Tubular and rod-like structures in nature can experience twist due to non-torque loadings such as inflation and extension. Interestingly, the twist can change its direction and even vanish along the loading path. These counter-intuitive phenomena are referred to as inversion and perversion, respectively, and stem from the anisotropic structure of the tubes. In this work we show that a similar response can be achieved with bi-layer tubes comprising two isotropic layers that are twisted in different directions and adhered together. We refer to these tubes as geometrically incompatible. By employing the Gent model, we find that the inversion and perversion effects stem from the changes in the torsional stiffness of the layers as a result of inflation or extension. We derive relations for the torsional stiffness in terms of the geometry, the stiffness, the lock-up stretch which accounts for the strain-stiffening effect, and the deformation. We illustrate that different thickness and stiffness ratios between the layers lead to a variety of induced twist responses. To better understand the influence of the geometric and the material properties of the layers on the overall twist response, we map the combinations of thickness and stiffness ratios that lead to inversion and perversion and demonstrate the richness of these phenomena. The findings and insights from this work are of value to a wide range of applications, including the design of soft rotational robots, artificial muscles, and soft torsional actuators.

管状和杆状结构在自然中会由于非扭矩载荷（例如膨胀和伸展）而发生扭曲。有趣的是，扭曲可以改变其方向，甚至在加载路径上消失。这些与直觉相反的现象分别称为反转和反转，它们是由于管道的各向异性结构引起的。在这项工作中，我们表明，使用包含两个各向同性层的双层管，可以实现相似的响应，这些层在不同方向上扭曲并粘附在一起。我们将这些管称为几何不兼容。通过使用Gent模型，我们发现反演和变态效应源于由于膨胀或伸展而引起的各层扭转刚度的变化。我们根据几何形状，刚度，锁定拉伸是考虑到应变加劲效果和变形的原因。我们说明了层之间不同的厚度和刚度比会导致多种诱发的扭曲响应。为了更好地理解层的几何和材料特性对整体扭转响应的影响，我们绘制了导致倒立和变形的厚度和刚度比的组合，并证明了这些现象的丰富性。这项工作的发现和见解对广泛的应用具有价值，包括软旋转机器人，人造肌肉和软扭转致动器的设计。我们说明了层之间不同的厚度和刚度比会导致多种诱发的扭曲响应。为了更好地理解层的几何和材料特性对整体扭转响应的影响，我们绘制了导致倒立和变形的厚度和刚度比的组合，并证明了这些现象的丰富性。这项工作的发现和见解对广泛的应用具有价值，包括软旋转机器人，人造肌肉和软扭转致动器的设计。我们说明了层之间不同的厚度和刚度比会导致多种诱发的扭曲响应。为了更好地理解层的几何和材料特性对整体扭转响应的影响，我们绘制了导致倒立和变形的厚度和刚度比的组合，并证明了这些现象的丰富性。这项工作的发现和见解对广泛的应用具有价值，包括软旋转机器人，人造肌肉和软扭转致动器的设计。我们绘制了导致倒立和变形的厚度和刚度比的组合，并证明了这些现象的丰富性。这项工作的发现和见解对广泛的应用具有价值，包括软旋转机器人，人造肌肉和软扭转执行器的设计。我们绘制了导致倒立和变形的厚度和刚度比的组合，并证明了这些现象的丰富性。这项工作的发现和见解对广泛的应用具有价值，包括软旋转机器人，人造肌肉和软扭转致动器的设计。