基于非局部塑性模型的应变局部化理论分析及数值模拟  

Theoretical analysis and numerical simulation of strain localization in nonlocal plasticity model

作　　者：吕玺琳[1] 黄茂松[2] 

机构地区：[1]同济大学地下建筑与工程系,上海200092 [2]同济大学岩土及地下工程教育部重点实验室,上海200092

出　　处：《计算力学学报》2011年第5期743-748,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金青年科学基金(50908171);国家杰出青年科学基金(50825803)资助项目

摘　　要：通过求解一个第二类Fredholm方程,得到了基于非局部塑性软化模型的应变局部化问题理论解,结果表明,只有在当采用过非局部修正形式的非局部塑性软化模型才能得到应变局部化解,且得到的塑性应变分布和荷载响应依赖于所引入的特征长度及过非局部权参数。通过一维应变局部化有限元数值解,验证了非局部理论的引入能克服计算结果的网格敏感性,塑性应变分布和荷载响应计算结果随着网格细化趋近于理论解。将非局部塑性软化模型用于双轴应变局部化试验数值模拟,并分析了非局部理论引入的参数对计算结果的影响及计算过程的收敛特性。By solving a Fredholm equation of the second kind, the analytical solution was derived for strain localization in nonlocal softening material, the solutions show that the distributions of plastic strain and load-displacement curve rely on the characteristic length and nonlocal parameter. It was validated by one-dimensional numerical solution that nonlocal model could make the distributions of plastic strain and the global load-displacement response mesh independent and approaching to analytical solutions with mesh refinement. The nonlocal formulation of softening plasticity was employed in the numerical simulation of strain localization in bi-axial compression test. The influence of the over-nonlocal parameter and characteristic length on the numerical results and the convergence of the equilibrium itera- tion were both obtained.

关 键 词：非局部塑性 应变局部化 特征长度 网格敏感性 

分 类 号：O344.3[理学—固体力学]