标题： 统一复合材料微观力学理论 显示英文标题

标题： Unified Micromechanics Theory of Composites

摘要： 我们考虑具有随机（统计均匀或非均匀）、周期性或确定性（既非随机也非周期性）结构的矩阵复合材料（CM）。 CM表现出线性或非线性行为，耦合或解耦的多物理现象，局部弹性、弱非局部（应变梯度和应力梯度）或强非局部（应变型和位移型，非局部力学）相特性。 一种改进的计算分析细观力学（CAM）方法引入了一个精确的加法通用积分方程（AGIE），适用于上述任何结构和相特性的CM。 静态AGIE的统一迭代解被用于具有紧支撑体力作为根本性新通用训练参数。 该方法还通过一种新颖的代表性体积单元（RVE）概念建立了过滤掉不合适的有效参数子数据集的关键阈值，该概念扩展了Hill的经典框架。 这种RVE概念消除了样本大小、边界层和边缘效应，使其适用于任何结构和相特性的CM，无论其是局部还是非局部，线性还是非线性。 将这种新的RVE概念纳入机器学习和神经网络技术中，能够构建任何未预先定义的代理非局部算子。 该方法论结构为模块化、基于块的框架，允许软件组件的独立开发和优化。 这种灵活且稳健的AGIE-CAM框架整合了数据驱动、多尺度和多物理建模，加速了任何微观拓扑和相特性的CM研究。 AGIE-CAM框架代表了复合材料细观力学中的突破性范式转变，重新定义了我们理解其在微观层面行为的基本哲学。 显示英文摘要

摘要： We consider the matrix composite materials (CM) of either random (statistically homogeneous or inhomogeneous), periodic, or deterministic (neither random nor periodic) structures. CMs exhibit linear or nonlinear behavior, coupled or uncoupled multi-physical phenomena, locally elastic, weakly nonlocal (strain gradient and stress gradient), or strongly nonlocal (strain-type and displacement-type, peridynamics) phase properties. A modified Computational Analytical Micromechanics (CAM) approach introduces an exact Additive General Integral Equation (AGIE) for CMs of any structure and phase properties mentioned above. The unified iteration solution of static AGIEs is adapted to the body force with compact support serving as a fundamentally new universal training parameter. The approach also establishes a critical threshold for filtering out unsuitable sub-datasets of effective parameters through a novel Representative Volume Element (RVE) concept, which extends Hill's classical framework. This RVE concept eliminates sample size, boundary layer, and edge effects, making it applicable to CMs of any structure and phase properties, regardless of local or nonlocal, linear or nonlinear. Incorporating this new RVE concept into machine learning and neural network techniques enables the construction of any unpredefined surrogate nonlocal operators. The methodology is structured as a modular, block-based framework, allowing independent development and refinement of software components. This flexible, robust AGIE-CAM framework integrates data-driven, multi-scale, and multi-physics modeling, accelerating research in CM of any microtopology and phase properties considered. The AGIE-CAM framework represents a groundbreaking paradigm shift in the micromechanics of composites, redefining the very philosophy that underpins our understanding of their behavior at the microscopic level.