Material modeling hyperelasticity

Hyperelastic finite element analysis Accommodates complex geometries. Can handle nonlinearity in material behavior and large strains. Rapid analysis possible. Standard material models available. Does not include rate-dependent behavior. Cannot predict permanent deformation. Does not handle hysteresis. Some material testing may be required. Can produce errors in multiaxial stress states. 

Sound knowledge of the joint behavior is required for a successful design of bonded joints. To characterize the bonded joint, the loading in the joint and the mechanical properties of the substrates and of the adhesives must be properly defined. The behavior of the bonded joint is investigated by finite element (FE) analysis methods. While for the design of large structures a cost-efficient modeling method is necessary, the nonlinear finite element methods with a hyperelastic material model are required for the detailed joint analysis. Our experience of joint analysis is presented below, and compared with test results for mass transportation applications. 

At 70 °C, both systems are above Tg and behave hke rubbery" materials. No permanent strain exists after fracture. At temperatures above Tg, viscous flow is hindered due to crosslinking. However, chain segments remain flexible and the adhesive can withstand high strains. Although these strains are not as high as in a mbber, they can no longer be considered small . Hence, a hyperelastic material model must be used. The second system (Fig. 33.2, right) already shows hyperelastic properties at 23 °C due to the low strain rate. 

For flexible (mbbery) adhesives which show Tg far below room temperature, hyperelastic material models are generally used. In the hyperelastic regime, standard solutions are available which use various types of potential functions [7]. The flexible adhesive systems investigated were best fitted by a potential function which is formulated in terms of the principal stretches Aj originally suggested by Ogden [Eq. (1)] [8]. 

All of these material models are so-called hyperelasticity models. The stress in the material is clearly a function of the elongation, i.e., each defined deformation state in a structural material component has exactly one correlative load application state [12]. 

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... 

A natural extension of linear elasticity is hyperelasticity (Ogden 1997). Hyperelasticity is a collective term for a family of models that all have a strain energy density that depends only on tiie currently applied deformation state (and not on the history of deformations). This class of material models is characterized by a nonlinear elastic response, and does not capture yielding, viscoplasticity, or time dependence. Strain energy density is the energy that is stored in the material as it is deformed, and is typically represented either in terms of invariants of the deformation gradient (F) /i, I2, and /, where... 

Mooney-Rivlin material Mooney and Rivlin developed a hyperelastic constitutive material model. The strain energy function is written in the form of series expansion of... 

Y. Shen, K. Chandrashekhara,W.F. Breig, LR. Oliver, (2005) Finite element analysis ofV-ribbed belts using neural network based hyperelastic material model, Intematimal Journal of Non-linear Mechanics 40 875 - 890... 

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

Material behaviour during the sketch blow moulding process is represented by different material models. Non-linear viscoelastic material models are used for B-SIM and visco-hyperelastic model is used for BlowView. In B-SIM software, time dependent deformation is described by K-BKZ model. 

Strain based hyperelastic Mooney-Rivlin material models were used. 

In a local detailed analysis, the flexible adhesive is modeled with three-dimensional solid elements to enable the refined capture of any local stress or strain gradients. The adhesive material is described as a rabber-like, nearly incompressible, hyperelastic material characterized by a strain energy function. Using U as the strain energy potential per unit of the reference volume, the form of the Ogden strain energy potential is shown in Eq. (1) jii and u are material parameters which are determined from adhesive material test data. 

In the paper, a theory for mechanical and diffiisional processes in hyperelastic materials was formulated in terms of the global stress tensor and chemical potentials. The approach described in was used as the basic principle and was generalized to the case of a multi-component mixture. An important feature of the work is that, owing to the structure of constitutive equations, the general model can be used without difficulty to describe specific systems. 

Swieszkowski et al. studied the use of PVA-C as cartilage replacement for the shoulder joint. PVA-C was used as the articular layer of the glenoid component. The mechanical effects of using this material in the glenoid component were evaluated and a model of the cryogel as a hyperelastic material was developed to allow design modifications to limit contact stress [96]. 

Isotropic hyperelastic materials For this model, the strain energy density function is written in terms of the principal stress invariants I, h, h). Equation 1 becomes... 

The main aspects of the nonlinear theory of elasticity are presented. As nonlinear elasticity, and, in particular, hyperelasticity, is such a useful tool in the description of the behavior of carbon black-filled rubber undergoing quasi-static loadings, the main methodologies for describing the behavior of materials subjected to large strains are introduced. Some of the results herein presented will be apphed to nonlinear viscoelastic constitutive models and discussed in subsequent review. 

Marckmann, G. and Verron, E. (2006) Comparison of hyperelastic models for mbber-like materials. Rubber Chem. Technol, 79, 835. 

Articular cartilage was modeled as a Imm-thick cartilage tissue layer with a 2mm-thick underlying bone (Fig 1). Cartilage was assumed to be a biphasic material that consists of a solid phase and a fluid phase. [17, 18, 19, 20]. The solid phase was taken as hyperelastic due to the large deformations that are normally encountered. 

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... 

---