A Probabilistic Model for Microstructure Evolution with Application to Smart Concrete Materials

该项目提出了在三个方向上表示和分析随机异质材料的方法。首先，建立了碳纤维水泥基复合材料微观结构的通用概率模型。这些模型是表征材料成分的几何、机械和电学特性的随机场。这些水泥基复合材料具有有趣的微观结构，并且在机械和电子学中用作机械性能的传感器。其次，开发了一个计算环境，用于计算在确定性载荷作用下微结构性能随时间的演变。有限元程序被用来计算的变化，例如，应力，应变，损伤和电场在水泥基复合材料试样产生的概率模型。有限元程序的发展需要数值求解技术的进步，以及制定新的数学健全的牵引位移关系来模拟粘性断裂。第三，利用有限元分析结果，（i）更新材料微观结构的概率模型，使其能够反映当前的损伤状态，（ii）利用均匀化过程建立水泥基复合材料的宏观损伤模型，材料状态的演变由一个数学对象监控，称为数字材料（DM），其在加载期间的任何时候唯一地限定了微结构的状态，并且可以存储在计算机中。分析和数值计算的结果验证了对实验测试提供的信息的属性的纤维基体相互作用和依赖的宏观试样的电导率对他们的损伤states.The项目的主要成果是一种新的方法来预测复合材料的结构行为和设计材料具有更好的结构性能和更好的能力，为传感损伤和应变。其他成果包括新的有限元代码，新的数学模型和强大的教育推广计划。

The project proposes to formulate methods for representing and analyzing randomheterogeneous materials in three directions. First, general probabilistic models are developedfor the microstructure of cement based composites with carbon fibers. The modelsare random fields characterizing the geometrical, mechanical, and electrical properties of thematerial constituents. These cement based composites have an interesting microstructure,and are used in both mechanics and electronics as sensors of mechanical properties. Second,a computational environment is developed for calculating the evolution in time of theproperties of microstructures subjected to deterministic loads. Finite element proceduresare used to calculate changes in, for example, the stress, strain, damage and electric fieldsin cement based composite specimens generated from their probabilistic models. Developmentof the finite element code entails advances in numerical solver techniques as well asformulation of new mathematically sound traction-displacment relationships to model cohesivefracture. Third, the results of the finite element analyses are used to (i) updatethe probabilistic models of the material microstructure so they reflect the current damagestate and (ii) develop macroscopic damage models for cement based composites by usinghomogenization procedures.The evolution of the material state is monitored by a mathematical object, referredto as digital material (DM), that defines uniquely the state of the microstructure at anytime during loading and can be stored in the computer. The results of the analytical andnumerical developments are validated against experimental tests providing information ofthe properties of the fiber matrix interaction and on the dependence of electric conductivityof macroscopic specimens on their damage state.The main outcome of the project is a novel methodology for predicting structural behaviorof composite materials and for designing materials with better structural propertiesand better capabilities for sensing damage and strain. Other outcomes include new finiteelement codes, new mathematical models, and a strong educational outreach program.