scholarly journals Nonlinear elastic inclusions in isotropic solids

2013 ◽  
Vol 469 (2160) ◽  
pp. 20130415 ◽  
Author(s):  
Arash Yavari ◽  
Alain Goriely
Keyword(s):  
Residual Stress ◽  
Spherical Inclusion ◽  
The Body ◽  
Model Systems ◽  
Stress Fields ◽  
Elastic Solids ◽  
Geometric Framework ◽  
Spherical Ball ◽  
Nonlinear Elastic ◽  
Nonlinear Solids

We introduce a geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains. Inclusions are regions in a body with different reference configurations from the body itself and can be described by distributed eigenstrains. Geometrically, the eigenstrains define a Riemannian 3-manifold in which the body is stress-free by construction. The problem of residual stress calculation is then reduced to finding a mapping from the Riemannian material manifold to the ambient Euclidean space. Using this construction, we find the residual stress fields of three model systems with spherical and cylindrical symmetries in both incompressible and compressible isotropic elastic solids. In particular, we consider a finite spherical ball with a spherical inclusion with uniform pure dilatational eigenstrain and we show that the stress in the inclusion is uniform and hydrostatic. We also show how singularities in the stress distribution emerge as a consequence of a mismatch between radial and circumferential eigenstrains at the centre of a sphere or the axis of a cylinder.

On Eshelby’s inclusion problem in nonlinear anisotropic elasticity

2021 ◽  
pp. 2150002
Author(s):  
Arash Yavari
Keyword(s):  
Spherical Inclusion ◽  
Anisotropic Elasticity ◽  
Inclusion Problem ◽  
Elastic Solids ◽  
Spherical Ball ◽  
Solid Circular Cylinder ◽  
Stress And Deformation ◽  
Nonlinear Elastic ◽  
Radially Inhomogeneous ◽  
Isotropic Solids

In this paper, the recent literature of finite eignestrains in nonlinear elastic solids is reviewed, and Eshelby’s inclusion problem at finite strains is revisited. The subtleties of the analysis of combinations of finite eigenstrains for the example of combined finite radial, azimuthal, axial and twist eigenstrains in a finite circular cylindrical bar are discussed. The stress field of a spherical inclusion with uniform pure dilatational eigenstrain in a radially-inhomogeneous spherical ball made of arbitrary incompressible isotropic solids is analyzed. The same problem for a finite circular cylindrical bar is revisited. The stress and deformation fields of an orthotropic incompressible solid circular cylinder with distributed eigentwists are analyzed.

scholarly journals The twist-fit problem: finite torsional and shear eigenstrains in nonlinear elastic solids

2015 ◽  
Vol 471 (2183) ◽  
pp. 20150596 ◽  
Author(s):  
Arash Yavari ◽  
Alain Goriely
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Stress Fields ◽  
Elastic Solids ◽  
Overall Response ◽  
Finite Shear ◽  
Torsional Shear ◽  
Isotropic Solid ◽  
Nonlinear Elastic

Eigenstrains in nonlinear elastic solids are created through defects, growth or other anelastic effects. These eigenstrains are known to be important as they can generate residual stresses and alter the overall response of the solid. Here, we study the residual stress fields generated by finite torsional or shear eigenstrains. This problem is addressed by considering a cylindrical bar made of an incompressible isotropic solid with an axisymmetric distribution of shear eigenstrains. As particular examples, we consider a cylindrical inhomogeneity and a double inhomogeneity with finite shear eigenstrains and study the effect of torsional shear eigenstrains on the axial and torsional stiffnesses of the circular cylindrical bar.

Tangent Moduli of the Hencky Material Model Derived from the Stored Energy Function at Finite Strains

2005 ◽  
Vol 482 ◽  
pp. 327-330
Author(s):  
Alena Kruisová ◽  
Jiří Plešek
Keyword(s):  
Residual Stress ◽  
Acoustic Waves ◽  
Ultrasonic Testing ◽  
Material Model ◽  
Stress Fields ◽  
Stored Energy ◽  
Elastic Solids ◽  
Logarithmic Model ◽  
Tangent Moduli ◽  
Theoretical Analyses

Tangent moduli associated with the linear logarithmic model of hyperelasticity are derived. These relations are crucial not only to theoretical analyses but also to wave propagation and ultrasonic testing. The tangent moduli as functions of stress determine the speed of propagating acoustic waves and, therefore, indirectly point to a possible occurrence of residual stress fields in elastic solids.

scholarly journals Weyl geometry and the nonlinear mechanics of distributed point defects

2012 ◽  
Vol 468 (2148) ◽  
pp. 3902-3922 ◽  
Author(s):  
Arash Yavari ◽  
Alain Goriely
Keyword(s):  
Residual Stress ◽  
Stress Field ◽  
Point Defect ◽  
Point Defects ◽  
Spherical Inclusion ◽  
The Body ◽  
Inclusion Problem ◽  
Spherically Symmetric ◽  
Residual Stress Field ◽  
Defect Distribution

The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects—where the body is stress-free—is a flat Weyl manifold, i.e. a manifold with an affine connection that has non-metricity with vanishing traceless part, but both its torsion and curvature tensors vanish. Given a spherically symmetric point defect distribution, we construct its Weyl material manifold using the method of Cartan's moving frames. Having the material manifold, the anelasticity problem is transformed to a nonlinear elasticity problem and reduces the problem of computing the residual stresses to finding an embedding into the Euclidean ambient space. In the case of incompressible neo-Hookean solids, we calculate explicitly this residual stress field. We consider the example of a finite ball and a point defect distribution uniform in a smaller ball and vanishing elsewhere. We show that the residual stress field inside the smaller ball is uniform and hydrostatic. We also prove a nonlinear analogue of Eshelby's celebrated inclusion problem for a spherical inclusion in an isotropic incompressible nonlinear solid.

scholarly journals Role of Chiral Configuration in the Photoinduced Interaction of D- and L-Tryptophan with Optical Isomers of Ketoprofen in Linked Systems

2021 ◽  
Vol 22 (12) ◽  
pp. 6198
Author(s):  
Aleksandra A. Ageeva ◽  
Ilya M. Magin ◽  
Alexander B. Doktorov ◽  
Victor F. Plyusnin ◽  
Polina S. Kuznetsova ◽  
...  
Keyword(s):  
Amino Acid ◽  
Excited States ◽  
Resonance Energy Transfer ◽  
Resonance Energy ◽  
Dipole Interaction ◽  
The Body ◽  
Model Systems ◽  
Optical Isomers ◽  
Amino Acid Properties ◽  
Parkinson’S Diseases

The study of the L- and D-amino acid properties in proteins and peptides has attracted considerable attention in recent years, as the replacement of even one L-amino acid by its D-analogue due to aging of the body is resulted in a number of pathological conditions, including Alzheimer’s and Parkinson’s diseases. A recent trend is using short model systems to study the peculiarities of proteins with D-amino acids. In this report, the comparison of the excited states quenching of L- and D-tryptophan (Trp) in a model donor–acceptor dyad with (R)- and (S)-ketoprofen (KP-Trp) was carried out by photochemically induced dynamic nuclear polarization (CIDNP) and fluorescence spectroscopy. Quenching of the Trp excited states, which occurs via two mechanisms: prevailing resonance energy transfer (RET) and electron transfer (ET), indeed demonstrates some peculiarities for all three studied configurations of the dyad: (R,S)-, (S,R)-, and (S,S)-. Thus, the ET efficiency is identical for (S,R)- and (R,S)-enantiomers, while RET differs by 1.6 times. For (S,S)-, the CIDNP coefficient is almost an order of magnitude greater than for (R,S)- and (S,R)-. To understand the source of this difference, hyperpolarization of (S,S)-and (R,S)- has been calculated using theory involving the electron dipole–dipole interaction in the secular equation.

Analysis of circumferentially welded thin-walled cylinders to study the effects of tack weld orientations and joint root opening on residual stress fields

2009 ◽  
Vol 223 (5) ◽  
pp. 1037-1049 ◽  
Author(s):  
N U Dar ◽  
E M Qureshi ◽  
A M Malik ◽  
M M I Hammouda ◽  
R A Azeem
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Arc Welding ◽  
Operating Conditions ◽  
Stress Fields ◽  
Welded Structures ◽  
Prime Concern ◽  
Thin Walled ◽  
Tack Weld ◽  
Welding Processes

In recent years, the demand for resilient welded structures with excellent in-service load-bearing capacity has been growing rapidly. The operating conditions (thermal and/or structural loads) are becoming more stringent, putting immense pressure on welding engineers to secure excellent quality welded structures. The local, non-uniform heating and subsequent cooling during the welding processes cause complex thermal stress—strain fields to develop, which finally leads to residual stresses, distortions, and their adverse consequences. Residual stresses are of prime concern to industries producing weld-integrated structures around the globe because of their obvious potential to cause dimensional instability in welded structures, and contribute to premature fracture/failure along with significant reduction in fatigue strength and in-service performance of welded structures. Arc welding with single or multiple weld runs is an appropriate and cost-effective joining method to produce high-strength structures in these industries. Multi-field interaction in arc welding makes it a complex manufacturing process. A number of geometric and process parameters contribute significant stress levels in arc-welded structures. In the present analysis, parametric studies have been conducted for the effects of a critical geometric parameter (i.e. tack weld) on the corresponding residual stress fields in circumferentially welded thin-walled cylinders. Tack weld offers considerable resistance to the shrinkage, and the orientation and size of tacks can altogether alter stress patterns within the weldments. Hence, a critical analysis for the effects of tack weld orientation is desirable.

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