scholarly journals Analytical solution of the cylindrical torsion problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)

2021 ◽  
pp. 108128652110235
Author(s):  
Gianluca Rizzi ◽  
Geralf Hütter ◽  
Hassam Khan ◽  
Ionel-Dumitrel Ghiba ◽  
Angela Madeo ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Torsion Problem ◽  
Generalized Continua ◽  
Material Parameters ◽  
Micromorphic Continuum

We solve the St. Venant torsion problem for an infinite cylindrical rod whose behaviour is described by a family of isotropic generalized continua, including the relaxed micromorphic and classical micromorphic model. The results can be used to determine the material parameters of these models. Special attention is given to the possible nonphysical stiffness singularity for a vanishing rod diameter, because slender specimens are, in general, described as stiffer.

scholarly journals Analytical solution of the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)

2021 ◽  
Author(s):  
Gianluca Rizzi ◽  
Hassam Khan ◽  
Ionel-Dumitrel Ghiba ◽  
Angela Madeo ◽  
Patrizio Neff
Keyword(s):  
Analytical Solution ◽  
Analytical Solutions ◽  
Size Effects ◽  
Uniaxial Extension ◽  
Extension Problem ◽  
Generalized Continua ◽  
Material Parameters ◽  
Micromorphic Continuum

AbstractWe derive analytical solutions for the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua. These solutions may help in the identification of material parameters of generalized continua which are able to disclose size effects.

TORSION OF FUNCTIONALLY GRADED OPEN-SECTION MEMBERS

2012 ◽  
Vol 04 (02) ◽  
pp. 1250020 ◽  
Author(s):  
M. R. HEMATIYAN ◽  
E. ESTAKHRIAN
Keyword(s):  
Shear Modulus ◽  
Cross Section ◽  
Analytical Method ◽  
Functionally Graded ◽  
Torsion Problem ◽  
Uniform Thickness ◽  
Analytical Formulation ◽  
Material Parameters ◽  
Open Section ◽  
Open Cross Section

There exist some approximate analytical methods for torsion analysis of homogeneous open cross-section members; however, no analytical formulation has been presented for solving a torsion problem of inhomogeneous open cross-section members yet. In this paper, an approximate analytical method for the torsion analysis of thin- to moderately thick-walled functionally graded open-section members with uniform thickness is presented. The shear modulus of rigidity is assumed to have a variation across the thickness. The cross-section is decomposed into some straight, curved and end segments. The torsion problem is then solved in each segment considering some appropriate approximations. By presenting three examples, accuracy of the presented method with respect to thickness, corner radius, and material parameters are investigated. The results show that the proposed method is useful for torsion analysis of thin- to moderately thick-walled functionally graded open-section members.

Stress Distribution in Front of the Crack - Analytical Solutions vs. Numerical. Can the Differences be Minimized?

2019 ◽  
Vol 810 ◽  
pp. 7-14
Author(s):  
Andrzej Neimitz ◽  
Sebastian Lipiec
Keyword(s):  
Stress Distribution ◽  
Analytical Solution ◽  
Large Strains ◽  
Stress Distributions ◽  
Fracture Criteria ◽  
Nonlinear Fracture Mechanics ◽  
The Real ◽  
Material Parameters ◽  
Nonlinear Fracture ◽  
Analytical Formulae

It is shown that it is possible to obtain such material parameters as α and Q, which, when used in the analytical formulae proposed by Hutchinson, Rice and Rosengren and O’Dowd and Shih, can lead to stress distributions similar to those obtained numerically (except for the region at the immediate crack front). The numerical solution obtained after calibration of the stress-strain uniaxial curve and assuming large strains is expected to be close to the “"real” stress distribution. Thus, the analytical solution is also close to the “real” stress distribution. These new values of α and Q can now be used in fracture criteria proposed within the scope of classical nonlinear fracture mechanics.

An analysis of lipid membrane morphology in the presence of coordinate-dependent non-uniformity

2020 ◽  
Vol 26 (1) ◽  
pp. 45-61
Author(s):  
Wenhao Yao ◽  
Chun IL Kim
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Linear Model ◽  
Energy Function ◽  
Lipid Membranes ◽  
Lipid Membrane ◽  
Membrane Interactions ◽  
Equilibrium Equations ◽  
Material Parameters ◽  
Membrane Morphology

A model for the mechanics of lipid membranes with non-uniform (coordinate-dependent) properties is discussed. The coordinate-dependent responses of the membranes are incorporated via the augmented non-uniform energy function and material parameters, which are dependent explicitly on the surface coordinates. We formulate the associated normal and tangential Euler equilibrium equations through which the coordinate-dependent responses of membranes are characterized. The admissible boundary conditions are taken from the existing non-linear model but reformulated and adopted to the present framework. Within the prescription of superposed incremental deformations, a compatible linear model is also formulated, from which a complete analytical solution describing the non-uniform responses of the membrane subjected to substrate–membrane interactions is obtained.

Cosserat Modeling of Size Effects in Crystalline Solids

2000 ◽  
Vol 653 ◽  
Author(s):  
Samuel Forest
Keyword(s):  
Stress State ◽  
Size Effects ◽  
Elastic Inclusion ◽  
Characteristic Size ◽  
Infinite Matrix ◽  
Crystalline Solids ◽  
Generalized Continua ◽  
Absolute Size ◽  
Kink Bands ◽  
The Matrix

AbstractThe mechanics of generalized continua provides an efficient way of introducing intrinsic length scales into continuum models of materials. A Cosserat framework is presented here to descrine the mechanical behavior of crystalline solids. The first application deals with the problem of the stress field at a crak tip in Cosserat single crystals. It is shown that the strain localization patterns developping at the crack tip differ from the classical picture : the Cosserat continuum acts as a bifurcation mode selector, whereby kink bands arising in the classical framework disappear in generalized single crystal plasticity. The problem of a Cosserat elastic inclusion embedded in an infinite matrix is then considered to show that the stress state inside the inclusion depends on its absolute size lc. Two saturation regimes are observed : when the size R of the inclusion is much larger than a characteristic size of the medium, the classical Eshelby solution is recovered. When R is much small than the inclusion, a much higher stress is reached (for an inclusion stiffer than the matrix) that does not depend on the size any more. There is a transition regime for which the stress state is not homogeneous inside the inclusion. Similar regimes are obtained in the study of grain size effects in polycrystalline aggregates of Cosserat grains.

Sign in / Sign up

Export Citation Format

Share Document