Homogenization and linearization in magnetoelasticity under small elastic response

2025/11/26 by Cherdantsev, Mikhail, Davoli, Elisa, D'Elia, Lorenza +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Thermoelastic and Magnetoelastic Phenomena

paper · doi:10.48550/arxiv.2511.21907

openalex publication_date 2025/11/26 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28

Abstract

We perform a simultaneous homogenization and linearization analysis for a magnetoelastic energy functional featuring a mixed Eulerian-Lagrangian structure. Neglecting Zeeman and anisotropic contributions, we characterize the asymptotic behavior in the sense of Gamma-convergence for the sum of a nonlinear magnetoelastic energy, a symmetric exchange term defined on the actual configuration, and for the associated magnetostatic self-energy. After establishing compactness of displacements and magnetizations with equibounded energy, we identify the limiting energy functional as the sum of a quadratic homogenized magnetoelastic contribution with a limiting homogenized exchange and magnetostatic term. This is, to the authors' knowledge, the first homogenization result for manifold-valued mixed Eulerian-Lagrangian energies.

Citations

• A variational approach to the emergence of domain structures in magnetostrictive solids
• Homogenization of magnetoelastic materials with rigid magnetic inclusions at small strains
• Variational models with Eulerian-Lagrangian formulation allowing for material failure
• Linearization in magnetoelasticity
• Quasistatic evolution in magnetoelasticity under subcritical coercivity assumptions
• Existence results in large-strain magnetoelasticity
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three‐dimensional elasticity

Related

• Linearization in magnetoelasticity
• Homogenization of magnetoelastic materials with rigid magnetic inclusions at small strains
• A reduced model for plates arising as low energy Γ-limit in nonlinear magnetoelasticity
• Homogenization of an elastodynamics system with a strong magnetic field and soft inclusions inducing a viscoelastic effective behavior
• Quasistatic evolution in magnetoelasticity under subcritical coercivity assumptions