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Lower semicontinuity for functionals defined on piecewise rigid functions and on GSBD
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Characterization of Optimal Carbon Nanotubes Under Stretching and Validation of the Cauchy–Born Rule
Carbon nanotubes are modeled as point configurations and investigated by minimizing configurational energies including two- and three-body interactions. Optimal configurations are identified with…
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A Piecewise Korn Inequality in SBD and Applications to Embedding and Density Results
TLDR
The result implies that $GSBD^2$ functions have bounded variation after subtraction of a piecewise infinitesimal rigid motion.
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A quantitative geometric rigidity result in SBD
We present a quantitative geometric rigidity estimate for special functions of bounded deformation in a planar setting generalizing the result by Friesecke, James, M\"uller obtained in nonlinear…
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Quasistatic crack growth in 2d-linearized elasticity
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A Korn-type inequality in SBD for functions with small jump sets
We present a Korn-type inequality in a planar setting for special functions of bounded deformation. We prove that for each function in SBD$^2$ with sufficiently small jump set the distance of the…
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Derivation of von Kármán Plate Theory in the Framework of Three-Dimensional Viscoelasticity
We apply a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in Kelvin’s-Voigt’s rheology to derive a viscoelastic plate model of von Kármán type. We start…
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On the Passage from Nonlinear to Linearized Viscoelasticity
We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in the Kelvin's-Voigt's rheology where the viscosity stress tensor complies with the…
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Graphene ground states
Graphene is locally two-dimensional but not flat. Nanoscale ripples appear in suspended samples and rolling up often occurs when boundaries are not fixed. We address this variety of graphene…
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Two-well rigidity and multidimensional sharp-interface limits for solid–solid phase transitions
We establish a quantitative rigidity estimate for two-well frame-indifferent nonlinear energies, in the case in which the two wells have exactly one rank-one connection. Building upon this novel…
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