Variational model order reduction for the prediction of plastic events in disordered materials

用于预测无序材料中塑性事件的变分模型降阶

• 批准号: 523939420
• 负责人: Dr. Franz Bamer
• 金额: --
• 依托单位: Lehrstuhl und Institut für Allgemeine Mechanik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/523939420?language=en
• 关键词: Variational; model; order; reduction; prediction

Disordered materials, such as glasses and amorphous solids, are ubiquitous in engineering and everyday life. The complex mechanics of disordered solids is governed by elementary inelastic events that happen on the nanoscale and are decoded in the local microscopic picture of the material. Consequently, the essential behavior of disordered materials can only be captured using molecular descriptions, which considerably limits the capability to describe such materials on larger scales. Thus, this project aims to develop a reduced-order model for the mechanical response description of disordered solids. Our objective builds on the idea that only a few response patterns, so-called soft vibrational modes, are activated during elementary inelastic events. Due to the high level of nonlinearity and the unpredictability of such slowly driven dynamics, we will predict the zones susceptible to local events using a new mechanical probing technique, which we will enhance using machine learning algorithms. This way, one can predict these elementary inelastic events before mechanical loading, identifying so-called local variation modes. A reduced order model will mathematically be realized using the Empirical Interpolation method, while the change in the reduced basis obtained by the eigenmodes of the Hessian occurring due to the high nonlinearity of the system will be considered using the perturbation theory and Grassmann extrapolation. The powerful high-fidelity reduced order model will be formulated by extending the reduced order basis by the local variation modes. The method will, firstly, be tested on two-dimensional benchmark molecular models and then on larger three-dimensional disordered materials.

无序材料，例如玻璃和无定形固体，在工程和日常生活中无处不在。无序固体的复杂力学受纳米尺度上发生的基本非弹性事件的控制，并在材料的局部微观图像中进行解码。因此，无序材料的基本行为只能使用分子描述来捕获，这极大地限制了在更大范围内描述此类材料的能力。因此，该项目旨在开发一个降阶模型来描述无序固体的机械响应。我们的目标建立在这样的想法之上：在基本非弹性事件期间，只有少数响应模式（所谓的软振动模式）被激活。由于这种缓慢驱动的动力学具有高度非线性和不可预测性，我们将使用新的机械探测技术来预测易受局部事件影响的区域，并使用机器学习算法来增强该技术。这样，人们就可以在机械加载之前预测这些基本非弹性事件，识别所谓的局部变化模式。采用经验插值法在数学上实现降阶模型，同时采用微扰理论和格拉斯曼外推法考虑由于系统的高度非线性而产生的Hessian本征模所获得的降阶基的变化。通过局部变化模式扩展降阶基础，将形成强大的高保真降阶模型。该方法将首先在二维基准分子模型上进行测试，然后在更大的三维无序材料上进行测试。