scholarly journals Connecting local active forces to macroscopic stress in elastic media

Soft Matter ◽  
2015 ◽  
Vol 11 (8) ◽  
pp. 1597-1605 ◽  
Author(s):  
Pierre Ronceray ◽  
Martin Lenz
Keyword(s):  
General Relation ◽  
Mechanical Stresses ◽  
Elastic Media ◽  
Linear Elastic ◽  
Active Elements ◽  
Macroscopic Stress ◽  
Internal Forces ◽  
Force Dipole ◽  
Living Materials

Many living materials exert mechanical stresses on their environment that originate from internal forces generated by embedded active elements. We derive a general relation between microscopic forces and macroscopic stresses, which takes the form of a conservation of the force dipole across scales in linear elastic media.

Analytical and 3D Finite Element Study of the Deflection of an Elastic Cantilever Bilayer Plate

2010 ◽  
Vol 78 (1) ◽  
Author(s):  
M. Chekchaki ◽  
V. Lazarus ◽  
J. Frelat
Keyword(s):  
Thin Films ◽  
Finite Element ◽  
Three Dimensional ◽  
Analytical Formula ◽  
Mechanical Stresses ◽  
Linear Elastic ◽  
Wide Range ◽  
Finite Element Calculations ◽  
Analytical Formulas ◽  
Three Dimensional Elasticity

The mechanical system considered is a bilayer cantilever plate. The substrate and the film are linear elastic. The film is subjected to isotropic uniform prestresses due for instance to volume variation associated with cooling, heating, or drying. This loading yields deflection of the plate. We recall Stoney’s analytical formula linking the total mechanical stresses to this deflection. We also derive a relationship between the prestresses and the deflection. We relax Stoney’s assumption of very thin films. The analytical formulas are derived by assuming that the stress and curvature states are uniform and biaxial. To quantify the validity of these assumptions, finite element calculations of the three-dimensional elasticity problem are performed for a wide range of plate geometries, Young’s and Poisson’s moduli. One purpose is to help any user of the formulas to estimate their accuracy. In particular, we show that for very thin films, both formulas written either on the total mechanical stresses or on the prestresses, are equivalent and accurate. The error associated with the misfit between our theorical study and numerical results are also presented. For thicker films, the observed deflection is satisfactorily reproduced by the expression involving the prestresses and not the total mechanical stresses.

Hashin–Shtrikman bounds of periodic linear elastic media with cubic symmetry

2020 ◽  
Vol 25 (5) ◽  
pp. 1182-1198 ◽  
Author(s):  
George Mejak
Keyword(s):  
Variational Principle ◽  
Boundary Value Problem ◽  
Elastic Media ◽  
Macroscopic Strain ◽  
Two Phase ◽  
Cubic Symmetry ◽  
Shear Moduli ◽  
Linear Elastic ◽  
Periodic Linear ◽  
Periodic Composite

Based on the Hashin–Shtrikman variational principle, novel bounds on the effective shear moduli of a two-phase periodic composite are derived. The composite constituents are assumed to be isotropic, while the microstructure is assumed to exhibit cubic symmetry. A solution of the subsidiary boundary value problem is expressed as a double contraction of a fourth-order cubic tensor with the applied macroscopic strain. The bounds for cubic shear moduli are new, while the bounds for the bulk modulus are equal to the classical ones. The new bounds are verified for composites with the cubic, frame, octet and cubic + octet structures. It is shown that they are nearly attained for the cubic, octet and cubic + octet structures.

On the existence of type-6 transonic states in linear elastic media of cubic symmetry

1987 ◽  
Vol 411 (1840) ◽  
pp. 251-263 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Elastic Solid ◽  
Mechanics Of Solids ◽  
Elastic Media ◽  
Slowness Surface ◽  
Cubic Symmetry ◽  
Linear Elastic ◽  
Surface Wave Propagation ◽  
Anisotropic Elastic

Crucial to the understanding of surface-wave propagation in an anisotropic elastic solid is the notion of transonic states, which are defined by sets of parallel tangents to a centred section of the slowness surface. This study points out the previously unrecognized fact that first transonic states of type 6 (tangency at three distinct points on the outer slowness branch S 1 ) indeed exist and are the rule, rather than the exception, in so-called C 3 cubic media (satisfying the inequalities c 12 + c 44 > c 11 - c 44 > 0); simple numerical analysis is used to predict orientations of slowness sections in which type-6 states occur for 21 of the 25 C 3 cubic media studied previously by Chadwick & Smith (In Mechanics of solids , pp. 47-100 (1982)). Limiting waves and the composite exceptional limiting wave associated with such type-6 states are discussed.

scholarly journals Proposed Method of Distribution of Horizontal Loads on Stiffening Walls

2021 ◽  
Vol 1203 (2) ◽  
pp. 022032
Author(s):  
Radosław Jasiński
Keyword(s):  
Numerical Methods ◽  
Shell Model ◽  
Analytical Model ◽  
Load Distribution ◽  
Shear Stiffness ◽  
Wall Structure ◽  
Simple Analytical Model ◽  
Linear Elastic ◽  
Internal Forces ◽  
Reliable Methods

Abstract Numerical methods are commonly used to determine internal forces in stiffening walls. Extreme internal forces can be easily generated not only in slab-and-wall structure, but also in the bar system. It is always time-consuming to build such a structure, thus it is not used in single- or multi-family buildings with a simple wall arrangement. Then, a simple analytical model can be used to calculate internal forces in walls. Eurocode 6 (prEN 1996-1-1:2017) does not contain specific guidelines to calculate internal forces in walls and to use numerical methods or other reliable methods. This paper presents the procedure for determining internal forces in a building with a simple wall arrangement. The proposed method is based on the division of a wall with openings into components. The results were compared with values of internal forces determined by the linear elastic FE shell model. Rotation centre (RC) of the wall plan was demonstrated to be a significant factor which, besides bending and shear stiffness, had an impact on load distribution.

scholarly journals Optimal Mass Design of 25 Bars Truss with Loading Conditions on Five Node Elements

2019 ◽  
Vol 4 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Koumbe Mbock ◽  
Etoua Remy Magloire ◽  
Lezin Seba Minsili ◽  
Okpwe Mbarga Richard
Keyword(s):  
Minimum Weight ◽  
Elastic Model ◽  
Loading Conditions ◽  
Cross Sectional ◽  
Linear Elastic ◽  
Space Truss ◽  
Mass Minimization ◽  
Internal Forces ◽  
Minimum Displacement ◽  
Weight Design

The optimal design of a twenty-five bar space truss commonly involves multiple loading conditions acting on 4 node elements in the linear elastic model. In this paper, we describe the behavior of the truss system with our experimental loading conditions on five node elements subject to minimum displacement and stresses that are used to formulate the constrained nonlinear optimization problem. Numerical computations are developed with the objective of mass minimization and the best structural design is selected by applying the interior point method with the guidance of Matlab Optimization Toolbox. Our numerical results show the optimal values of cross-sectional areas, material densities, and internal forces which satisfy the minimum weight design. These results provide the appropriate mass to the experimental data and allow substantial changes in size, shape, and topology.

scholarly journals Interaction of highly nonlinear solitary waves with linear elastic media

2011 ◽  
Vol 83 (4) ◽  
Author(s):  
Jinkyu Yang ◽  
Claudio Silvestro ◽  
Devvrath Khatri ◽  
Luigi De Nardo ◽  
Chiara Daraio
Keyword(s):  
Solitary Waves ◽  
Elastic Media ◽  
Linear Elastic ◽  
Highly Nonlinear ◽  
Highly Nonlinear Solitary Waves ◽  
Nonlinear Solitary Waves
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