scholarly journals Dynamic measurements of the nonlinear elastic parameter α in rock under varying conditions

2004 ◽  
Vol 109 (B2) ◽  
Author(s):  
Paul A. Johnson ◽  
Bernard Zinszner ◽  
Patrick Rasolofosaon ◽  
Frederic Cohen-Tenoudji ◽  
Koen Van Den Abeele
Keyword(s):  
Elastic Parameter ◽  
Dynamic Measurements ◽  
Nonlinear Elastic

scholarly journals How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity

2017 ◽  
Vol 473 (2207) ◽  
pp. 20170607 ◽  
Author(s):  
L. Angela Mihai ◽  
Alain Goriely
Keyword(s):  
Elastic Material ◽  
Mechanical Response ◽  
Finite Elasticity ◽  
Experimental Tests ◽  
Elastic Parameter ◽  
Hyperelastic Materials ◽  
Poisson Function ◽  
Elastic Responses ◽  
Nonlinear Elastic ◽  
Constitutive Parameters

The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young’s modulus and the Poisson’s ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests. These parameters represent changes in the material properties as the deformation progresses, and can be identified with their linear equivalent when the deformations are small. Universal relations between certain of these parameters are further established, and then used to quantify nonlinear elastic responses in several hyperelastic models for rubber, soft tissue and foams. The general parameters identified here can also be viewed as a flexible basis for coupling elastic responses in multi-scale processes, where an open challenge is the transfer of meaningful information between scales.

Brain tissue elastic behavior and experimental brain compression

1988 ◽  
Vol 255 (5) ◽  
pp. R799-R805 ◽  
Author(s):  
A. Schettini ◽  
E. K. Walsh
Keyword(s):  
Brain Tissue ◽  
Mechanical Response ◽  
Fluid Pressure ◽  
Elastic Parameter ◽  
Elastic Behavior ◽  
Present Observation ◽  
Tissue Elasticity ◽  
Tissue Pressure ◽  
Brain Compression ◽  
Nonlinear Elastic

This study was designed to test the hypothesis that the progressive expansion of an extradural mass causes detectable changes in brain mechanical response properties, in particular the nonlinear elastic behavior, before any significant changes in intracranial cerebrospinal fluid pressure can be detected. In 10 chronically prepared and anesthetized dogs, incremental inflation (0.07 ml/s) of an extradural balloon caused 1) a progressive fall in the brain nonlinear elastic parameter (G0, mmHg/mm2), 2) nonsignificant changes in brain tissue elasticity (G0, mmHg/mm), 3) a disproportionate progressive rise in subpial tension, and 4) a progressive fall in local cerebral blood flow (H2 clearance), despite a modest decrease in cerebral perfusion pressure (extracranial). In previous brain compression experiments (Brain Res. 305: 141-143, 1984) we have shown that the compression site becomes compacted and stiffer (increased G0) and its nonlinear elastic parameter (G0) increases markedly. These earlier findings, coupled with the present observation of a loss in tissue nonlinearity distally to the compression site, are most likely the major mechanisms by which, with a rapidly expanding intracranial mass, tissue pressure gradients and brain displacement, including transtentorial herniation, develop.

Study on Nondestructive Testing Method of Vertical Prestressed Reinforcement Tension in Box Girder

2014 ◽  
Vol 587-589 ◽  
pp. 1395-1401
Author(s):  
Yong Qing Gao ◽  
Jin Peng Zhu ◽  
Feng Zhang ◽  
Guang Zhi Qi
Keyword(s):  
Vibration Frequency ◽  
Tensile Force ◽  
Elastic Parameter ◽  
Elastic Support ◽  
Box Girder ◽  
Testing Method ◽  
Nondestructive Testing Method ◽  
Girder Bridge ◽  
Prestressed Reinforcement ◽  
Nonlinear Elastic

The diagonal cracks in the web of box girder bridge which caused by excessive loss of vertical prestressed tensioning force are particularly common. In order to effectively detect the real force of the vertical prestressed rebars. Take the exposed section of the vertical prestressed rebar as an analysis entity, and take the rebar as a rigid body; the anchoring segment is simulated by an annular outrigger and an annular elastic support. When vertical pretress tension changes, the stiffness of elastic support and the vibration frequency also change accordingly, the change of the value of tensile force can be reflected by the vibration frequency. Combined with the model test data, the nonlinear elastic parameter model between the finish .deformed rebar vertical tensioning force T and the space elastic support stiffness K is established. The validity of the method was checked by extension test. The study indicate that this method is accurate, fast and convenient for engineering applications, can effectively improve the construction quality.

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

Rubber Composition–Properties Relationships during Tire Numerical Simulation and Design Optimization

2017 ◽  
Vol 45 (1) ◽  
pp. 71-84 ◽  
Author(s):  
Alexey Mazin ◽  
Alexander Kapustin ◽  
Mikhail Soloviev ◽  
Alexander Karanets
Keyword(s):  
Numerical Simulation ◽  
Design Optimization ◽  
Strain Tensor ◽  
General Purpose ◽  
Orthogonal Functions ◽  
Element Analysis ◽  
Time Investment ◽  
Footprint Analysis ◽  
Composition Properties ◽  
Nonlinear Elastic

ABSTRACT Numerical simulation based on finite element analysis is now widely used during the design optimization of tires, thereby drastically reducing the time investment in the design process and improving tire performance because it is obtained from the optimized solution. Rubber material models that are used in numerical calculations of stress–strain distributions are nonlinear and may include several parameters. The relations of these parameters with rubber formulations are usually unknown, so the designer has no information on whether the optimal set of parameters is reachable by the rubber technological possibilities. The aim of this work was to develop such relations. The most common approach to derive the equation of the state of rubber is based on the expansion of the strain energy in a series of invariants of the strain tensor. Here, we show that this approach has several drawbacks, one of which is problems that arise when trying to build on its basis the quantitative relations between the rubber composition and its properties. An alternative is to use a series expansion in orthogonal functions, thereby ensuring the linear independence of the coefficients of elasticity in evaluation of the experimental data and the possibility of constructing continuous maps of “the composition to the property.” In the case of orthogonal Legendre polynomials, the technique for constructing such maps is considered, and a set of empirical functions is proposed to adequately describe the dependence of the parameters of nonlinear elastic properties of general-purpose rubbers on the content of the main ingredients. The calculated sets of parameters were used in numerical tire simulations including static loading, footprint analysis, braking/acceleration, and cornering and also in design optimization procedures.

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