软材料大变形断裂的相场建模与应用

田富成; 冀家乐; 陈树昱; 李良彬

doi:10.11777/j.issn1000-3304.2024.24224

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软材料大变形断裂的相场建模与应用

专论 | 更新时间：2025-01-24

- 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
- 高分子学报 2025年56卷第2期页码：179-199
- 作者机构：
  
  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
- 作者简介：
  
  [ "田富成，男，1992年出生. 2015年本科毕业于郑州大学工程力学专业，2020年博士毕业于中国科学技术大学核科学与技术专业. 2020~2022年在中国科学技术大学工程科学学院从事博士后研究. 2023年1月至今，受日本学术振兴会(JSPS)资助在北海道大学从事软材料动态断裂失稳方面的研究." ]
  [ "李良彬，男，1972年生. 1994年本科毕业于四川师范大学近代物理专业，2000年博士毕业于四川大学高分子材料科学与工程系. 2000~2004年在荷兰国家原子分子物理研究所和Delft科技大学从事博士后研究，2004~2006年在荷兰联合利华食品与健康研究所担任研究员. 2006年至今，任中国科学技术大学国家同步辐射实验室研究员、兼任化学与材料科学学院高分子科学与工程系教授、博士生导师. 2013年获国家自然科学基金杰出青年基金资助. 担任Macromolecules副主编，Polym. Cryst.、Chinese J. Polym. Sci.、J. Polym. Sci.和《高分子材料科学与工程》编委. 主要从事同步辐射时间空间能量分辨技术、原位研究方法和高分子材料加工-结构-性能关系方面的研究." ]
- 基金信息：
  
  国家重点研发计划(2018YFB0704200);国家自然科学基金(基金号 ┣51890872);52003262┫
- DOI：10.11777/j.issn1000-3304.2024.24224
  中图分类号：
- CSTR：32057.14.GFZXB.2024.7308
- 纸质出版日期：2025-02-20，
  
  网络出版日期：2025-01-09，
  
  收稿日期：2024-08-27，
  
  录用日期：2024-10-23
- 稿件说明：
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田富成, 冀家乐, 陈树昱, 李良彬. 软材料大变形断裂的相场建模与应用[J]. 高分子学报, 2025,56(2):179-199.

FU-CHENG TIAN, JIA-LE JI, SHU-YU CHEN, LIANG-BIN LI. Large Deformation Fracture in Soft Materials: Phase-field Modeling and Applications. [J]. Acta polymerica sinica, 2025, 56(2): 179-199.
田富成, 冀家乐, 陈树昱, 李良彬. 软材料大变形断裂的相场建模与应用[J]. 高分子学报, 2025,56(2):179-199. DOI： 10.11777/j.issn1000-3304.2024.24224. CSTR： 32057.14.GFZXB.2024.7308.

FU-CHENG TIAN, JIA-LE JI, SHU-YU CHEN, LIANG-BIN LI. Large Deformation Fracture in Soft Materials: Phase-field Modeling and Applications. [J]. Acta polymerica sinica, 2025, 56(2): 179-199. DOI： 10.11777/j.issn1000-3304.2024.24224. CSTR： 32057.14.GFZXB.2024.7308.

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.

Abstract

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 address adaptive scenarios involving crack nucleation

a new energy-based mesh refinement criterion is proposed. Additionally

this paper comprehensively elaborates on the numerical treatment of the stable hybrid finite element formulation and the core operations of adaptive mesh refinement and deletion techniques. The accuracy

efficiency

and robustness of the proposed formulation are verified through a series of representative numerical cases.

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

Keywords

Phase field modelSoft materialsLarge deformation fractureComplex cracksIncompressibility constraint

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