Material modeling isotropic -plasticity

The more rigorous stress/strain nonlinear material model, oflen referred to as the plastic zone method, is theoretically capable of handling any general cross section Both isotropic and kinematic hardening rules are usually available. This method is... 

Closed-form analytical solution (using an isotropic plastic material model) Fast and easy to perform More accurate than a linear elastic solution Handbook solutions are available only for very few geometries and loading conditions May give inaccurate results... 

FE analysis using a simple material model (e.g., linear elastic, hyperelastic, linear viscoelastic, isotropic plasticity) Can account for complex geometries Relatively easy to perform Does not consider the true material behavior in general deformation states Typically valid only for small-intermediate deformations May give inaccurate results... 

An example of a material model based on the physics of material behavior is classical metals plasticity theory. This theory, often referred to as /2-flow theory, is based on a Mises yield surface with an associated flow rule, followed by rate-independent isotropic hardening (Khan and Huang 1995). Physically, plastic flow in metals is a result of dislocation motion, a mechanism known to be driven by shear stresses and to be insensitive to hydrostatic pressure. 

What are the main disadvantages of isotropic plasticity as a material model for UHMWPE ... 

For the material models, the following assumptions are made (i) the fibers obey a linear elastic and anisotropic material law, (ii) the matrix follows an isotropic, linear elastic-plastic material law, (iii) the material behavior of the interface elements is described in Section 5.1.2, and (iv) the material model of the anisotropic outer layer is the same as that of the macro-contact model. 

Closed-form analytical solution (e.g., using an isotropic plastic material model) [4]... 

Finite element analysis using a simple material model (e.g., linear elasticity, hyperelasticity, linear viscoelasticity, isotropic plasticity)... 

The anisotropic material behavior of injection-molded, short-fiber reinforced thermoplastic parts can be taken into account in mechanical simulation today by linking process simulation and structural analysis. However, the prediction of the crashworthiness of short-fiber reinforced parts is still performed predominantly using isotropic material models as a substitute. An approach to include anisotropic material behavior into crash-simulation has been developed at the Institute of Plastics Processing in order to advance simulation quality. 

For the simulation of isotropic thermoplastics elasto-viscoplastic material models are used. They are composed of an elastic part consisting of a constant Young s modulus and Poisson s ration and a plastic part being described by true stress/strain-curves depending on the true plastic strain-rate. As a failure criterion a maximal endurable hydrostatic stress, a critical equivalent plastic strain or a combination of these can be used. The strain criterion can also be set as a function of the strain-rate. 

The procedure to calculate fiber orientation is the same as explained above, but their implementation into explicit solvers and non-linear material models is more complex than it is for quasi-static load-cases and purely elastic material models. The fiber orientation is characterized by a so called orientation distribution function (ODE) that describes the chance of a fiber being oriented into a certain direction. For isotropic, elastic matrix materials an integral of the individual stiffness in every possible direction weighted with the ODE provides the complete information about the anisotropic stiffness of the compound. However, this integral can not be solved in case of plastic deformation as needed for crash-simulation. Therefore it is necessary to approximate and reconstruct the full information of the ODE by a sum of finite, discrete directions with their stiffness, so called grains [10]. Currently these grains are implemented into a material description and different methods of formulation are tested. 

The cellular anisotropy of plastic foams may be evaluated by e.g. an anisotropy coefficient q which is equal to the ratio between average cell dimensions along the major symmetry axes of the respective model. An isotropic material Is characterized by only one anisotropy coefficient (q = 1), a transversally anisotropic material by two(qj = q and q ) and an orthotropic medium by three coefficients (q q q ). 

Strains and stresses were computed for the joined specimen cooled uniformly to room temperature from an assumed stress-free elevated temperature using numerical models described in detail previously [19, 20]. The coordinate system and an example of the finite element mesh utilized are shown in Figure 3. Elastie-plastic response was permitted in both the Ni and Al203-Ni composite materials a von Mises yield condition and isotropic hardening were assumed. 

Fig. 7.17. Variation of normalized equi-biaxial film stress as a function of normalized temperature, for the example considered in Section 7.5.2 where the film material is modeled as an isotropically hardening solid. The solid lines denote the response obtained from the numerical integration of (7.65) for the first three thermal cycles where it is assumed that the material properties do not vary with temperature, over the range considered. The dashed lines denote the corresponding behavior for the case where the thin film plastic response is taken to be temperature-dependent.

Formulations of isotropic quasi-brittle materials behavior consider, generally, different inelastic criteria for tension and compression. The new model introduced in (Lourengo et al. 1997), extended to accommodate shell masonry behavior (Lourengo 2000), combines the advantages of modem plasticity concepts with a powerful representation of anisotropic material behavior, which includes different... 

UHMWPE specimens subjected to very small strains, while exploration of hyperelasticity theory led to the conclusion that it is often safer to use a more sophisticated constitutive model when modeling UHMWPE. The use of linear viscoelasticity theory led to a reasonable prediction for the response of the material during a uniaxial compression test however, even small changes to the strain rate rendered the previously identified material parameters unsatisfactory. Isotropic J2-plasticity theory provided excellent predictions under monotonic, uniaxial, constant-strain rate, constant-temperature conditions, but it was unable to predict reasonable results for a cyclic test. The augmented Hybrid Model was capable of predicting the behavior of UHMWPE during a uniaxial tension test, a cyclic uniaxial fully... 

The matrix material was chosen to be a polyester resin for both the inner and outer layer. The FEA model consisted of four parts namely the helmet shell, the foam liner, the head-form and the hemispherical test anvil. The foam liner was modeled using a set of 8500 solid elements, the woven ply was modeled as an orthotropic material with damage and the glass mat polyester layer was modeled as an isotropic elastic-plastic material with kinematic hardening. 

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