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I owe a selected debt of gratitude to Ashwani Kumar Goel, who did most of the simulations, and Lili Zhang, who rigorously learn and checked all of the equations and representations; they have been true companions on this endeavor. he one-dimensional principle of straight bars. This method will permit us to focus on the concepts central to continuum mechanics and plasticity without having to take care of the various problems that seem when coping with multidimensional theories.
With this in thoughts, the one-dimensional principle offered on this chapter is developed on the identical theoretical foundations that the multidimensional principle is predicated on. As such, we’ll keep away from introducing simplifications or developments that don’t simply generalize to a number of dimensions. As soon as we have now turn out to be accustomed to the essential ideas central to the event, then within the following chapters, we’ll research the multidimensional principle. It’s my hope that this methodology of presentation will help the reader to higher perceive plasticity.
By following the presentation on this chapter, the reader additionally ought to develop a robust understanding of how plasticity suits into continuum mechanics and continuum thermodynamics, which then ought to assist the reader in understanding the construction of the developments within the later chapters. Regardless that plasticity usually refers to “rate-independent and temperature independent plasticity,” we is not going to restrict ourselves to this.
After we introduce the essential ideas for a bar, we’ll take a look at the mechanical principle of rate-independent plasticity, adopted by temperature-dependent plasticity, and then rate-dependent plasticity. To finish the presentation, we’ll take a look at the stability legal guidelines and soar circumstances and contemplate particular issues that use these legal guidelines of their answer course of. Earlier than we proceed to take a look at the idea of bars, allow us to check out plasticity.
Plasticity refers to a selected sort of materials response usually characterized, for instance, by the cyclic loading and unloading response of the aluminum proven in Determine 1.1. The schematic loading diagram for elastic plastic response is proven in Determine 1.2. The determine exhibits the load extension plot for a uniform bar present process a homogeneous deformation.
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