Wave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gaps
In this paper, the relaxed micromorphic model proposed in Ghiba et al.(Math Mech Solids,
2013), Neff et al.(Contin Mech Thermodyn, 2013) has been used to study wave propagation …
2013), Neff et al.(Contin Mech Thermodyn, 2013) has been used to study wave propagation …
Geometry of logarithmic strain measures in solid mechanics
We consider the two logarithmic strain measures=||\mathrm dev _n\mathrm log U||=||\mathrm
dev _n\mathrm log F^ TF||\quad and\quad\vol=|\mathrm tr (\mathrm log U)=|\mathrm tr …
dev _n\mathrm log F^ TF||\quad and\quad\vol=|\mathrm tr (\mathrm log U)=|\mathrm tr …
Cosserat micropolar elasticity: classical Eringen vs. dislocation form
We give a comparative presentation of the linear isotropic Cosserat elastic model from two
perspectives: the classical Mindlin–Eringen–Nowacki description in terms of a microrotation …
perspectives: the classical Mindlin–Eringen–Nowacki description in terms of a microrotation …
Numerical treatment of a geometrically nonlinear planar Cosserat shell model
We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell.
The kinematical model is similar to the general six-parameter resultant shell model with …
The kinematical model is similar to the general six-parameter resultant shell model with …
Existence of minimizers in the geometrically non-linear 6-parameter resultant shell theory with drilling rotations
This paper is concerned with the geometrically non-linear theory of 6-parametric elastic
shells with drilling degrees of freedom. This theory establishes a general model for shells …
shells with drilling degrees of freedom. This theory establishes a general model for shells …
On Grioli's minimum property and its relation to Cauchy's polar decomposition
In this paper we rediscover Grioli's important work on the optimality of the orthogonal factor
in the polar decomposition in an euclidean distance framework. We also draw attention to …
in the polar decomposition in an euclidean distance framework. We also draw attention to …
Regularity for a geometrically nonlinear flat Cosserat micropolar membrane shell with curvature
A Gastel, P Neff - Annales de l'Institut Henri Poincaré C, 2024 - ems.press
We consider the rigorously derived thin shell membrane-limit of a three-dimensional
isotropic geometrically nonlinear Cosserat micropolar model and deduce full interior …
isotropic geometrically nonlinear Cosserat micropolar model and deduce full interior …
Existence theorem for geometrically nonlinear Cosserat micropolar model under uniform convexity requirements
We reconsider the geometrically nonlinear Cosserat model for a uniformly convex elastic
energy and write the equilibrium system as a minimization problem. Applying the direct …
energy and write the equilibrium system as a minimization problem. Applying the direct …
A logarithmic minimization property of the unitary polar factor in the spectral and Frobenius norms
The unitary polar factor Q=U_p in the polar decomposition of Z=U_p\,H is the minimizer over
unitary matrices Q for both ‖\rmLog(Q^*Z)‖^2 and its Hermitian part ‖\rmsym__*\!(\rmLog …
unitary matrices Q for both ‖\rmLog(Q^*Z)‖^2 and its Hermitian part ‖\rmsym__*\!(\rmLog …
Quadratic-stretch elasticity
A nonlinear small-strain elastic theory is constructed from a systematic expansion in Biot
strains, truncated at quadratic order. The primary motivation is the desire for a clean …
strains, truncated at quadratic order. The primary motivation is the desire for a clean …