#6982. Strong ellipticity conditions and infinitesimal stability within nonlinear strain gradient elasticity

December 2026publication date
Proposal available till 05-06-2025
4 total number of authors per manuscript0 $

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Journal’s subject area:
Mechanical Engineering;
Civil and Structural Engineering;
Mechanics of Materials;
Condensed Matter Physics;
Materials Science (all);
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Abstract:
We discuss connections between the strong ellipticity condition and the infinitesimal instability within the nonlinear strain gradient elasticity. The strong ellipticity (SE) condition describes the property of equations of statics whereas the infinitesimal stability is introduced as the positive definiteness of the second variation of an energy functional. Here we establish few implications which simplify the further analysis of stability using formulated SE conditions. The results could be useful for the analysis of solutions of homogenized models of beam-lattice materials at different scales.
Keywords:
Infinitesimal stability; Nonlinear elasticity; Strain gradient elasticity; Strong ellipticity

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