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Preprints  [18]

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Preprints from members of the UM School of Mathematics, September 2008 - present.

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Existence and stability of viscoelastic shock profiles

Barker, Blake; Lewicka, Marta; Zumbrun, Kevin (2010-06-09)
We investigate existence and stability of viscoelastic shock profiles for a class of planar models including the incompressible shear case studied by Antman and Malek-Madani. We establish that the resulting equations ...

Reduced theories in nonlinear elasticity

Lewicka, Marta (2010-06-09)
The purpose of this note is to report on the recent development concerning the analysis and the rigorous derivation of thin film models for structures with nontrivial geometry. This includes: (i) shells with mid-surface ...

The Foppl-von Karman equations for plates with incompatible strains

Lewicka, Marta; Mahadevan, L.; Pakzad, Reza (2010-02-24)
We provide a derivation of the Foppl-von Karman equations for the shape of and stresses in an elastic plate with residual strains. These might arise from a range of causes: inhomogeneous growth, plastic deformation, ...

Scaling laws for non-Euclidean plates and the W^{2,2} isometric immersions of Riemannian metrics

Lewicka, Marta; Pakzad, Reza (2009-07-09)
This paper concerns the elastic structures which exhibit non-zero strain at free equilibria. Many growing tissues (leaves, flowers or marine invertebrates) attain complicated configurations during their free growth. Our ...

The infinite hierarchy of elastic shell models: some recent results and a conjecture

Lewicka, Marta; Pakzad, Reza (2009-07-09)
We summarize some recent results of the authors and their collaborators, regarding the derivation of thin elastic shell models (for shells with mid-surface of arbitrary geometry) from the variational theory of $3$d nonlinear ...

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