A classification of higher-order strain-gradient models – linear analysis

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Variational formulation and isogeometric analysis for fourth-order boundary value problems of gradient-elastic bar and plane strain/stress problems (2016, background): “1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 in the context of analytical solutions for a one-dimensional model problem in [21, 22] by introducing the term ”si”
Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results (2011, methodology): “Instabilities are also related to loss of uniqueness in static boundary value problems – see Askes et al. (2002) for a discussion and examples of instabilities in statics and dynamics.”
A new formulation and 𝒞0‐implementation of dynamically consistent gradient elasticity (2007, background): “The model of Equation (1) was devised for use in statics, and its straightforward use in dynamics may lead to infinite phase velocities, which is not realistic [32, 33].”