三维黏弹性模型在月球冷却产生的热应力计算中的应用

doi:10.7523/j.ucas.2022.059

摘要/Abstract

摘要： 月球冷却过程中积累的热应力是影响月球内部力学环境的重要因素之一。使用三维黏弹性有限元模型计算月球热应力的积累过程，并通过对比实验分析黏性参数对热应力大小的影响。计算结果表明月幔深部和浅部的热应力状态存在截然的分界。浅部热应力以切向挤压为主，挤压应力最大值出现在月壳底部；深部径向和切向正应力的大小主要受浅部径向正应力的控制，径向和切向热应力均为拉张，但由于黏性松弛差应力的积累和松弛动态平衡，而处于接近“静水压”状态。假设月球岩石圈的黏度大于10²⁸ Pa·s，则现今月壳和浅部月幔水平挤压热应力可以达到数百MPa，而月幔深部的拉张热应力可达到数十~100 MPa。因此，震源深度较浅的浅源月震可以用热应力来解释。而深源月震成因仍是一个困难的问题，推测深部月幔的拉张热应力为孔隙结构的发育提供了条件，而月幔底部的熔融层提供了高压孔隙流体，从而降低了深部月幔介质的破裂强度。

关键词: 黏弹性介质, 有限元法, 热应力, 月震

Abstract: Thermal stress of the moon due to cooling process is non-negligible in lunar evolution. We calculate the accumulation of thermal stress with 3-D viscoelastic model, and explore the influence of viscosity parameters on thermal stress through comparative experiments. Numerical results suggest that the thermal stress of lithosphere is utterly distinct from deep mantle. The lithosphere is under tangential compression that concentrates at the bottom of the crust because of unevenly distributed cooling rate and elastic strength; on the other hand, the accumulation and relaxation of thermal stress in deep mantle is balanced due to low viscosity, and the thermal stress is in a “hydrostatic” state, which is mainly controlled by the elastic surface. Under the assumption that viscosity of lunar lithosphere is greater than 10²⁸ Pa·s, the tangential compressive stress in lithosphere accumulates to several hundreds of MPa in the present day, while the tensile stress in deep mantle reaches up to 100 MPa. Consequently, part of the shallow moonquake events can be explained by thermal stress. However, the focal mechanism of deep moonquakes is still unclear. We speculate that the tensile thermal stress in deep mantle helps to develop pore structures, and the melting layer provides pore fluid with high pressure, which reduces the fracture strength of mantle medium.

Key words: viscoelastic medium, finite element method, thermal stress, moonquake

中图分类号:

P184

金一民, 陶莎, 石耀霖. 三维黏弹性模型在月球冷却产生的热应力计算中的应用[J]. 中国科学院大学学报, 2024, 41(1): 1-10.

JIN Yimin, TAO Sha, SHI Yaolin. Calculating the thermal stress of the moon in cooling process with 3-D viscoelastic model[J]. Journal of University of Chinese Academy of Sciences, 2024, 41(1): 1-10.

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