Validation of an interaction law for the Eshelby inclusion problem in elasto-viscoplasticity

2005 ◽  
Vol 42 (7) ◽  
pp. 1923-1941 ◽  
Author(s):  
S. Mercier ◽  
N. Jacques ◽  
A. Molinari
Author(s):  
Luqun Ni ◽  
Xanthippi Markenscoff

The dynamic generalization of the celebrated Eshelby inclusion with transformation strain is the (subsonically) self-similarly expanding ellipsoidal inclusion starting from the zero dimension. The solution of the governing system of partial differential equations was obtained recently by Ni & Markenscoff (In press. J. Mech. Phys. Solids ( doi:10.1016/j.jmps.2016.02.025 )) on the basis of the Radon transformation, while here an alternative method is presented. In the self-similarly expanding motion, the Eshelby property of constant constrained strain is valid in the interior domain of the expanding ellipsoid where the particle velocity vanishes (lacuna). The dynamic Eshelby tensor is obtained in integral form. From it, the static Eshelby tensor is obtained by a limiting procedure, as the axes' expansion velocities tend to zero and time to infinity, while their product is equal to the length of the static axis. This makes the Eshelby problem the limit of its dynamic generalization.


2016 ◽  
Vol 97-98 ◽  
pp. 530-542 ◽  
Author(s):  
Jean-François Barthélémy ◽  
Albert Giraud ◽  
Francis Lavergne ◽  
Julien Sanahuja

Author(s):  
Mohammad Kazemi-Lari ◽  
John Shaw ◽  
Alan Wineman ◽  
Rafael Shimkunas ◽  
Leighton Izu ◽  
...  

We present a mathematical model to guide and interpret ongoing Cell-in-Gel experiments, where isolated cardiac myocytes are embedded in a constraining viscoelastic hydrogel, to study mechano-chemo-transduction mechanisms at the single cell level. A recently developed mathematical model, based on the elastic Eshelby inclusion problem, is here extended to account for viscoelasticity of the inclusion (cell) and the matrix (gel). This provides a tool to calculate time-dependent 3D stress and strain fields of a single myocyte contracting periodically inside a viscoelastic matrix, which is used to explore the sensitivity of the cell’s mechanical response to constitutive properties and geometry. A parametric study indicates that increased gel crosslink concentration significantly alters the strain and stress fields inside the cell and creates an increased time-lag in the mechanical response of the cell during contraction. It is also found that autoregulation at the cellular level in response to afterload, potentially in the form of increased cell stiffness, has a strong influence on cell contraction.


2011 ◽  
Vol 21 (1) ◽  
pp. 97-127 ◽  
Author(s):  
K. Yanase ◽  
J. W. Ju

The effective elastic moduli of composite materials are investigated in the presence of imperfect interfaces between the inclusions and the matrix. The primary focus is on the spherical particle reinforced composites. By admitting the displacement jumps at the particle–matrix interface, the modified Eshelby inclusion problem is studied anew. To derive the modified Eshelby tensor, three approximate methods are presented and compared by emphasizing the existence of a unique solution and computational efficiency. Subsequently, the effective elastic stiffness tensor of the composite is formulated based on the proposed micromechanical framework and homogenization. Specifically, by incorporating imperfect interface, the modified versions of the Mori–Tanaka method, the self-consistent method, and the differential scheme are presented. By comparing these three methods, the effects of interfacial sliding and separation on the degradation (damage) of the effective elastic moduli of composites are analyzed and assessed. Finally, a critical aspect of the presented formulations is specifically addressed.


Author(s):  
L.P Liu

We present solutions to the Eshelby conjectures based on a variational inequality. We first discuss the meanings of Eshelby's original statement. By Fourier analysis, we establish the connection between the homogeneous Eshelby inclusion problem and the classic Newtonian potential problem. We then proceed to the solutions of the Eshelby conjectures. Under some hypothesis on the material properties and restricted to connected inclusions with Lipschitz boundaries, we show that one version of the Eshelby conjectures is valid in all dimensions and the other version is valid in two dimensions. We also show the existence of multiply connected inclusions in all dimensions and the existence of non-ellipsoidal connected inclusions in three and higher dimensions such that, in physical terms and in the context of elasticity, some uniform eigenstress of the inclusion induces uniform strain on the inclusion. We numerically calculate these special inclusions based on the finite-element method.


2020 ◽  
Vol 01 ◽  
Author(s):  
Zheng Zuo ◽  
Zongyun Chen ◽  
Zhijian Cao ◽  
Wenxin Li ◽  
Yingliang Wu

: The scorpion toxins are the largest potassium channel-blocking peptide family. The understanding of toxin binding interfaces is usually restricted by two classical binding interfaces: one is the toxin α-helix motif, the other is the antiparallel β-sheet motif. In this review, such traditional knowledge was updated by another two different binding interfaces: one is BmKTX toxin using the turn motif between the α-helix and antiparallel β-sheet domains as the binding interface, the other is Ts toxin using turn motif between the β-sheet in the N-terminal and α-helix domains as the binding interface. Their interaction analysis indicated that the scarce negatively charged residues in the scorpion toxins played a critical role in orientating the toxin binding interface. In view of the toxin negatively charged amino acids as “binding interface regulator”, the law of scorpion toxin-potassium channel interaction was proposed, that is, the polymorphism of negatively charged residue distribution determines the diversity of toxin binding interfaces. Such law was used to develop scorpion toxin-potassium channel recognition control technique. According to this technique, three Kv1.3 channel-targeted peptides, using BmKTX as the template, were designed with the distinct binding interfaces from that of BmKTX through modulating the distribution of toxin negatively charged residues. In view of the potassium channel as the common targets of different animal toxins, the proposed law was also shown to helpfully orientate the binding interfaces of other animal toxins. Clearly, the toxin-potassium channel interaction law would strongly accelerate the research and development of different potassium channelblocking animal toxins in the future.


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