scholarly journals Transient Solutions for One-Dimensional Problems With Strain Softening

1987 ◽  
Vol 54 (3) ◽  
pp. 513-518 ◽  
Author(s):  
T. Belytschko ◽  
Xiao-Jun Wang ◽  
Z. P. Bazant ◽  
Y. Hyun
Keyword(s):  
Strain Rate ◽  
Closed Form ◽  
Transient Response ◽  
Softening Point ◽  
Strain Softening ◽  
Stress Strain ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Transient Solutions

Closed-form solutions are presented for the transient response of rods in which strain softening occurs and the stress-strain laws exhibit nonvanishing stresses after the strain-softening regime. It is found that the appearance of any strain softening results in an infinite strain rate if the material is inviscid. For a stress-strain law with a monotonically decreasing stress the strains are infinite also. If the stress increases after the strain-softening portion, the strains remain finite and the strain-softening point moves through the rod.

One-Dimensional Dynamic Compressive Behavior of EPDM Rubber

2003 ◽  
Vol 125 (3) ◽  
pp. 294-301 ◽  
Author(s):  
B. Song ◽  
W. Chen
Keyword(s):  
Strain Rate ◽  
High Speed ◽  
Dynamic Stress ◽  
Split Hopkinson Pressure Bar ◽  
Constant Strain Rate ◽  
Strain Rates ◽  
Hopkinson Pressure Bar ◽  
Stress Strain ◽  
Epdm Rubber ◽  
One Dimensional

Dynamic compressive stress-strain curves at various strain rates of an Ethylene-Propylene-Diene Monomer Copolymer (EPDM) rubber have been determined with a modified split Hopkinson pressure bar (SHPB). The use of a pulse-shaping technique ensures that the specimen deforms at a nearly constant strain rate under dynamically equilibrated stress. The validity of the experiments was monitored by a high-speed digital camera for specimen edge deformation, and by piezoelectric force transducers for dynamic stress equilibrium. The resulting dynamic stress-strain curves for the EPDM indicate that the material is sensitive to strain rates and that the strain-rate sensitivity depends on the value of strain. Based on a strain energy function theory, a one-dimensional dynamic constitutive equation for this rubber was modified to describe the high strain-rate experimental results within the ranges of strain and strain rates presented in this paper.

Constitutive Model of Shape Memory Alloys: One-Dimensional Phase Transformation Model

2008 ◽  
Vol 56 ◽  
pp. 84-91
Author(s):  
Tadashige Ikeda
Keyword(s):  
Phase Transformation ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Strain Rate ◽  
Shape Memory ◽  
Strain Rate Effect ◽  
Rate Effect ◽  
Reverse Transformation ◽  
Stress Strain ◽  
One Dimensional

A simple yet accurate macroscopic constitutive model of shape memory alloys has been developed. The features of this model are (1) energy-based phase transformation criterion, (2) one-dimensional phase transformation rule based on a micromechanical viewpoint, (3) dissipated energy with a form of a sum of two exponential functions, (4) duplication of the strain rate effect, and (5) adaptability to multi-phase transformation. This model is further improved to be able to express stress-strain relationships such that the reverse transformation starts at a higher stress than the martensitic transformation starts. Here, the ideal reversible transformation temperature is empirically described by a function of the martensite volume fraction. In this paper, an outline of our model is given, where the improvement is introduced. Then, it is shown that the model can quantitatively duplicate the major and minor hysteresis loops, strain rate effect, and asymmetry in tension and compression on the stress-strain relationship. And that it can also duplicate the stress-strain relationships having the reverse transformation start stress higher than the forward one.

AN EXPERIMENTAL STUDY ON THE IMPACT DEFORMATION AND THE STRAIN RATE SENSITIVITY IN SOME STRUCTURAL ADHESIVES

2008 ◽  
Vol 22 (31n32) ◽  
pp. 5590-5595 ◽  
Author(s):  
TOSHIMASA NAGAI ◽  
TAKESHI IWAMOTO ◽  
TOSHIYUKI SAWA ◽  
YASUHISA SEKIGUCHI ◽  
HIDEAKI KURAMOTO ◽  
...  
Keyword(s):  
Strain Rate ◽  
Inelastic Deformation ◽  
Strain Softening ◽  
Peak Stress ◽  
Stress Strain ◽  
Structural Adhesives ◽  
Strain Behavior ◽  
Impact Deformation ◽  
The Impact ◽  
Softening Stage

The impact deformation behavior and the strain sensitivity of structural adhesives are experimentally investigated by using INSTRON-type universal testing machine and split Hopkinson pressure bar apparatus. The experimental results show some fundamental features of the typical compressive stress-strain behavior of polymers with linear elastic and nonlinear inelastic deformation stages. In the inelastic deformation, the peak stress, and the strain-softening stage after the peak can be observed at the entire range of strain-rate from 10-4 to 103 /s. In addition, it can be found that the relationship between the peak stress at the strain-softening stage and strain-rate for a semi-logarithm curve is linear in a range of low strain rate, however, that becomes nonlinear at high strain rate. Finally, some constitutive models try to be applied for to describe the stress-strain behavior of structural adhesives.

scholarly journals Uniaxial Dynamic Compressive Behaviors of Hydraulic Asphalt Concrete under the Coupling Effect between Temperature and Strain Rate

Materials ◽  
2020 ◽  
Vol 13 (23) ◽  
pp. 5348
Author(s):  
Rui Tang ◽  
Zhenpeng Yu ◽  
Guoqing Liu ◽  
Furong Li ◽  
Wenbin Tang
Keyword(s):  
Quantitative Analysis ◽  
Strain Rate ◽  
Temperature Effect ◽  
Asphalt Concrete ◽  
Brittle Failure ◽  
Failure Modes ◽  
Strain Softening ◽  
Coupling Effect ◽  
Peak Stress ◽  
Stress Strain

To investigate the compressive dynamic properties of hydraulic asphalt concrete under various temperatures, four temperatures and four strain rates have been set to perform the uniaxial compression experiments using hydraulic servo machine in this paper. The influence of temperature and strain rate on the failure modes, stress-strain curves and mechanical characteristic parameters of hydraulic asphalt concrete is analyzed and the results reveal that the failure modes and stress-strain curves have significant temperature effect. When the temperature is between −20 °C and 0 °C, the failure mode is dominated by brittle failure of asphalt binder, and hydraulic asphalt concrete shows obvious strain softening. With the addition of temperature, the failure modes of specimens are transferred from brittle failure to ductile failure since the asphalt changes from elastic-brittleness to viscoelasticity. Influenced by temperature effect, the compressive stress-strain curves of hydraulic asphalt concrete show strain hardening while the peak stress of hydraulic asphalt concrete is obviously decreased, and the variation coefficient of peak stress has a power relation with temperature. With successive increases in strain rate, the stress-strain curves of hydraulic asphalt concrete gradually are transferred from strain hardening to strain softening. The peak stress and stiffness modulus of specimens under compression gradually increase, and the dynamic increase factor of peak stress is linearly related with the logarithm value of strain rate after dimensionless treatment. In terms of the quantitative analysis of the experimental data, two relationship models of the coupling effect between temperature and strain rate are proposed. The proposed models have good applicability to the quantitative analysis of the experimental results in the manuscript. This paper offers important insights into the application and development of hydraulic asphalt concrete in hydraulic engineering.

Relaxation and creep in twist and flexure

2014 ◽  
Vol 10 (3) ◽  
pp. 304-327 ◽  
Author(s):  
V. Kobelev
Keyword(s):  
Strain Rate ◽  
Closed Form ◽  
Stress Function ◽  
Constitutive Models ◽  
Analytic Description ◽  
Secondary Creep ◽  
Common Procedure ◽  
Content Type ◽  
Closed Form Solutions ◽  
Analytical Expressions

Purpose – The purpose of this paper is to derive the exact analytical expressions for torsion and bending creep of rods with the Norton-Bailey, Garofalo and Naumenko-Altenbach-Gorash constitutive models. These simple constitutive models, for example, the time- and strain-hardening constitutive equations, were based on adaptations for time-varying stress of equally simple models for the secondary creep stage from constant load/stress uniaxial tests where minimum creep rate is constant. The analytical solution is studied for Norton-Bailey and Garofalo laws in uniaxial states of stress. Design/methodology/approach – The creep component of strain rate is defined by material-specific creep law. In this paper the authors adopt, following the common procedure Betten, an isotropic stress function. The paper derives the expressions for strain rate for uniaxial and shear stress states for the definite representations of stress function. First, in this paper the authors investigate the creep for the total deformation that remains constant in time. Findings – The exact analytical expressions giving the torque and bending moment as a function of the time were derived. Research limitations/implications – The material isotropy and homogeneity preimposed. The secondary creep phase is considered. Practical implications – The results of creep simulation are applied to practically important problem of engineering, namely for simulation of creep and relaxation of helical and disk springs. Originality/value – The new, closed form solutions with commonly accepted creep models allow a deeper understanding of such a constitutive model's effect on stress and deformation and the implications for high temperature design. The application of the original solutions allows accurate analytic description of creep and relaxation of practically important problems in mechanical engineering. Following the procedure the paper establishes closed form solutions for creep and relaxation in helical, leaf and disk springs.

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