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Introduction
Published in Xi Frank Xu, Multiscale Theory of Composites and Random Media, 2018
In the field of mechanics of materials, there are two classical and fundamental modeling methodologies, phenomenological and micro–macro, as shown in Figure 1.1. A phenomenological model is defined as a mechanics model that describes the empirical relationships of macroscopic phenomena to each other, in a way that directly applies or is at least consistent with fundamental laws of mechanics, but has no use of microscopic information including physical mechanisms and statistics. Note that, according to this definition, a model traditionally falling into the category of so-called mechanistic models would still be a phenomenological one when no microscopic information is explicitly taken into account. A phenomenological model in mechanics of materials typically consists of the following three basic steps: Define a number of state variables and parameters (e.g. constitutive parameters),Formulate a mathematical model using the defined variables and parameters to describe an observed phenomenon, andMeasure the parameters and validate the model experimentally.
Soil shear–the phenomenological model
Published in Paul G. Joseph, Dynamical Systems-Based Soil Mechanics, 2017
A phenomenological model is a model that describes observed behavior (phenomena), without trying to model the underlying physical processes that cause or drive such behavior. Often in problems that appear to be complex, the first step in modeling something is simply to model only the observed behavior. Then, with this model in hand, one can dig deeper and search for the likely physical basis of the observed behavior. This chapter describes this initial work modeling the observed behavior of a soil sample when sheared. With the phenomenological model firmly in hand, the next chapter will proceed to determine the root cause of the behavior, i.e., the physical basis of the behavior and use this to create the so-called “physical model.”1
Bionic Design of Artificial Muscle Based on Biomechanical Models of Skeletal Muscle
Published in Yuehong Yin, Biomechanical Principles on Force Generation and Control of Skeletal Muscle and their Applications in Robotic Exoskeleton, 2020
Phenomenological model is the other type of mathematical model, and the representative ones are Preisach model and Prandtl–Ishlinskii model. However, most of these models are used to describe the hysteresis character of PZT, and only a few have been used to describe that of SMA. This is due to the fact that the hysteresis behavior of SMA is more complex than that of PZT. The hysteresis property of SMA is not only related to actuation frequency, but also depends on external load, and the nonlinearity is saturable and unsmooth, as illustrated in Figure 6.32 [89]. Preisach model is one of the most widely used models to describe the hysteresis curve of SMA [88]. American scholar Hughes proved by experiments that SMA hysteresis curve satisfies two features of Preisach model: the congruence property and erase property [90]. Thus, it proved that Preisach model can be used to describe SMA hysteresis. After that, scholars are able to describe and compensate SMA hysteresis by using Preisach model [91–97]. However, it is hard to acquire the analytical solution of Preisach model; thus, it is hard to be applied in real-time control system. Prandtl–Ishlinskii model has analytical solutions; thus, it can be applied in the hysteresis compensation of SMA easily [98–100], but there are many nonlinear weight factors in the model, increasing the computing complexity. Thus, it is not proper to be applied in real-time control system [101] either. Besides, the influence of stress and actuation frequency on SMA hysteresis property is not considered in these models. Model control methods, such as neural network control [102], genetic algorithm [103], variable structure control [104], sliding mode control [105], have all been used to describe the hysteresis phenomenon of SMA, while all these control strategies are aimed at the description and compensation of SMA under specific stress or frequency state without considering the influence of dynamically varying stress and frequency.
Proposing a novel double sigmoidal model to fit the master curve for various polymer-modified asphalt
Published in International Journal of Pavement Engineering, 2022
Chuanqi Yan, Jiqiang Yan, Baohao Shi, You Zhan, Allen Zhang
The mathematical model is also known as phenomenological model or constitutive model. Three mathematical models that feature different and representative shapes were evaluated, namely CAM model, sigmoidal model and the newly proposed double sigmoidal model. The selection of these models is based on the temperature sweep test results, which will be discussed in Section 5. This following section will introduce the mathematical expression and the shape of these three models.
Experimental Parametric Study and Phenomenological Modeling of a Deformable Rolling Seismic Isolator
Published in Journal of Earthquake Engineering, 2023
Antonios A. Katsamakas, Michalis F. Vassiliou
Among the 3 isolators discussed in this section, the highest average absolute error is 28.1% and 7.4% for umax and PSA, respectively. Moreover, the phenomenological model does not consistently under- or overpredict the response.