Study of the plane problem for a physically nonlinear elastic solid by methods of the theory of functions of one complex Variable

A weak line inclusion model in a nonlinear elastic solid is proposed to analytically quantify and investigate, for the first time, the stress state and growth conditions of a finite-length shear band in a ductile prestressed metallic material. The deformation is shown to become highly focused and aligned coaxial to the shear band—a finding that provides justification for the experimentally observed strong tendency towards rectilinear propagation—and the energy release rate to blow up to infinity, for incremental loading occurring when the prestress approaches the elliptic boundary. It is concluded that the propagation becomes ‘unrestrainable’, a result substantiating the experimental observation that shear bands are the preferential near-failure deformation modes.

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Application of holographic interferometry for strain soliton observation in nonlinear elastic solid waveguides

10.1117/12.212671 ◽

1995 ◽

Author(s):

Galina V. Dreiden ◽

A. V. Porubov ◽

A. F. Samsonov ◽

Irina V. Semenova ◽

E. V. Sokurinskaya

Keyword(s):

Holographic Interferometry ◽

Elastic Solid ◽

Nonlinear Elastic

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Complex Variable Solution of Plane Problem for Functionally Graded Materials

Solid Mechanics and Its Applications - IUTAM Symposium on Dynamics of Advanced Materials and Smart Structures ◽

10.1007/978-94-017-0371-0_44 ◽

2003 ◽

pp. 449-458 ◽

Cited By ~ 1

Author(s):

Wang Xianfeng ◽

Norio Hasebe

Keyword(s):

Plane Problem ◽

Functionally Graded Materials ◽

Complex Variable ◽

Functionally Graded ◽

Graded Materials

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Universal deformations in inhomogeneous isotropic nonlinear elastic solids

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2021.0547 ◽

2021 ◽

Vol 477 (2253) ◽

Author(s):

Arash Yavari

Keyword(s):

Strain Energy ◽

Elastic Solid ◽

Necessary Condition ◽

Density Functions ◽

Elastic Solids ◽

Universal Deformations ◽

Green Strain ◽

The Right ◽

Nonlinear Elastic ◽

Isotropic Solids

Universal (controllable) deformations of an elastic solid are those deformations that can be maintained for all possible strain-energy density functions and suitable boundary tractions. Universal deformations have played a central role in nonlinear elasticity and anelasticity. However, their classification has been mostly established for homogeneous isotropic solids following the seminal works of Ericksen. In this article, we extend Ericksen’s analysis of universal deformations to inhomogeneous compressible and incompressible isotropic solids. We show that a necessary condition for the known universal deformations of homogeneous isotropic solids to be universal for inhomogeneous solids is that inhomogeneities respect the symmetries of the deformations. Symmetries of a deformation are encoded in the symmetries of its pulled-back metric (the right Cauchy–Green strain). We show that this necessary condition is sufficient as well for all the known families of universal deformations except for Family 5.

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A Multi-State HLL Approximate Riemann Solver for Solid/Vacuum Riemann Problem

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.872.393 ◽

2017 ◽

Vol 872 ◽

pp. 393-398

Author(s):

Wei Zhang ◽

Jin Song Bai ◽

De Jun Sun

Keyword(s):

Riemann Problem ◽

Elastic Solid ◽

Riemann Solver ◽

Finite Volume Schemes ◽

Approximate Riemann Solver ◽

Practical Applications ◽

Piecewise Parabolic ◽

Nonlinear Elastic ◽

Fast Waves ◽

Hll Approximate Riemann Solver

A new multi-state HLLD (‘‘D’’ stands for Discontinuities.) approximate Riemann solver for Riemann problem of nonlinear elastic solid is developed based on the assumption that a wave configuration for the solution that consists of five waves (two slow waves, two fast waves and a contact discontinuity) separating six constant states. Since the intermediate states satisfied with the Rankine-Hugoniot relations in this approximate Riemann system are analytically obtained, the HLLD Riemann solver can be constructed straightforwardly. The Piecewise Parabolic Method (PPM) is used directly to construct high-order finite-volume schemes. Numerical tests demonstrate that the scheme PPM coupled with HLLD is robust and efficient. It indicates that the scheme PPM+ HLLD can be useful in practical applications for the non-linear elasticity.

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A Mechanical Model for Mammalian Tendon

Journal of Applied Mechanics ◽

10.1115/1.3423699 ◽

1975 ◽

Vol 42 (4) ◽

pp. 755-758 ◽

Cited By ~ 23

Author(s):

D. E. Beskos ◽

J. T. Jenkins

Keyword(s):

Mechanical Model ◽

Elastic Solid ◽

Material Behavior ◽

Circular Cylinders ◽

Elastic Solids ◽

Fiber Reinforced Composite ◽

Reinforced Composite ◽

Constant Pitch ◽

Inextensible Fibers ◽

Nonlinear Elastic

A theoretical model is proposed to describe the mechanical behavior of mammalian tendon. The tendon is modeled as an incompressible fiber-reinforced composite with continuously distributed inextensible fibers. The fibers describe helices with constant pitch on concentric right circular cylinders. The analysis is, essentially, independent of the material behavior and, for example, applies to nonlinear elastic solids and viscoelastic materials. A boundary-value problem for tendon extension is discussed in detail and, for a particular nonlinear elastic solid, the deformation and stress are determined to be in qualitative agreement with existing experimental results.

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