Jena Jeong

Existence, Uniqueness and Stability in Linear Cosserat Elasticity for Weakest Curvature Conditions

We investigate the weakest possible constitutive assumptions on the curvature energy in linear Cosserat models still providing for existence, uniqueness and stability. The assumed curvature energy is μL2 c ∥dev sym ∇axl A∥2 where axl A is the axial vector of the skewsymmetric microrotation A ∈ so(3) and dev is the orthogonal projection on the Lie-algebra sl(3) of trace free matrices. The proposed Cosserat parameter values coincide with values adopted in the experimental literature by R. S. Lakes. It is observed that unphysical stiffening for small samples is avoided in torsion and bending while size effects are still present. The number of Cosserat parameters is reduced from six to four. One Cosserat coupling parameter µc > 0 and only one length scale parameter L c > 0. Use is made of a new coercive inequality for conformal Killing vectorfields. An interesting point is that no (controversial) essential boundary conditions on the microrotations need to be specified; thus avoiding boundary layer effects. Since the curvature energy is the weakest possible consistent with non-negativity of the energy, it seems that the Cosserat couple modulus µc > 0 remains a material parameter independent of the sample size which is impossible for stronger curvature expressions.

THE REISSNER–MINDLIN PLATE IS THE Γ-LIMIT OF COSSERAT ELASTICITY

The linear Reissner–Mindlin membrane-bending plate model is the rigourous Γ-limit for zero thickness of a linear isotropic Cosserat bulk model with symmetric curvature. For this result we use the natural nonlinear scaling for the displacements u and the linear scaling for the infinitesimal microrotations Ā ∈ 𝔰𝔬(3). We also provide formal calculations for other combinations of scalings by retrieving other plate models previously proposed in the literature by formal asymptotic methods as corresponding Γ-limits. No boundary conditions on the microrotations are prescribed.

Linear Cosserat Elasticity, Conformal Curvature and Bounded Stiffness

We describe a principle of bounded stiffness and show that bounded stiffness in torsion and bending implies a reduction of the curvature energy in linear isotropic Cosserat models leading to the so called conformal curvature case \(\frac{1}{2}\mu L_{c}^{2}\Vert{\operatorname{dev}\operatorname{sym}\nabla \operatorname{axl}\overline{A}}\Vert^{2}\) where \(\overline{A}\in\mathfrak{so}(3)\) is the Cosserat microrotation. Imposing bounded stiffness greatly facilitates the Cosserat parameter identification and allows a well-posed, stable determination of the one remaining length scale parameter L c and the Cosserat couple modulus μ c .

Chemo-Micro-Dilatation Modeling of Carbonation Shrinkage Phenomenon of the Porous Mortars

In this paper, we investigate the CO2 carbonation on porous materials such as the cement paste mortar. Our scientific goal is to model the CO2 carbonation effect on the porous cement mortar by the micro-dilatation theory and to determine the chemo-mechanical stress development due to the chemical reactions. In fact, this phenomenon will modify not only the pH value of the cement paste but also the micro-structure due to collapsing pore-network. Based upon the micro-dilatation theory originally proposed by Cowin and Nunziato, four unknown parameters related to the micro-structure will be determined for the cement mortar using the semi-empirical method and numerical modeling. The experimental carbonation tests on two different types of cement paste (CEMI and CEMIII) have been realized to capture carbonated affected zones and to measure their shrinkage deformations.