Even if a ceramic's homogenized properties (such as anisotropically evolving stiffness) truly can be predicted from complete knowledge of sub-continuum morphology (e.g., locations, sizes, shapes, orientations, and roughness of trillions of crystals, dislocations, impurities, pores, inclusions, and/or cracks), the necessary calculations are untenably hypervariate. Non-productive (almost derailing) debates over shortcomings of various first-principles ceramics theories are avoided in this work by discussing numerical coarsening in the context of a pedagogically appealing buckling foundation model that requires only sophomore-level understanding of springs, buckling hinges, dashpots, etc. Bypassing pre-requisites in constitutive modeling, this work aims to help students to understand the difference between damage and plasticity while also gaining experience in Monte-Carlo numerical optimization via scale-bridging that reduces memory and processor burden by orders of magnitude while accurately preserving aleatory (finite-sampling) perturbations that are crucial to accurately predict bifurcations, such as ceramic fragmentation.

即使完全可以从亚连续谱的形态学知识（例如位置，大小，形状，方向和粗糙度以及数万亿个晶体，位错，杂质，孔隙，夹杂物的粗糙度）完全预测出陶瓷的均质特性（例如各向异性演化的刚度）和/或裂缝），则必要的计算是高变的。在这项工作中，通过在教学方法上具有吸引力的屈曲基础模型的背景下讨论数值粗化，从而避免了对各种第一性原理陶瓷理论缺点的非生产性（几乎脱轨）的争论，该模型仅需要大二水平的弹簧，屈曲铰链，阻尼器，等等。 这项工作旨在绕过本构模型的先决条件，旨在帮助学生理解损伤和可塑性之间的差异，同时通过比例桥接将蒙特卡洛数值优化的经验减少到数量级，同时准确地保留临时性内容，从而获得蒙特卡洛数值优化的经验。 （有限采样）扰动对于准确预测分叉至关重要，例如陶瓷碎裂。