Asymptotic analysis of single-slip crystal plasticity in the limit of vanishing thickness and rigid elasticity
-
Dominik Engl
,
Stefan Krömer
and
Martin Kružík
Abstract
We perform via Γ-convergence a 2d-1d dimension reduction analysis of a single-slip elastoplastic body in large deformations. Rigid plastic and elastoplastic regimes are considered. In particular, we show that limit deformations can essentially freely bend even if subjected to the most restrictive constraints corresponding to the elastically rigid single-slip regime. The primary challenge arises in the upper bound where the differential constraints render any bending without incurring an additional energy cost particularly difficult. We overcome this obstacle with suitable non-smooth constructions and prove that a Lavrentiev phenomenon occurs if we artificially restrict our model to smooth deformations. This issue is absent if the differential constraints are appropriately softened.
Funding source: Grantová Agentura České Republiky
Award Identifier / Grant number: 21-06569K
Funding statement: D. Engl acknowledges the financial support by the NDNS + Ph.D. travel grant and would like to thank Carolin Kreisbeck for suggesting this project and sharing some initial ideas. The work of S. Krömer and M. Kružík was supported by the GA ČR project 21-06569K.
Acknowledgements
This work had started while D. Engl was still affiliated with Universiteit Utrecht.
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Articles in the same Issue
- Frontmatter
- Another proof of the existence of homothetic solitons of the inverse mean curvature flow
- A Weierstrass extremal field theory for the fractional Laplacian
- Minimizing movements for anisotropic and inhomogeneous mean curvature flows
- A singular Yamabe problem on manifolds with solid cones
- Uniqueness for volume-constraint local energy-minimizing sets in a half-space or a ball
- Limit of solutions for semilinear Hamilton–Jacobi equations with degenerate viscosity
- Monotonicity of entire solutions to reaction-diffusion equations involving fractional p-Laplacian
- Hierarchy structures in finite index CMC surfaces
- No breathers theorem for noncompact harmonic Ricci flows with asymptotically nonnegative Ricci curvature
- Wolff potentials and local behavior of solutions to elliptic problems with Orlicz growth and measure data
- Asymptotic analysis of single-slip crystal plasticity in the limit of vanishing thickness and rigid elasticity
- On the regularity of optimal potentials in control problems governed by elliptic equations
- Sobolev embeddings and distance functions
- Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure: The limiting regimes
- On the area-preserving Willmore flow of small bubbles sliding on a domain’s boundary
- Sobolev contractivity of gradient flow maximal functions
- Discrete approximation of nonlocal-gradient energies
- Symmetry and monotonicity of singular solutions to p-Laplacian systems involving a first order term
- Flat flow solution to the mean curvature flow with volume constraint
