A review on split Hopkinson bar experiments on the dynamic characterisation of concrete

Specimen shape and size effects on the concrete compressive strength under static and dynamic tests

The effects of strain rate on the dynamic stress-strain behavior of cement mortar were investigated in split Hopkinson pressure bar (SHPB) tests; the resulting strain rates ranged from 20 to 280  s−1. A total of 39 specimens were subjected to static and dynamic axial compressive loadings. The results showed that cement mortar is a typical strain-rate dependent material. Both dynamic compressive strength and critical strain increased with strain-rate increases. However, there seemed to be no strain-rate effects on the initial elastic modulus of cement mortar. Based on the stress-strain curves of different strain rates, as well as the random statistical distribution hypothesis for strength, a dynamic damage constitutive model of cement model under compression was used. The relationships of the primary parameters for strain rate are also presented in this paper. The simulated stress-strain curves matched the experimental results well. The results showed that the strength of cement mortar obeyed a Wei...

Stress-Strain Behavior and Statistical Continuous Damage Model of Cement Mortar under High Strain Rates

Based on extensive literature review the behaviour of concrete under wide range of compressive and tensile strain rates is presented. The dynamic compressive strength of concrete can achieve the value of DIF (dynamic increase factor) equal about 3.5, and the dynamic tensile strength even 13. However, the strain rate response of concrete in tension and compression in all range of strain rate differs much. In compression strain rate sensitivity should be investigated in two domains, because of the shift of test results. The reason of division is probably connected with influence of the method of testing and especially with the specimen shape and size. The article presents also the strain rate sensitivity of new types of cement-based materials, like RPC, which appears not to differ much from the sensitivity of normal concrete.

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The influence of the strain rate on the strength of concrete taking into account the experimental techniques

Static and dynamic properties of concrete with different types and shapes of fibrous reinforcement

In this paper, a second approximate solution of nonlinear jerk equations (third order differential equation) can be obtained by using modified harmonic balance method. The method is simpler and easier to carry out the solution of nonlinear differential equations due to less number of nonlinear equations are required to solve than the classical harmonic balance method. The results obtained from this method are compared with those obtained from the other existing analytical methods that are available in the literature and the numerical method. The solution shows a good agreement with the numerical solution as well as the analytical methods of the available literature.

Modified harmonic balance method for the solution of nonlinear jerk equations

In this paper, an efficient analytical solution method, namely, multi-level residue harmonic balance, is introduced and developed for the nonlinear vibrations of multi-mode flexible beams on an elastic foundation subject to external harmonic excitation. The main advantage of this solution method is that only one set of nonlinear algebraic equations is generated in the zero level solution procedure while the higher level solutions for any desired accuracy can be obtained by solving a set of linear algebraic equations. In other words, the computation effort to find more accurate nonlinear solutions is much less. In this paper, a multi-mode formulation, which represents the nonlinear beam vibration, is derived and set up. Then, the solution procedures are developed for obtaining the nonlinear multi-mode solution. The results from the multi-level residue harmonic balance method agree well with those from a numerical integration method. The effects of various parameters such as vibration amplitude, foundation ...

The multi-level residue harmonic balance solutions of multi-mode nonlinearly vibrating beams on an elastic foundation

Stress-Strain Behavior of Normal Strength Concrete Subjected to High Strain Rate

Nonlinear vibration behavior of beam is an important issue of structural engineering. In this study, a mathematical modeling of a forced nonlinear vibration of Euler-Bernoulli beam resting on nonlinear elastic foundation is presented. The nonlinear vibration behavior of the beam is investigated by using a modified multi-level residue harmonic balance method. The main advantage of the method is that only one nonlinear algebraic equation is generated at each solution level. The computational time of using the new method is much less than that spent on solving the set nonlinear algebraic equations generated in the classical harmonic balance method. Besides the new method can generate higher-level nonlinear solutions neglected by previous multi-level residue harmonic balance methods. The results obtained from the proposed method compared with those obtained by a classical harmonic balance method to verify the accuracy of the method which shows good agreement between the proposed and classical harmonic balance method. Besides, the effect of various parameters such as excitation magnitude, linear and nonlinear foundation stiffness, shearing stiffness etc. on the nonlinear vibration behaviors are examined

https://jacm.scu.ac.ir/article_13841_fc277fb49e1c23b2f454cce9c6745ef9.pdf

Modified Multi-level Residue Harmonic Balance Method for Solving Nonlinear Vibration Problem of Beam Resting on Nonlinear Elastic Foundation

This paper investigates the effect of friction angle and flow ratio on stress-strain relationship of high performance concrete (HPC) subjected to dynamic load. The simulation reveals that ultimate compressive strength of HPC shows a discrepancy from 111 to 139 MPa for friction angles between 30° and 50° at a loading rate of 800 GPa/s compared to 87 MPa under static loading. The influence of friction angle on strain is found to be nearly constant, that is, at 0.004. Lower value of flow ratio leads to larger deformation. In turn, the strength is lower. The results show that both friction angle and flow ratio exhibit some degree of sensitivity on either the stress or strain or both. The dynamic strength dependencies on friction angle and flow ratio are correlated. The equation contributes in defining material model parameters in the analysis of HPC dynamic behavior.

A. S. M. Z. Hasan

Papers

Modified harmonic balance method for the solution of nonlinear jerk equations

The multi-level residue harmonic balance solutions of multi-mode nonlinearly vibrating beams on an elastic foundation

Stress-Strain Behavior of Normal Strength Concrete Subjected to High Strain Rate

Modified Multi-level Residue Harmonic Balance Method for Solving Nonlinear Vibration Problem of Beam Resting on Nonlinear Elastic Foundation

Sensitivity of Model Parameter on Dynamic Behavior Simulation of HPC