotropic hyperelastic constitutive models for soft tissue. In this study we uncover the underlying mechanism of such behaviour; high levels of in-plane compaction occurs due to increasing tension in strain-stiffening fibres, leading to unphysical out-of-plane expansion. We demonstrate that auxetic behaviour is primarily influenced by the ratio of fibre to matrix stiffness, and is accentuated by strain-stiffening fibres in a constant stiffness matrix (e.g., the widely used neo-Hookean matrix with exponentially stiffening fibres). We propose a new bilinear strain stiffening fibre and matrix (BLFM) model which allows close control of the fibre-matrix stiffness ratio, thereby robustly eliminating auxetic behaviour. We demonstrate that our model provides accurate prediction of experimentally observed out-of-plane compaction, in addition to stress-stretch anisotropy, for arterial tissue subjected to uniaxial tension testing.

在软组织的经典各向异性超弹性本构模型中，惯性行为是单轴拉伸过程中的非物理横向膨胀，这是常见的和不希望的特征。在这项研究中，我们发现了这种行为的潜在机制。由于应变增强纤维中张力的增加，发生了高水平的平面内压实，从而导致非物理的平面外膨胀。我们证明，拉力行为主要受纤维与基质刚度之比的影响，并由恒定刚度基质（例如，广泛使用的具有指数刚度纤维的新胡克矩阵）中的应变刚化纤维所加重。我们提出了一种新的双线性应变增强纤维和基质（BLFM）模型，该模型允许对纤维-基质刚度比进行严格控制，从而稳健地消除了膨胀行为。