热机械模拟的“ROM+DDCM”框架

N. Blal, A. Gravouil
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摘要

由于数据科学和数值算法的重大进步,面对当前的工业和社会挑战,基于物理的数据驱动计算建模将在基于模拟的设计中发挥重要作用,用于开发创新材料和新产品。在[1]提出的数据驱动计算力学新范式下,本构定律可以直接被一组实验数据取代,从而避免了提出最适合实验的数学模型和校准其固有参数的关键步骤。DDCM绕过经验本构定律,并将其作为物理空间(因此尊重物理普遍定律)和物质数据流形(没有明确数学模型的离散数据点集)之间的双距离最小化问题的解决方案进行搜索。尽管DDCM算法最近在数值模拟中得到了应用,但其实际应用仍然局限于可逆行为,其在不可逆耗散问题上的推广需要进一步发展。此外,数据生成阶段需要更多的努力来降低其高昂的(数值或实验)成本。在这项研究中,我们提出了一种策略,利用降阶模型(ROM)和数据驱动计算模型(DDCM)将这种自由材料范式扩展到更复杂的问题,即不可逆和多尺度模拟。“ROM+DDCM”框架在二维弹塑性问题和三维多尺度热模拟中的应用将得到说明。DDCM[2]算法采用基于切线空间的双距离算法,ROM步进采用HOPGD[3]方法。
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A "ROM+DDCM" framework for thermo-mechanical simulations
Thanks to the significant advances in data sciences and numerical algorithms, and face to the current industrial and societal challenges, Physically-based data-driven computational modeling would have an important role in simulations based design for the development of innovative materials and new products. With the new paradigm of data Driven Computational Mechanics proposed by [1], the constitutive laws can be directly replaced by a collection of experimental data avoiding thus the crucial step of proposing a mathematical model that best fit the experiments and calibrating its inherent parameters. The DDCM bypasses the empirical constitutive laws and searches the solution as a double distance minimizing problem between the physical space (respecting thus the physical universal laws) and the material data manifold (discrete set of data points with no explicit mathematical model). Despite the recent applications of DDCM algorithms in numerical simulations, their practical using still remains limited to reversible behaviors and their extension to irreversible dissipation problems needs further developments. Moreover, the data generation phase needs more efforts to reduce its high (numerical or experimental) cost. We propose in this study a strategy that makes the most of Reduced Order Models (ROM) and Data Driven Computational Modeling (DDCM) to extend such a free material paradigm to more complicated problems, namely irreversible and multi-scale simulations. The application of the ”ROM+DDCM” framework will be illustrated for a 2D elasto-plastic problem and 3D multiscale thermal simulations. A tangent space based double distance algorithm is adopted for the DDCM [2] algorithm and the HOPGD [3] method is used for the ROM step.
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