Nanomechanical modeling of materials with defects and microstructure using gradient theories

当前项目的目标是进一步系统地发展梯度理论及其概念，以便在项目的第一部分中获得小尺度下的缺陷和微观结构材料的有效建模。具有缺陷和微结构的材料在材料科学、工程科学、固体物理和纳米力学中起着基础作用。为此，应开发和增强广义连续介质模型，以便在小尺度下描述此类材料的物理意义和数学校正行为。主要重点在于新材料，如“智能材料”，“先进材料”或“混合材料”。其目的是研究缺陷（位错，点缺陷，裂纹）和广义连续介质理论（梯度弹性理论，非局部弹性理论，非局部梯度弹性理论）的正则化行为，这样的有前途的材料。该项目的一个重要组成部分是具有内部特征长度的现代连续介质理论（如梯度理论和非局部理论）以及新材料（准晶体）的广义连续介质理论及其与原子学的联系。特别是，准晶的建模通过梯度弹性理论将被开发。此外，梯度电弹性理论，包括重要的影响，如挠曲电和纳米压电将被开发。使用分析和数值方法进行预测，可以通过实验和模拟（纳米力学和先进材料）进行检查，并用作数值代码的基准测试。因此，该项目将提供一个重要的贡献，利用增强梯度理论的缺陷和微观结构的材料建模。

The aim of the current project is the further systematic development of gradient theories and their concepts, for the efficient modeling of materials with defects and microstructure at small scales, obtained in the first part of the project (sign removed). Materials with defects and microstructure play a fundamental role in materials science, engineering science, solid state physics, and nanomechanics. For this purpose, generalized continuum models should be developed and enhanced in order to describe physically meaningful and mathematically correct the behavior of such materials at small scales. The main focus lies on novel materials such as "smart materials", "advanced materials" or "hybrid materials". The aim is to investigate defects (dislocations, point defects, cracks) and the regularization behavior of generalized continuum theories (gradient elasticity theory, nonlocal elasticity theory, nonlocal gradient elasticity theory) for such promising materials. An important part of the project are modern continuum theories with internal characteristic lengths (such as gradient theories and nonlocal theories) as well as generalized continuum theories for new materials (quasicrystals) and their connection to atomistics. In particular, the modeling of quasicrystals by means of a gradient elasticity theory will be developed. In addition, a gradient electroelasticity theory including important effects like flexoelectricity and nano-piezoelectricity will be developed. Using analytical and numerical methods, predictions are to be made, which can be checked by experiments and simulations (in nanomechanics and advanced materials) and used as benchmark tests for numerical codes. Therefore, the project will provide an important contribution to the modeling of materials with defects and microstructure using enhanced gradient theories.