A NUMERICAL CALCULATION APPROACH BASED ON FEM FOR LONG-TERM DEFORMATION OF LITHOSPHERE
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摘要: 有限单元法以其灵活性和精确性，成为固体地球科学中广为使用的数值方法。从短周期的地震活动到长周期的岩石圈变形、地幔对流，甚至行星演化，有限单元法几乎在固体地球科学的各个领域都占据着十分重要的位置。随着研究的深入，某些特定的地学问题给有限元计算带来挑战，尤其是岩石圈尺度大变形的数值计算，比如俯冲带的演化、剪切带中塑性流变导致的应力集中。基于显式有限元，尝试考虑粘弹塑性岩石圈大变形过程的数值计算。应用Marker-In-Cell（MIC）方法处理物质迁移。在描述基本原理和流程的基础上，对粘弹性变形、弹塑性变形、大变形过程及热传递过程等核心模块分别做了基准测试，而这四个模块是模拟岩石圈长期变形的关键。由测试结果和其他学者的（解析或数值）研究结果比对情况来看，受测试的核心模块基本达到了测试要求。可以预见，现有的基本算法可以满足研究岩石圈大变形的需要，进一步的具体研究工作将探讨这类问题。从科学问题层面讲，逐渐复杂的科学问题有利于数值模型的成熟。已达到基准测试的数值方法对下一步开展一些具体的地球动力学数值模拟研究有实际意义。Abstract: Finite element method (FEM), which is very important in almost all fields of solid earth sciences, has been widely used in numerical experiments in solid earth sciences due to its flexibility and precision, ranging from short-term seismic activity to long-term lithospheric deformation, mantle convection and even planetary evolution. However, with the deepening of the research, some specific geological problems bring challenges to the finite element calculation, especially the numerical calculation of large-scale lithosphere deformation, such as the evolution of subduction zone and stress localization caused by plastic rheology in shear zone. Based on explicit FEM, an attempt is made to numerical calculation in the process of large deformation of lithosphere considering visco-elastic-plasticity in this study. Marker-In-Cell (MIC) approach was used in processing each material migration. On the basis of describing the basic principle and process, the core modules of visco-elastic deformation, elastic-plastic deformation, large deformation and heat transfer were tested. These four modules are the key to simulate the long-term deformation of the lithosphere. According to the comparison between the test results and the previous simulation results, the tested core modules basically meet the test requirements. It can be predicted that the existing basic algorithms can meet the needs of studying the large deformation of the lithosphere, and further specific research work will explore this kind of problem.
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Key words:
- finite element method /
- large deformation /
- visco-elastic-plastic materials /
- geodynamics
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图 1 直角坐标中的三角形单元(e)的面积坐标
Figure 1. Triangle' s area-coordinates in cartesian coordinates
图 2 马克斯韦尔体应力积累过程的边界条件和数值解与解析解的对比
a—边界条件；b—数值解(线)与解析解(圈)的对比
Figure 2. Stress accumulation of a Maxwell body: boundary conditions and the comparison between numerical solutions (line) and analytical solutions (circle)
图 3 弹塑性体应力积累过程的边界条件和数值解与解析解的对比
a—边界条件；b—数值解(线)与解析解(圈)的对比
Figure 3. Stress accumulation of elastic-plastic body: boundary conditions and the comparison between numerical solutions (line) and analytical solutions (circle)
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