有旋热力学流的辛结构与岩土非关联塑性的热动力学机制研究

Distinctive non-associated plasticity is a key characteristic of the deformation behavior of geomaterials, impairing the bearing capacity and stability of geotechnical structures. The state-of-art of geomechanics chiefly studies non-associated flow in the framework of classical plasticity or its modification, namely, based on yield function and flow potential function. Nevertheless, as phenomenological as it is, classical plasticity cannot reveal the intrinsic mechanism of non-associated plasticity. A new idea is proposed and to be checked by this study: “the intrinsic mechanism of non-associated plasticity resides in the rotational thermodynamic fluxes”. In this proposal, the rotational thermodynamic fluxes will be studied based on normality structure of Rice and the theory of symplectic geometry, highlighted by a) the breakdown condition of the nonlinear Onsager reciprocal relation and b) the multiple-potential-based representative theorem of the rotational thermodynamic fluxes and its significance to geo-plasticity. These two propositions respectively corresponds to the initiation and evolution of non-associated plastic flow. Laboratory tests on rock specimens will be carried out, to verify the macroscopic definition of non-association based on the Voigt symmetry of the tangent compliance tensor. The study may on one hand promote the theory of non-equilibrium thermodynamics and on the other hand help to understand the essence of non-associated plasticity in geomaterials.

显著的非关联塑性是岩土类材料的重要宏观变形特性，对岩土工程结构的承载力与稳定性产生不利影响。目前对非关联塑性的认识与描述主要局限于经典塑性力学或其修正，即屈服函数与塑性势函数。但塑性力学本身是宏观唯象的，无法揭示非关联塑性的内在机制。本项目提出并将论证一个新的学术思想：“非关联塑性的微观机制是有旋热力学流”。在此基础上，拟基于Rice正则结构与辛几何理论，对内变量纺射空间的有旋热力学流开展数学研究，包括：① 非线性Onsager倒易关系的瓦解条件（类似于流体力学中层流到紊流的转涙点）；② 有旋热力学流的多位势表达定理及其物理意义。上述两点分别对应非关联塑性的萌生条件与演化规律，进而从数学角度阐明其微观热动力学机制。最后，拟通过岩石试验，验证基于柔度张量Voigt对称性的非关联塑性宏观判定定理。研究一方面对非平衡态热力学基本理论框架有一定发展，另一方面有助于加深对非关联塑性本质的认识。

本项目针对岩土材料与岩土工程结构宏观变形特征与稳定性展开理论研究，取得如下成果：1）基于非线性Onsager倒异关系提出远平衡态（far-from-equilibrium），给出远平衡态有旋热力学流与非关联塑性应变率的确定关系；2）证明满足非线性Onsager倒异关系的连续介质的Lyapunov渐近稳定原理；该原理给出岩土材料与结构变形失稳的条件与路径，从弹塑形理论上证明新奥法等岩土工程实用原理；3）提出基于有旋耗散修正的标准线性固体模型并应用于地震波传播。基于上述研究成果完成学术论文3篇，其中一篇获得美国地球物理学会（American Geophysical Union）杰出论文奖。