Existence theorem for geometrically nonlinear Cosserat micropolar model\n under uniform convexity requirements

2014/10/13 by Patrizio Neff, Mircea Bîrsan, Neff, Patrizio +3 · 1 citation
Engineering · Materials Science · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Elasticity and Material Modeling #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlocal and gradient elasticity in micro/nano structures #Quantum Electrodynamics and Casimir Effect #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.1410.4225

openalex publication_date 2014/10/13 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We reconsider the geometrically nonlinear Cosserat model for a uniformly\nconvex elastic energy and write the equilibrium problem as a minimization\nproblem. Applying the direct methods of the calculus of variations we show the\nexistence of minimizers. We present a clear proof based on the coercivity of\nthe elastically stored energy density and on the weak lower semi-continuity of\nthe total energy functional. Use is made of the dislocation density tensor\n\ boldsymbolK=\ boldsymbolR^T ,\Curl ,\ boldsymbolR\nas a suitable Cosserat curvature measure.\n

Citations

• Some geometrical relations in dislocated crystals
• Existence of minimizers for a finite-strain micromorphic elastic solid
• Theories of elasticity with couple-stress
• Convexity conditions and existence theorems in nonlinear elasticity
• Local Symmetry Group in the General Theory of Elastic Shells

Cited by

• Cosserat micropolar and couple-stress elasticity models of flexomagnetism at finite deformations

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