The active response of cells to mechanical cues due to their interaction with the environment has been of increasing interest, since it is involved in many physiological phenomena, pathologies, and in tissue engineering. In particular, several experiments have shown that, if a substrate with overlying cells is cyclically stretched, they will reorient to reach a well-defined angle between their major axis and the main stretching direction. Recent experimental findings, also supported by a linear elastic model, indicated that the minimization of an elastic energy might drive this reorientation process. Motivated by the fact that a similar behaviour is observed even for high strains, in this paper we address the problem in the framework of finite elasticity, in order to study the presence of nonlinear effects. We find that, for a very large class of constitutive orthotropic models and with very general assumptions, there is a single linear relationship between a parameter describing the biaxial deformation and \(\cos ^2\theta _{\mathrm{eq}}\), where \(\theta _{\mathrm{eq}}\) is the orientation angle of the cell, with the slope of the line depending on a specific combination of four parameters that characterize the nonlinear constitutive equation. We also study the effect of introducing a further dependence of the energy on the anisotropic invariants related to the square of the Cauchy–Green strain tensor. This leads to departures from the linear relationship mentioned above, that are again critically compared with experimental data.

由于细胞与环境的相互作用，细胞对机械线索的主动反应越来越受到关注，因为它涉及许多生理现象、病理学和组织工程。特别是，一些实验表明，如果具有覆盖细胞的基底被循环拉伸，它们将重新定向以在它们的主轴和主拉伸方向之间达到一个明确定义的角度。最近的实验结果也得到了线性弹性模型的支持，表明弹性能量的最小化可能会推动这种重新定向过程。受即使在高应变下也观察到类似行为这一事实的推动，在本文中，我们在有限弹性的框架内解决该问题，以研究非线性效应的存在。我们发现，\(\cos ^2\theta _{\mathrm{eq}}\)，其中\(\theta _{\mathrm{eq}}\)是单元的方向角，线的斜率取决于表征非线性本构方程的四个参数的特定组合。我们还研究了引入能量对与柯西-格林应变张量平方相关的各向异性不变量的进一步依赖的影响。这导致偏离上述线性关系，再次与实验数据进行严格比较。