Fitting Strains and Displacements by Minimizing Dislocation Energy

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We present a procedure for matching a displacement field to a given strain field, or vice- versa, over an arbitrary domain, which can be a finite element. The fitting criterion used is minimization of a dislocation energy functional. The strain field, whether given or fitted, need not be compatible. The method has four immediate applications: (i) finite element stiffness formulation based on fitting assumed-natural-strain (ANS) fields to node displacements; (ii) pointwise recovery of an internal displacement field in ANS elements as required for consistent mass, body load or geometric stiffness computations; (iii) recovery of smoothed strains from node displacements for stress post-processing, and (iv) system identification and damage detection from experimental data. The article focuses on application (i) for the strain fitting (SF) problem and (ii) for the displacement fitting (DF) problem. The separation of mean and deviatoric strains is emphasized whenever it is found convenient to simplify calculations.