Elastoplastic deformation

Models and numerical solutions based on principles of mechanics of porous media for coupled THM processes, using closed-form solutions (Xu and Xu, 1999a,b,c Xu et al., 1999 Zhang and Li, 1997 Cai Wu, 2001), dynamic consolidation problems (Li et al., 2001a), with elastoplastic deformation and FEM (Liu Gen,... 

The in-plane extensional strain and curvature in the film-substrate system arises as a consequence of thermal expansion mismatch between the film and substrate materials during temperature excursion from the reference temperature. Conditions are assumed to be such that the temperature is uniform throughout the film and substrate at all times during thermal cycling. Some particular temperatures at which distinct transitions occur in the elastoplastic deformation of the film material are first identified by adopting the assumption that, over the range of temperature, the properties of the film and substrate materials remain essentially unchanged effects of temperature dependence of plastic yield or flow behavior on the evolution of film stress and substrate curvature are examined subsequently. 

Shen, Y.-L. and Suresh, S. (1995a), Elastoplastic deformation of multilayered... 

At solid body deformation the heat flow is formed, which is due to deformation. The thermodynamics first law establishes that the internal eneigy change in sample dU is equal to the sum of woik dW, carried out on a sample, and the heat flow dQ into sample (see the Eq. (4.31)). This relation is valid for any deformation, reversible or irreversible. There are two thermo-d5mamically irreversible cases, for which dQ = -dW, uniaxial deformation of Newtonian liquid and ideal elastoplastic deformation. For solid-phase polymers deformation has an essentially different character the ratio QIW is not equal to one and varies within the limits of 0.35 0.75, depending on testing conditions [37]. In other words, for these materials thermodynamically ideal plasticity is not realized. The cause of such effect is thermodynamically nonequilibrium nature or fractality of solid-phase polymers structure. Within the frameworks of fractal analysis it has been shown that this results to polymers yielding process realization not in the entire sample volume, but in its part only. 

The experimental data on elastoplastics deformation are usually interpreted within the frameworks of entropic high-elasticity classical theory, which corresponds well to experiment only in a relatively small strains region (e < 0.2, where e is strain)... 

Load-displacement curve for an elastoplastic specimen loaded with a spherical indenter (radius Rj) showing both loading and unloading response. Upon loading, there is an initial elastic response followed by elastoplastic deformation. Upon unloading, the specimen shows elastic response and comes back to the residual displacement fi, with the residual impression of radius... 

While the scratch test is advantageous for its simplicity in the geometry and ease of the sample preparation, there are several disadvantages. The test is limited to hard brittle coating and nonlinear elastoplastic deformation comes into play, where the failure mode of the scratch test is not well understood (Bull 2001). Furthermore, the test is very sensitive to the material and the surface geometry or topography of the stylus (Oroshnik and Croll 1978). 

In elastoplastic models, it is assumed that there exist plastic deformations denoted by ij. The Hencky law implies that the following relations hold (Annin, Cherepanov, 1983 Duvaut, Lions, 1972) ... 

Here ij denotes a plastic deformation velocity. Adding the relations (1.10), (1.11), we obtain the quasi-static elastoplastic model... 

For most practical purposes, the onset of plastic deformation constitutes failure. In an axially loaded part, the yield point is known from testing (see Tables 2-15 through 2-18), and failure prediction is no problem. However, it is often necessary to use uniaxial tensile data to predict yielding due to a multidimensional state of stress. Many failure theories have been developed for this purpose. For elastoplastic materials (steel, aluminum, brass, etc.), the maximum distortion energy theory or von Mises theory is in general application. With this theory the components of stress are combined into a single effective stress, denoted as uniaxial yielding. Tlie ratio of the measure yield stress to the effective stress is known as the factor of safety. 

Fig. 10. Internal energy changes as a function of deformation for oriented LDPE (I) and stress softened thermo-elastoplastic polyurethanes with 50% (2) and 42 % (3) hard phase content and polyether-polyester block copolymer with 48% hard phase content (4). The dotted curves 1 and 2 represent intramolecular energy changes for the corresponding polymers119 ...

The material properties of solids are affected by a number of complex factors. In a gas-solid flow, the particles are subjected to adsorption, electrification, various types of deformation (elastic, plastic, elastoplastic, or fracture), thermal conduction and radiation, and stresses induced by gas-solid interactions and solid-solid collisions. In addition, the particles may also be subjected to various field forces such as magnetic, electrostatic, and gravitational forces, as well as short-range forces such as van der Waals forces, which may affect the motion of particles. 

Most solids are subjected to permanent deformation or breakup once the applied stresses exceed a certain limit. Hence, most solid particles may be classified into two categories elastoplastic particles and elastic-brittle particles. Typical elastoplastic materials include metals and polymers, while typical elastic-brittle materials include coal, activated carbon, and ceramics. Materials that are elastoplastic at room temperature may become brittle at low temperatures and those that are brittle at room temperature may become plastic at high temperatures. 

Some plastic materials have different tensile and compressive characteristics. For example, polystyrene is tough under compressive load but very brittle in tension. However, for most elastoplastic materials, the stress-strain curves in compression are the same as in tension. Hence, the deformation properties of these materials in tension may also be applied to those in compression, which is of great interest to gas-solid flows. 

In contrast to the simplicity of elastic deformation, plastic deformation occurs in diverse ways. Figure 1.9 illustrates the stress-strain curves for two typical elastoplastic materials (hardened metal and polymer). Both materials show similar linear relationships between stress and strain for the elastic deformation (i.e., before yield strength) but quite different correlations in the yielding processes before fracture. 

Figure 1.9. Deformation of typical elastoplastic materials (hardened metal and polymer) in the stress-strain diagram (after Guy, 1976).

The demonstration of the validity of the continuum-based modelling approach to tablet compaction requires familiarity with fundamental concepts of applied mechanics. Under the theory of such a mechanism, powder compaction can be viewed as a forming event during which large irrecoverable deformation takes place as the state of the material changes from loose packing to near full density. Moreover, it is important to define the three components of the elastoplastic constitutive models which arose from the growing theory of plasticity, that is the deformation of materials such as powder within a die ... 

Elastoplastic materials Elastoplastic materials deform elastically for small strains, but start to deform plastically (permanently) for larger ones. In the small-strain regime, this behavior may be captured by writing the total strain as the sum of elastic and plastic parts (i.e., e = e -I- gP, where e and gP are the elastic and plastic strains, respectively). The stress in the material is generally assumed to depend on the elastic strain only (not on the plastic strain or the strain rate), and hence, no unique functional relationship exists between stress and strain. This fact also implies that energy is dissipated during plastic deformation. The point at which the material starts to deform plastically (the yield locus) is usually specified via a yield condition, which for one-dimensional plasticity may be stated as (38)... 

Yoshimoto et have proposed an elastoplastic model for pattern collapse, in which the maximum feature displacement 8max from mean position arising from pattern-hending deformation is described hy the equation... 

Yoshimoto et al., A two dimensional model of the deformation of photoresist structures using elastoplastic polymer properties, J. Appl. Phys. 96(4), 1857 (2004). 

The stress-strain behaviour of the rock, including fracture formation, is a crucial component of the aperture changes. As mentioned before the deformation normal to the fracture is considered in equation (S) in order to obtain aperture changes. If an elastoplastic model is considered for the rock mass behaviour, fracture initiation can be associated with tension stresses. Fracture orientation is sensitive to the stress tensor orientation so the plane where the minimum principal stress (compression positive) occurs defines the plane of fracture formation. 

Wang Z and Du Z. 2001. Mathematical models and numerical simulations of multiphase fluid flow and solid deformation processes under non-isothermal conditions for elastoplastic oil reservoir formations. Petroleum Exploration and Development, 28(6), pp. 68-72. 

Fig. 7. (a) Load-displacement curve of a typical elastoplastic material and (b) the schematic of the indentation model of Oliver and Pharr [40]. S—contact stiffness he— contact depth /imax—indenter displacement at peak load hf—plastic deformation after load removal hs—displacement of the surface at the perimeter of the contact. 

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