弹性模型-毕业论文外文翻译.docx

word文档可编辑 附录1 外文翻译原文 Elastic models Anisotropy An isotropic material has the same properties in all directions—we cannot dis-tinguish any one direction from any other. Samples taken out of the ground with any orientation would behave identically. However, we know that soils have been deposited in some way—for example, sedimentary soils will know about the vertical direction of gravitational deposition. There may in addition be seasonal variations in the rate of deposition so that the soil contains more or less marked layers of slightly different grain size and/or plasticity. The scale of layering may be suffciently small that we do not wish to try to distinguish separate materials, but the layering together with the directional deposition may nevertheless be suffcient to modify the properies of the soil in different directions—in other words to cause it to be anisotropic. We can write the stiffness relationship between elastic strain increment and stress increment compactly as whereis the stiffness matrix and henceis the compliance matrix. For a completely general anisotropic elastic material whereeachlettera,b,... is,inprinciple,anindependentelasticpropertyandthe necessary symmetry of the sti?ness matrix for the elastic material has reduced the maximum number of independent properties to 21. As soon as there are material symmetries then the number of independent elastic properties falls (Crampin, 1981). For example, for monoclinic symmetry (z symmetry plane) the compliance matrix has the form: and has thirteen elastic constants. Orthorhombic symmetry (distinct x, y and z symmetry planes) gives nine constants: whereas cubic symmetry (identical x, y and z symmetry planes, together with planes joining opposite sides of a cube) gives only three constants: Figure 3.9: Independent modes of shearing for cross-anisotropic material If we add the further requirement that and set and ，t