The Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard \(\varGamma \)-convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard \(\varGamma \)-convergence also appears to be removed in the cases where contact with that method and ours can be made.

基尔霍夫-洛夫（Kirchhoff-Love）假设表达了一个运动学约束，当它的一个尺寸远小于其他两个尺寸时，就可以认为对三维物体的变形是有效的，板的情况就是这样。这个假设具有悠久的历史，与生活的沧桑格格不入：甚至对其父权制也提出了质疑，并且最近使用了严格的降维工具（基于标准\（\ varGamma \）-convergence）与它不兼容。我们发现，对基希霍夫-洛夫（Kirchhoff-Love）假设的适当修订版是从三维非线性自由能泛函导出弹性板的二维变分模型的有价值的手段。如此获得的用于多种材料的弯曲能量还显示出了对板中表面进行拉伸的措施（以及预期的弯曲措施）。在可以使用该方法和我们的方法的情况下，似乎也消除了与标准\（\ varGamma \）-收敛的不兼容。