A model for the mechanics of lipid membranes with non-uniform (coordinate-dependent) properties is discussed. The coordinate-dependent responses of the membranes are incorporated via the augmented non-uniform energy function and material parameters, which are dependent explicitly on the surface coordinates. We formulate the associated normal and tangential Euler equilibrium equations through which the coordinate-dependent responses of membranes are characterized. The admissible boundary conditions are taken from the existing non-linear model but reformulated and adopted to the present framework. Within the prescription of superposed incremental deformations, a compatible linear model is also formulated, from which a complete analytical solution describing the non-uniform responses of the membrane subjected to substrate–membrane interactions is obtained.

中文翻译：

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存在坐标依赖性非均匀性时脂质膜形态的分析

讨论了具有非均匀（坐标相关）特性的脂质膜力学模型。膜的坐标相关响应通过增强的非均匀能量函数和材料参数合并，这些参数明确依赖于表面坐标。我们制定了相关的法向和切向欧拉平衡方程，通过这些方程表征膜的坐标相关响应。可接受的边界条件取自现有的非线性模型，但重新制定并采用到当前框架中。在叠加增量变形的规定内，还制定了一个兼容的线性模型，