韧性单晶在平面应变简单剪切下晶界的形成：一种块坐标有限元方法
Formation of grain boundaries in ductile single crystals under plane-strain simple shear: a block-coordinate finite element method
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中文总结 AI 辅助
针对韧性单晶平面应变简单剪切，提出块坐标有限元方法，结合多凸弹性能和位错密度正则化，数值再现了由大变形驱动的自发晶粒细分层状结构。
中文摘要 AI 辅助
大塑性变形能够驱动初始均匀的单晶自发地细分为由薄位错墙分隔的取向错晶粒——这是一种图案形成不稳定性，其根源在于晶体弹性能在较大应变下失去凸性。我们在连续位错理论框架内，针对平面应变简单剪切下的韧性晶体研究这一现象，采用一种多凸（Ciarlet-Geymonat）弹性能，该能量保证了耦合变形-滑移问题极小值的存在性。对塑性滑移求极小值可得到双阱形式的凝聚能，其非拟凸性有利于层状微结构的形成；几何必要位错密度的梯度对其正则化，使晶界具有有限厚度和能量，且这些量是取向错角的函数。一种块坐标有限元方案——交替进行凸非光滑滑移求解和Levenberg正则化牛顿变形求解——在数值上解析了该微结构并检测到其自发出现，再现了与闭式分析一致的层状晶粒结构。
英文摘要
Large plastic deformation can drive an initially uniform single crystal to spontaneously subdivide into misoriented grains separated by thin dislocation walls -- a pattern-forming instability rooted in the loss of convexity of the crystal's elastic energy at large strain. We study this phenomenon for a ductile crystal in plane-strain simple shear within continuum dislocation theory, using a polyconvex (Ciarlet--Geymonat) elastic energy that guarantees existence of minimizers for the coupled deformation--slip problem. Minimizing over the plastic slip yields a condensed energy of double-well form whose non-quasiconvexity favours a lamellar microstructure; the gradient of the geometrically necessary dislocation density regularizes it, giving the grain boundaries a finite thickness and energy as functions of the misorientation angle. A block-coordinate finite element scheme -- alternating a convex non-smooth solve for the slip with a Levenberg-regularized Newton solve for the deformation -- resolves this microstructure numerically and detects its spontaneous onset, reproducing the lamellar grain structure in agreement with the closed-form analysis.
发表机构
- Faculty of Civil Engineering, Ton Duc Thang University（土木工程学院，Ton Duc Thang大学）
- Faculty of Mathematics and Statistics, Ton Duc Thang University（数学与统计学院，Ton Duc Thang大学）
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