软材料大变形断裂的相场建模与应用  

Large Deformation Fracture in Soft Materials:Phase-field Modeling and Applications

作　　者：田富成 冀家乐 陈树昱 李良彬[1] Fu-cheng Tian;Jia-le Ji;Shu-yu Chen;Liang-bin Li(National Synchrotron Radiation Laboratory,Anhui Provincial Engineering Laboratory of Advanced Functional Polymer Film,CAS Key Laboratory of Soft Matter Chemistry,University of Science and Technology of China,Hefei 230026)

机构地区：[1]中国科学技术大学、国家同步辐射实验室、安徽省先进功能高分子薄膜工程实验室、中国科学院软物质化学重点实验室,合肥230026

出　　处：《高分子学报》2025年第2期179-199,共21页Acta Polymerica Sinica

基　　金：国家重点研发计划(项目号2018YFB0704200);国家自然科学基金(基金号51890872,52003262)资助

摘　　要：软材料具有承受大应变和高可恢复性的独特特性,使其在生命科学和软机器人等前沿领域具有不可替代的作用.了解此类材料的复杂断裂行为不仅具有迫切的应用需求,也是材料科学、物理学和连续介质力学等基础学科的研究重点.本文介绍了作者在断裂相场模型方面所做的一些工作,主要关注软材料的大变形断裂相场建模、算法实施以及应用.在有限变形理论框架下,作者发展一种新的混合多场断裂相场模型,用于模拟近不可压缩软材料的大变形断裂.从物理裂纹拓扑的角度清楚阐述了不可压缩性与扩散裂纹张开之间的内在矛盾.为了解决这个问题,该模型利用相场退化函数放松了损伤材料的不可压缩性约束,而不影响完好材料的不可压缩性.通过修改经典的摄动拉格朗日乘子方法,导出了用于近不可压缩大变形断裂问题的新型多场混合变分格式.虽然该混合格式切实有效,但通常需要采用满足inf-sup条件的混合有限元(FE)配置,这进一步加剧了本已昂贵的相场断裂建模的计算负担.为了能够使用具有数值优势的低阶线性单元,作者采用压力投影技术开发了一种稳定的混合公式.该公式的优点在于其简单性和多功能性,允许对所有场变量采用低阶单元离散.考虑到这一特性,作者进一步设计了一种高效的自适应网格划分策略,从而大幅提高了计算效率.为了更好地应对涉及裂纹成核的自适应场景,提出了一种新的基于能量的网格细化判据.此外,本文也完整阐述了稳定混合有限元公式的数值处理,以及自适应网格细化,删除技术的核心操作.所提出的格式的准确性、效率和稳健性已经通过一系列具有代表性的数值案例得到了充分的验证.Soft materials possess unique traits,such as the ability to withstand large strains and high recoverability,rendering them indispensable in cutting-edge fields like life sciences and soft robotics.Understanding the complex fracture behaviors of such materials is not only crucial for practical applications but also a key research focus in fundamental disciplines such as materials science,physics,and continuum mechanics.This paper presents the authors’work on fracture phase field models,primarily focusing on modeling the large deformation fracture of soft materials,algorithm implementation,and applications.Within the framework of finite deformation theory,a novel hybrid multi-field fracture phase field model is developed to simulate the large deformation fracture of nearly incompressible soft materials.The inherent conflict between incompressibility and diffusive crack opening is clearly elucidated from the perspective of physical crack topology.To address this issue,the model employs phase field degradation functions to relax the incompressibility constraint of damaged materials without affecting the incompressibility of intact materials.By modifying the classical perturbed Lagrange multiplier method,a novel hybrid variational formulation is derived for nearly incompressible large deformation fracture problems.Although this hybrid formulation is effective,it typically requires the use of mixed finite element(FE)configurations that satisfy the inf-sup condition,further increasing the computational burden of the already expensive phase field fracture modeling.To enable the use of numerically advantageous low-order linear elements,the authors further develop a stable hybrid formulation by employing a pressure projection technique.The advantage of this formulation lies in its simplicity and versatility,allowing low-order element discretization for all field variables.Considering this feature,the authors design an efficient adaptive mesh refinement strategy,significantly enhancing computational efficiency.To better a

关 键 词：相场模型 软材料 大变形断裂 复杂裂纹 不可压缩约束 

分 类 号：O346.1[理学—固体力学] O341[理学—力学]