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The theory of plasticity is in poor condition relative to linear elasticity. All existing formulations are approximate at best, and few have any connection to the fundamental (micromechanical) material mechanism responsible. For this reason, all plasticity theories must be considered empirical. Even worse, detailed testing of a plasticity theory re...
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Context 1
... constitutive equation defines the relation between the stresses and strains. It is generally based on experimental observations [10]. The type of constitutive model employed depends on the material under investigation and on the applied loads. The stress-strain relation obtained from a tensile test is illustrated in Fig. 1. The material behaves in a linear elastic way up to the initial yield stress σ y0 with a slope E -Young's modulus. When the material is unloaded the elastic deformation ε e is totally recovered. Above the initial yield stress σ y0 the material is plastically deformed. The total deformation can be split up into an elastic and a plastic ...
Context 2
... yield stress σ y increases when the material is plastically deformed and this phenomenon is called hardening. When the material is unloaded, the stress decreases again linearly according to E. The plastic deformation ε p is not recovered, Fig. 1. Upon further plastic deformation the load has to come above the increased yield stress σ y ...
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Citations
... There are many solid mechanics problems which can be equivalently considered from the fluid mechanics perspective, for example, in the analysis of extrusion and drawing. Eulerian "fluid" approaches are often used to solve such problems, for example, [46, 48, 50-52, 54, 286, 287, [381][382][383][384][385][386][387][388][389][390][391][392][393]. These methods are more closely related to CFD procedures and are not discussed further here. ...
Since early publications in the late 1980s and early 1990s, the finite volume method has been shown suitable for solid mechanics analyses. At present, there are several flavours of the method, which can be classified in a variety of ways, such as grid arrangement (cell-centred vs. staggered vs. vertex-centred), solution algorithm (implicit vs. explicit), and stabilisa- tion strategy (Rhie–Chow vs. Jameson–Schmidt–Turkel vs. Godunov upwinding). This article gives an overview, historical perspective, comparison and critical analysis of the different approaches where a close comparison with the de facto standard for computational solid mechanics, the finite element method, is given. The article finishes with a look towards future research directions and steps required for finite volume solid mechanics to achieve more widespread acceptance.
