多尺度损伤本构模型及其在岩土力学中的应用

Multiscale methods in geomechanics are devoted to describing and modelling global mechanical behaviors of geomaterials from microstructural insights. For example,stress-strain relations of granular materials can be established from local information at contact planes (force network, contact and sliding). As for microcracked rocks, homogenization-based micromechanical constitutive damage formulations allow properly taking into account some complex phenomena, such as cracks' propagation, spatial distribution, opening or closed state as well as frictional sliding occurring at the lips. Theoretically, capable of overcoming, to a large extent, some limitations shown by macroscopic phenomenological damage models, microscopics-based damage models are proved more suitable for modeling cracks-induced material anisotropies and nonlinear mechanical behaviors. Multi-scale approaches have been viewed as the effecitve and promising tool in material and engineering science. The present research project is thus dedicated to further studies on multiscale methods in geomechanics on both theoretical and numerical aspects. The objective here is triple: firstly, bridge theoretically phenomenological damage theory to micromechanics-based damage theory and construct for cracked solids new constitutive models which should possess the advantages of damage models of both the types; secondly, in order to avoid mesh-dependence due to strain softening phenomena often encountered in structural analyses, explore a new regularization technique, which will provide some theoretical consistence between material characteristic length and REV size and large easiness in its numerical implementation; thirdly, develop one multiscale computational method with the aim to enhance numerical modeling of nonlinear processes of material damage and structure failure in rock engineering.

多尺度方法致力于从材料的细观结构及其变化等信息来描述和模拟其宏观的物理力学行为。例如基于颗粒间的受力网络、接触和滑移可以建立颗粒材料宏观的应力-应变关系。对于裂隙岩体，基于均质化理论的细观损伤本构模型能够有效描述裂纹的发展、空间分布、张开或闭合状态以及裂隙面的摩擦等复杂现象，因而更适于模拟材料的各向异性和非线性力学行为。多尺度方法已被认为是研究材料本构的有效工具。本项目拟在连续损伤本构理论方面开展探索性研究，力求解决以下三个理论应用问题：1) 建立现象学损伤模型和细观损伤模型之间的内在联系，结合两类损伤模型的优点发展新的损伤模型，基于均质化方法，实现损伤摩擦耦合模型向水-热-力学多场耦合模型的扩展；2) 探索损伤非局部化的新方法，消除结构计算中由于应变软化引起的网格依赖现象；3) 发展一种多尺度数值方法，模拟从材料损伤到结构破坏的非线性过程。

多尺度模拟是近年来岩土材料研究领域的热点之一。青年基金项目“多尺度损伤本构模型及其在岩土力学中的应用”是本人在岩土材料多尺度本构理论研究方面的拓展和深化。研究内容主要包括裂隙岩石多尺度非局部化损伤本构理论、基于实验数据的数值模拟以及相关的多尺度数值方法等三个方面。通过三年的努力，项目研究圆满完成了各项任务，提出了一个仅包含五个参数的各向异性单边损伤摩擦耦合模型，开展了水力耦合和时效变形本构模型研究，研制了相关的数值程序，基于脆性岩石材料完成了模型的数值验证；开发了基于一种弹性问题Lippmann-Schwinger方程的增量迭代无网格算法，并利用图像分析技术获取的混凝土细观结构进行了数值模型；在基于细观力学的强度准则及参数跨尺度关联、强耦合非线性模型的解析解等方面取得了超出预期的研究成果。该项目提供了一个损伤和破坏机理清晰、参数少且物理意义明确的统一的多尺度岩石力学本构模型，研究表明基于单边损伤和摩擦耦合分析能够解释和模拟准脆性岩石类材料绝大部分的物理现象和力学行为；提出的数值算法为各向异性强耦合本构模型用于大型岩体结构的分析提供技术支撑。