Rate Independent Hysteresis

A new identification method that determines the parameters of Bouc-Wen hysteretic systems is presented. It is based on a hybrid evolutionary algorithm which utilizes selected stochastic operators, heuristics and problem-specific information. The proposed method exhibits efficiency, robustness and insensitivity to noise-corrupted data, while it identifies accurately both hysteretic and viscous damping based on suitable experiments. Its performance is investigated with respect to the information content of the input-output data. The scheme is verified by a hysteretic system representing a full-scale steel cantilever beam which is identified successfully. A series of parametric studies are also conducted that illustrate the inner workings of the proposed method, suggesting appropriate values for the controlling parameters.

In this work, a consistent smooth Bouc-Wen-type degrading hysteretic model is presented which incorporates stiffness degradation, strength deterioration, pinching, asymmetric hysteresis and strainhardening characteristics. The smooth rate-independent model originally proposed by Bouc [1] and later extended by Wen [2] was further developed by Sivaselvan and Reinhorn [3] to incorporate degradation phenomena. This is extended herein to incorporate two specific modifications; one accounting for the loading history effect in stiffness degradation, pointed out by Wang and Foliente , and another related to compatibility with plasticity postulates. The latter is independently enforced based on the method developed by Charalampakis and Koumousis [5], eliminating the model's displacement drift, force relaxation and non-closure of hysteretic loops when subjected to short unloading-reloading paths. Numerical examples are presented for a single-degree-of-freedom system demonstrating the effect of the modifications, particularly for seismic excitations.

The versatile Bouc-Wen model has been used extensively to describe hysteretic phenomena in various fields of engineering. Nevertheless, it is known that it exhibits displacement drift, force relaxation and nonclosure of hysteretic loops when subjected to short unloading-reloading paths. Consequently, it locally violates Drucker's or Ilyushin's postulate of plasticity. In this study, an effective modification of the model is proposed which eliminates these problems. A stiffening factor is introduced into the hysteretic differential equation which enables the distinction between virgin loading and reloading. Appropriate reversal points are utilized effectively to guide the entire process. It is shown that the proposed modification corrects the nonphysical behavior of the model under short unloading-reloading paths without affecting its response in all other cases. It is further demonstrated that the original and modified model exhibit significantly different response under seismic excitation.

T he large amount of rain that falls on the land surface of the Earth either runs off the soil surface or moves through unsaturated soil and passes through a series of processes such as infiltration, drainage, evaporation, and absorption by plant roots. The region of the soil that is unsaturated is known as the vadose zone (or simply the unsaturated zone), where the most interesting hysteresis-type behavior occurs. We use the term soil-water hysteresis to describe this phenomenon in terrestrial hydrology. The essence of this phenomenon is that "less mechanical work is required to insert water into unsaturated soil than to remove it-good for agriculture!" .

An efficient formulation for the response and dissipated energy of Bouc-Wen hysteretic model is proposed. The displacement is associated with the hysteretic parameter in terms of Gauss' hypergeometric function. The hysteretic equation is solved analytically for specific values of the exponential parameter that controls the transition between elastic and inelastic regime. This formulation is used to provide analytical expressions of the dissipated energy under symmetric cyclic excitation, based solely on the model parameters and the displacement amplitude. For arbitrary values of the exponential parameter, the equations are solved numerically. For fully yielding systems, approximate relations are determined using suitable curve fitting. The derived expressions facilitate considerably the preliminary design of hysteretic systems. r

A new identification method that determines the parameters of Bouc-Wen hysteretic systems is presented. It is based on a hybrid evolutionary algorithm which utilizes selected stochastic operators, heuristics and problem-specific information. The proposed method exhibits efficiency, robustness and insensitivity to noise-corrupted data, while it identifies accurately both hysteretic and viscous damping based on suitable experiments. Its performance is investigated with respect to the information content of the input-output data. The scheme is verified by a hysteretic system representing a full-scale steel cantilever beam which is identified successfully. A series of parametric studies are also conducted that illustrate the inner workings of the proposed method, suggesting appropriate values for the controlling parameters. r

In this work, a consistent smooth Bouc-Wen-type degrading hysteretic model is presented which incorporates stiffness degradation, strength deterioration, pinching, asymmetric hysteresis and strainhardening characteristics. The smooth rate-independent model originally proposed by Bouc [1] and later extended by Wen [2] was further developed by Sivaselvan and Reinhorn [3] to incorporate degradation phenomena. This is extended herein to incorporate two specific modifications; one accounting for the loading history effect in stiffness degradation, pointed out by Wang and Foliente , and another related to compatibility with plasticity postulates. The latter is independently enforced based on the method developed by Charalampakis and Koumousis [5], eliminating the model's displacement drift, force relaxation and non-closure of hysteretic loops when subjected to short unloading-reloading paths. Numerical examples are presented for a single-degree-of-freedom system demonstrating the effect of the modifications, particularly for seismic excitations.

A new identification method that determines the parameters of Bouc-Wen hysteretic systems is presented. It is based on a hybrid evolutionary algorithm which utilizes selected stochastic operators, heuristics and problem-specific information. The proposed method exhibits efficiency, robustness and insensitivity to noise-corrupted data, while it identifies accurately both hysteretic and viscous damping based on suitable experiments. Its performance is investigated with respect to the information content of the input-output data. The scheme is verified by a hysteretic system representing a full-scale steel cantilever beam which is identified successfully. A series of parametric studies are also conducted that illustrate the inner workings of the proposed method, suggesting appropriate values for the controlling parameters. r

A number of improvements have been added to the existing analytical model of hysteresis loops defined in parametric form. In particular, three phase shifts are included in the model, which permits us to tilt the hysteresis loop smoothly by the required angle at the split point as well as to smoothly change the curvature of the loop. As a result, the error of approximation of a hysteresis loop by the improved model does not exceed 1%, which is several times less than the error of the existing model. The improved model is capable of approximating most of the known types of rate-independent symmetrical hysteresis loops encountered in the practice of physical measurements. The model allows building smooth, piecewise-linear, hybrid, minor, mirror-reflected, inverse, reverse, double, and triple loops. One of the possible applications of the model developed is linearization of a probe microscope piezoscanner. The improved model can be found useful for the tasks of simulation of scientific instruments that contain hysteresis elements.

An efficient formulation for the response and dissipated energy of Bouc-Wen hysteretic model is proposed. The displacement is associated with the hysteretic parameter in terms of Gauss' hypergeometric function. The hysteretic equation is solved analytically for specific values of the exponential parameter that controls the transition between elastic and inelastic regime. This formulation is used to provide analytical expressions of the dissipated energy under symmetric cyclic excitation, based solely on the model parameters and the displacement amplitude. For arbitrary values of the exponential parameter, the equations are solved numerically. For fully yielding systems, approximate relations are determined using suitable curve fitting. The derived expressions facilitate considerably the preliminary design of hysteretic systems. r

The versatile Bouc-Wen model has been used extensively to describe hysteretic phenomena in various fields of engineering. Nevertheless, it is known that it exhibits displacement drift, force relaxation and nonclosure of hysteretic loops when subjected to short unloading-reloading paths. Consequently, it locally violates Drucker's or Ilyushin's postulate of plasticity. In this study, an effective modification of the model is proposed which eliminates these problems. A stiffening factor is introduced into the hysteretic differential equation which enables the distinction between virgin loading and reloading. Appropriate reversal points are utilized effectively to guide the entire process. It is shown that the proposed modification corrects the nonphysical behavior of the model under short unloading-reloading paths without affecting its response in all other cases. It is further demonstrated that the original and modified model exhibit significantly different response under seismic excitation. r

A new identification method that determines the parameters of Bouc-Wen hysteretic systems is presented. It is based on a hybrid evolutionary algorithm which utilizes selected stochastic operators, heuristics and problem-specific information. The proposed method exhibits efficiency, robustness and insensitivity to noise-corrupted data, while it identifies accurately both hysteretic and viscous damping based on suitable experiments. Its performance is investigated with respect to the information content of the input-output data. The scheme is verified by a hysteretic system representing a full-scale steel cantilever beam which is identified successfully. A series of parametric studies are also conducted that illustrate the inner workings of the proposed method, suggesting appropriate values for the controlling parameters. r

An efficient formulation for the response and dissipated energy of Bouc-Wen hysteretic model is proposed. The displacement is associated with the hysteretic parameter in terms of Gauss' hypergeometric function. The hysteretic equation is solved analytically for specific values of the exponential parameter that controls the transition between elastic and inelastic regime. This formulation is used to provide analytical expressions of the dissipated energy under symmetric cyclic excitation, based solely on the model parameters and the displacement amplitude. For arbitrary values of the exponential parameter, the equations are solved numerically. For fully yielding systems, approximate relations are determined using suitable curve fitting. The derived expressions facilitate considerably the preliminary design of hysteretic systems. r

The versatile Bouc-Wen model has been used extensively to describe hysteretic phenomena in various fields of engineering. Nevertheless, it is known that it exhibits displacement drift, force relaxation and nonclosure of hysteretic loops when subjected to short unloading-reloading paths. Consequently, it locally violates Drucker's or Ilyushin's postulate of plasticity. In this study, an effective modification of the model is proposed which eliminates these problems. A stiffening factor is introduced into the hysteretic differential equation which enables the distinction between virgin loading and reloading. Appropriate reversal points are utilized effectively to guide the entire process. It is shown that the proposed modification corrects the nonphysical behavior of the model under short unloading-reloading paths without affecting its response in all other cases. It is further demonstrated that the original and modified model exhibit significantly different response under seismic excitation. r

An efficient formulation for the response and dissipated energy of Bouc-Wen hysteretic model is proposed. The displacement is associated with the hysteretic parameter in terms of Gauss' hypergeometric function. The hysteretic equation is solved analytically for specific values of the exponential parameter that controls the transition between elastic and inelastic regime. This formulation is used to provide analytical expressions of the dissipated energy under symmetric cyclic excitation, based solely on the model parameters and the displacement amplitude. For arbitrary values of the exponential parameter, the equations are solved numerically. For fully yielding systems, approximate relations are determined using suitable curve fitting. The derived expressions facilitate considerably the preliminary design of hysteretic systems. r