In this paper, we develop a non-singular continuum theory of point defects based on a second strain gradient elasticity theory, the so-called gradient elasticity of bi-Helmholtz type. Such a generalized continuum theory possesses a weak nonlocal character with two internal material lengths and provides a mechanics of defects without singularities. Gradient elasticity of bi-Helmholtz type gives a natural and physical regularization of the classical singularities of defects, based on higher order partial differential equations. Point defects embedded in an isotropic solid are considered as eigenstrain problem in gradient elasticity of bi-Helmholtz type. Singularity-free fields of point defects are presented. The displacement field as well as the first, the second and the third gradients of the displacement are derived and it is shown that the classical singularities are regularized in this framework. This model delivers non-singular expressions for the displacement field, the first displacement gradient and the second displacement gradient. Moreover, the plastic distortion (eigendistortion) and the gradient of the plastic distortion of a dilatation centre are also non-singular and are given in terms of a form factor (shape function) of a point defect. Singularity-free expressions for the interaction energy and the interaction force between two dilatation centres and for the interaction energy and the interaction force of a dilatation centre in the stress field of an edge dislocation are given. The results are applied to calculate the finite self-energy of a dilatation centre.
On gradient enriched elasticity theories: A reply to "Comment on 'On non-singular crack fields in Helmholtz type enriched elasticity theories' " and important theoretical aspects
Aifantis的评论，该评论批评了“关于Helmholtz型丰富弹性理论中的非奇异裂纹场”一文[Lazar，M.，Polyzos，D.，2014. Int. J. Solids Struct. doi：10.1016/j.ijsolstr.2014.01.002]通过明确和直接的论点进行反驳。梯度丰富的弹性理论，在这项工作中出现的重要理论方面也进行了讨论。
A three dimensional field formulation, and isogeometric solutions to point and line defects using Toupin's theory of gradient elasticity at finite strains
A model for the interaction of dislocations with planar defects based on Allen-Cahn type microstructure evolution coupled to strain gradient elasticity
Compatible Instability: Gauge Constraints of Elasticity Inherited by Electronic Nematic Criticality
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；The Grainger College of Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格兰杰工程学院）；Anthony J. Leggett Institute for Condensed Matter Theory, The Grainger College of Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格兰杰工程学院安东尼·J·利格特凝聚态理论研究所）
Plasticity from Symmetry: A Gauge-Theoretic Framework
National Institute of Physics, University of the Philippines Diliman（菲律宾大学迪里曼分校国立物理研究所）；Institute of Theoretical Physics, Wrocław University of Science and Technology（弗罗茨瓦夫科技大学理论物理研究所）
