# Space-time integral currents of bounded variation

@inproceedings{Rindler2021SpacetimeIC, title={Space-time integral currents of bounded variation}, author={Filip Rindler}, year={2021} }

Motivated by a recent model for elasto-plastic evolutions that are driven by the flow of dislocations [12], this work develops a theory of space-time integral currents with bounded variation in time. Based on this, we further introduce the notion of Lipschitz deformation distance between integral currents, which arises physically as a (simplified) dissipation distance. Several results are obtained: A Helly-type compactness theorem, a deformation theorem, an isoperimetric inequality, and the…

## One Citation

Elasto-plastic evolution of single crystals driven by dislocation flow

- Physics
- 2021

This work introduces a model for large-strain, geometrically nonlinear elasto-plastic dynamics in single crystals. The key feature of our model is that the plastic dynamics are entirely driven by the…

## References

SHOWING 1-10 OF 20 REFERENCES

Energetic solutions to rate-independent large-strain elasto-plastic evolutions driven by discrete dislocation flow

- Mathematics
- 2021

This work rigorously implements a recent model, introduced in [34], of large-strain elasto-plastic evolution in single crystals where the plastic flow is driven by the movement of discrete…

Liftings

- Young measures, and lower semicontinuity, Arch. Ration. Mech. Anal. 232
- 2019

Strong approximation in h-mass of rectifiable currents under homological constraint

- Physics, MathematicsAdvances in Calculus of Variations
- 2019

Abstract Let h : ℝ → ℝ + {h:\mathbb{R}\to\mathbb{R}_{+}} be a lower semicontinuous subbadditive and even function such that h ( 0 ) = 0 {h(0)=0} and h ( θ ) ≥ α | θ |…

Variational Evolution of Dislocations in Single Crystals

- Mathematics, Computer ScienceJ. Nonlinear Sci.
- 2019

This paper provides an existence result for the energetic evolution of a set of dislocation lines in a three-dimensional single crystal and discusses a novel dissipation structure for such currents, namely the flat distance, that will drive the evolution of the dislocation clusters.

Liftings, Young Measures, and Lower Semicontinuity

- MathematicsArchive for Rational Mechanics and Analysis
- 2018

AbstractThis work introduces liftings and their associated Young measures as new tools to study the asymptotic behaviour of sequences of pairs (uj, Duj)j for $${(u_j)_j\subset {\rm…

Gradient flows and a generalized Wasserstein distance in the space of Cartesian currents

- 2017

On the lower semicontinuous envelope of functionals defined on polyhedral chains

- Mathematics
- 2017

Abstract In this note we prove an explicit formula for the lower semicontinuous envelope of some functionals defined on real polyhedral chains. More precisely, denoting by H : R → [ 0 , ∞ ) an even,…

The Line-Tension Approximation as the Dilute Limit of Linear-Elastic Dislocations

- Mathematics
- 2015

We prove that the classical line-tension approximation for dislocations in crystals, that is, the approximation that neglects interactions at a distance between dislocation segments and accords…

Modeling of dislocations and relaxation of functionals on 1-currents with discrete multiplicity

- Mathematics, Physics
- 2014

In the modeling of dislocations one is led naturally to energies concentrated on lines, where the integrand depends on the orientation and on the Burgers vector of the dislocation, which belongs to a…

Physical Metallurgy Principles - SI Edition

- Cengage Learning
- 2009