Elastic-Inelastic Self-Consistent Model for Polycrystals

2002 ◽  
Vol 69 (3) ◽  
pp. 309-316 ◽  
Author(s):  
A. Abdul-Latif ◽  
J. P. Dingli ◽  
K. Saanouni
Keyword(s):  
Complex Loading ◽  
Small Strain ◽  
Elastic Behavior ◽  
Inelastic Behavior ◽  
Surface Evolution ◽  
Heterogeneous Distribution ◽  
Strain Behavior ◽  
Loading Paths ◽  
Nonlinear Stress ◽  
Nonlinear Elastic

Based on a well-established nonincremental interaction law for fully anisotropic and compressible elastic-inelastic behavior of polycrystals, tangent formulation-based and simplified interaction laws, of softened nature, are derived to describe the nonlinear elastic-inelastic behavior of fcc polycrystals under different loading paths. Within the framework of small strain hypothesis, the elastic behavior, which is defined at granular level, is assumed to be isotropic, uniform, and compressible neglecting the grain rotation. The heterogeneous inelastic deformation is microscopically determined using the slip theory. In addition, the granular elastic behavior and its heterogeneous distribution from grain to grain within a polycrystal are taken into account. Comparisons between these two approaches show that the simplified one is more suitable to describe the overall responses of polycrystals notably under multiaxial loading paths. Nonlinear stress-strain behavior of polycrystals under complex loading, especially a cyclic one, is of particular interest in proposed modeling. The simplified model describes fairly well the yield surface evolution after a certain inelastic prestraining and the principle cyclic features such as Bauschinger effect, additional hardening, etc.

Mesodamage Evolution in Polycrystals

2005 ◽  
Vol 127 (2) ◽  
pp. 214-221 ◽  
Author(s):  
M. Chadli ◽  
A. Abdul-Latif
Keyword(s):  
Fatigue Life ◽  
Micromechanical Model ◽  
Small Strain ◽  
Cyclic Stress ◽  
Damage Variable ◽  
Thermodynamic Force ◽  
Inelastic Behavior ◽  
Loading Paths ◽  
Localized Plastic Deformation ◽  
Phase Angles

A micromechanical model of damaged elasto-inelastic behavior is proposed to predict the plastic fatigue life for fcc metallic polycrystals under multiaxial loading paths. This model is expressed in the time-dependent plasticity for a small strain assumption. In order to generalize and then to increase the model applicability (with respect to other works of the author) in describing the cyclic stress-strain evolution during plastic fatigue, it is therefore assumed that a damage variable initiates and then evolves at the grain level where the phenomenon of the localized plastic deformation occurs. The associated thermodynamic force of the damage variable is determined as a total granular energy (elastic and inelastic). The transition of the elastic strain from the single to the polycrystal, which is classically performed by averaging procedures in this type of modeling, is modified due to the coupling of such a strain with damage. The developed model is tested under different multiaxial cyclic loading situations (tension-compression and tension-torsion with different out-of-phase angles). The effects the loading paths and the grains aggregate type on the fatigue life are appropriately investigated. It is demonstrated that the model can correctly describe the overall and local damaged behavior of polycrystals.

The Use of Line and Point Contacts in Determining Lubricant Rheology Under Low Slip Elastohydrodynamic Conditions

1983 ◽  
Vol 105 (2) ◽  
pp. 280-287 ◽  
Author(s):  
D. M. Heyes ◽  
C. J. Montrose
Keyword(s):  
Maxwell Model ◽  
Small Strain ◽  
Elastic Behavior ◽  
Point Contacts ◽  
Strain Behavior ◽  
Mineral Oils ◽  
Convolution Integral Equation ◽  
Shear Relaxation ◽  
Maximum Contact ◽  
Contact Pressures

A theoretical study has been made of the elastohydrodynamic small strain behavior of lubricants in line and point contacts. The model for the lubricants is more realistic than those proposed to date and involves a reformulation of the Maxwell model in terms of a Volterra convolution integral equation. In addition to being more physically appealing, the approach can be easily generalized to describe coupled structural and shear relaxation of a nonexponential nature. The calculations predict that certain mineral oils change from exhibiting compressional viscoelastic to elastic behavior at maximum contact pressures and rolling speeds of order 0.5 GPa and 1.0 m/s.

Inelastic Strain Accumulation in Cortical Bone During Rapid Transient Tensile Loading

1999 ◽  
Vol 121 (6) ◽  
pp. 616-621 ◽  
Author(s):  
M. T. Fondrk ◽  
E. H. Bahniuk ◽  
D. T. Davy
Keyword(s):  
Cortical Bone ◽  
Axial Strain ◽  
Human Bone ◽  
Elastic Behavior ◽  
Transverse Strain ◽  
Bovine Bone ◽  
Stress Strain ◽  
Nonlinear Strain ◽  
Strain Behavior ◽  
Nonlinear Stress

An experimental study examined the tensile stress-strain behavior of cortical bone during rapid load cycles to high strain amplitudes. Machined bovine and human cortical bone samples were subjected to loading cycles at a nominal load/unload rate of ±420 MPa/s. Loads were reversed at pre-selected strain levels such that load cycles were typically completed in 0.5-0.7 seconds. Axial strain behavior demonstrated considerable nonlinearity in the first load cycle, while transverse strain behavior was essentially linear. For the human bone 29.1 percent (S.D. = 4.7 percent), and for the bovine bone 35.1 percent (S.D. = 10.8 percent) of the maximum nonlinear strain accumulated after load reversal, where nonlinear strain was defined as the difference between total strain and strain corresponding to linear elastic behavior. Average residual axial strain on unloading was 35.4 percent (S.D. = 1.2 percent) for human bone and 35.1 percent (S.D. = 2.9 percent) of maximum nonlinear strain. Corresponding significant volumetric strains and residual volumetric strains were found. The results support the conclusions that the nonlinear stress-strain behavior observed during creep loading also occurs during transient loading at physiological rates. The volume increases suggest that damage accumulation, i.e., new internal surfaces and voids, plays a major role in this behavior. The residual volume increases and associated disruptions in the internal structure of bone provide a potential stimulus for a biological repair response.

Determination, Derivation, Influence and Discussions of Parameters for Deformation Analyses with Duncan-Chang Modified E-B Model

2011 ◽  
Vol 90-93 ◽  
pp. 157-164
Author(s):  
Han Peng Liu ◽  
Dong Yuan Wang ◽  
Zhi Jun Ma
Keyword(s):  
Laboratory Tests ◽  
Small Strain ◽  
Hebei Province ◽  
Experimental Results ◽  
Model Parameters ◽  
Horizontal Deformation ◽  
Strain Behavior ◽  
Nonlinear Stress ◽  
Confining Pressures ◽  
New Apparatus

This paper presents a study on influence of model parameters on deformation analyses with Duncan-Chang Modified Nonlinear Stress-strain (E-B) model for an ore mining tailings located in Chengde, Hebei Province of China. How to determine and derive these parameters from the laboratory experimental results was introduced first. Findings from numerical analyses performed with Midas GTS indicate that model parameters K and n most significantly affect the vertical and horizontal deformation respectively. Based on the analysis, the accuracy and effectiveness of these parameters were discussed further. Principles of the model and the parameter derivations suggest the model and parameters work better for small strain cases, hence model parameters shall be better determined with laboratory tests with low confining pressures or using new apparatus to measure small strain behavior of soil to ensure analysis results reliable.

Finite Deformation and Nonlinear Elastic Behavior of Flexible Composites

1988 ◽  
Vol 55 (1) ◽  
pp. 149-155 ◽  
Author(s):  
Shen-Yi Luo ◽  
Tsu-Wei Chou
Keyword(s):  
Present Theory ◽  
Elastic Behavior ◽  
Stress Strain ◽  
Flexible Composites ◽  
Elastomeric Matrix ◽  
Eulerian Description ◽  
Stress Strain Relation ◽  
Nonlinear Stress ◽  
Material Nonlinear ◽  
Nonlinear Elastic

The flexible composites discussed in this paper are composed of continuous fibers in an elastomeric matrix. The usable range of deformation of these composites is much larger than that of conventional rigid composites. Due to the material as well as geometric factors, the stress-strain relations for these composites are generally nonlinear under finite deformations. A constitutive model has been developed based upon the Eulerian description. The material nonlinear stress-strain relation is derived by using the stress energy density referring to the deformed volume. The stretching-shear coupling and the effects of the in-plane reorientation of fibers are also considered in the theoretical analysis. Comparisons are made between predictions of the present theory and experimental data for tirecord/rubber and Kevlar/silicone-elastomer flexible composite laminae; very good correlations have been found.

Nonlinear Elastic Behavior of Unidirectional Composites With Fiber Waviness Under Compressive Loading

1996 ◽  
Vol 118 (4) ◽  
pp. 561-570 ◽  
Author(s):  
H. M. Hsiao ◽  
I. M. Daniel
Keyword(s):  
Constitutive Relations ◽  
Compressive Loading ◽  
Nonlinear Material ◽  
Elastic Behavior ◽  
Compression Tests ◽  
Fiber Waviness ◽  
Unidirectional Composites ◽  
Nonlinear Stress ◽  
Material Nonlinear ◽  
Nonlinear Elastic

Nonlinear elastic behavior of unidirectional composites with fiber waviness under compressive loading was investigated theoretically and experimentally. Unidirectional carbon/epoxy composites with uniform, graded, and localized fiber waviness were studied. Complementary strain energy was used to derive the material nonlinear stress-strain relations. Nonlinear material properties obtained from shear and longitudinal and transverse compression tests were incorporated into the analysis. Compression tests of specimens with known fiber waviness were conducted to verify the constitutive relations. Experimental results were in good agreement with predictions based on the constitutive model.

scholarly journals Black rubber and the non-linear elastic response of scale invariant solids

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Matteo Baggioli ◽  
Víctor Cáncer Castillo ◽  
Oriol Pujolàs
Keyword(s):  
Strain Curve ◽  
Effective Field ◽  
Elastic Response ◽  
Elastic Behaviour ◽  
Scale Invariant ◽  
Stress Strain ◽  
Nonlinear Stress ◽  
Hyper Elastic ◽  
Simple Class ◽  
Nonlinear Elastic

Abstract We discuss the nonlinear elastic response in scale invariant solids. Following previous work, we split the analysis into two basic options: according to whether scale invariance (SI) is a manifest or a spontaneously broken symmetry. In the latter case, one can employ effective field theory methods, whereas in the former we use holographic methods. We focus on a simple class of holographic models that exhibit elastic behaviour, and obtain their nonlinear stress-strain curves as well as an estimate of the elasticity bounds — the maximum possible deformation in the elastic (reversible) regime. The bounds differ substantially in the manifest or spontaneously broken SI cases, even when the same stress- strain curve is assumed in both cases. Additionally, the hyper-elastic subset of models (that allow for large deformations) is found to have stress-strain curves akin to natural rubber. The holographic instances in this category, which we dub black rubber, display richer stress- strain curves — with two different power-law regimes at different magnitudes of the strain.

Cord/Rubber Material Properties

1985 ◽  
Vol 58 (4) ◽  
pp. 830-856 ◽  
Author(s):  
R. J. Cembrola ◽  
T. J. Dudek
Keyword(s):  
Finite Element ◽  
Material Model ◽  
Rubber Composites ◽  
Stress Strain ◽  
Element Analysis ◽  
Rubber Layer ◽  
Strain Behavior ◽  
Nonlinear Stress ◽  
Interlaminar Shear ◽  
Mechanics Of Composite Materials

Abstract Recent developments in nonlinear finite element methods (FEM) and mechanics of composite materials have made it possible to handle complex tire mechanics problems involving large deformations and moderate strains. The development of an accurate material model for cord/rubber composites is a necessary requirement for the application of these powerful finite element programs to practical problems but involves numerous complexities. Difficulties associated with the application of classical lamination theory to cord/rubber composites were reviewed. The complexity of the material characterization of cord/rubber composites by experimental means was also discussed. This complexity arises from the highly anisotropic properties of twisted cords and the nonlinear stress—strain behavior of the laminates. Micromechanics theories, which have been successfully applied to hard composites (i.e., graphite—epoxy) have been shown to be inadequate in predicting some of the properties of the calendered fabric ply material from the properties of the cord and rubber. Finite element models which include an interply rubber layer to account for the interlaminar shear have been shown to give a better representation of cord/rubber laminate behavior in tension and bending. The application of finite element analysis to more refined models of complex structures like tires, however, requires the development of a more realistic material model which would account for the nonlinear stress—strain properties of cord/rubber composites.

Continuum Description of the Time- and Strain-Dependent Poisson’s Ratio of Ligament Under Finite Deformation

2013 ◽  
Author(s):  
Aaron M. Swedberg ◽  
Shawn P. Reese ◽  
Steve A. Maas ◽  
Benjamin J. Ellis ◽  
Jeffrey A. Weiss
Keyword(s):  
Large Scale ◽  
Mechanical Response ◽  
Tensile Deformation ◽  
Large Strain ◽  
Fiber Direction ◽  
Strain Behavior ◽  
Nonlinear Stress ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Strain Dependent

Ligament volumetric behavior controls fluid and thus nutrient movement as well as the mechanical response of the tissue to applied loads. The reported Poisson’s ratios for tendon and ligament subjected to tensile deformation loading along the fiber direction are large, ranging from 0.8 ± 0.3 in rat tail tendon fascicles [1] to 2.98 ± 2.59 in bovine flexor tendon [2]. These Poisson’s ratios are indicative of volume loss and thus fluid exudation [3,4]. We have developed micromechanical finite element models that can reproduce both the characteristic nonlinear stress-strain behavior and large, strain-dependent Poisson’s ratios seen in tendons and ligaments [5], but these models are computationally expensive and unfeasible for large scale, whole joint models. The objectives of this research were to develop an anisotropic, continuum based constitutive model for ligaments and tendons that can describe strain-dependent Poisson’s ratios much larger than the isotropic limit of 0.5. Further, we sought to demonstrate the ability of the model to describe experimental data, and to show that the model can be combined with biphasic theory to describe the rate- and time-dependent behavior of ligament and tendon.

scholarly journals Small Strain Behavior of Geomaterials: Modelling of Strain Rate Effects

1997 ◽  
Vol 37 (2) ◽  
pp. 127-138 ◽  
Author(s):  
Hervé Di Benedetto ◽  
Fumio Tatsuoka
Keyword(s):  
Strain Rate ◽  
Small Strain ◽  
Strain Rate Effects ◽  
Strain Behavior ◽  
Rate Effects
Sign in / Sign up

Export Citation Format

Share Document