Composite Materials Behaviour. Study, Development and Implementation of the Hypoelastic Model

The purpose of this research is to study and develop the formulation of a rheological law for composite materials with elasto-plastic behaviour in cold compression. Starting from the generally known relationships in literature, the hypoelastic model proposed for the composite materials behaviour (as powder materials) has been developped/explained, ensuring the understanding of the research. The hypolastic theory has been used for modeling the continuous transition from elastic to plastic state for a powder material. The material behaviour is described through an isotropic tensor relationship between the deformation speed tensor, Cauchy�s stress tensor and its derivative in relation to time (the Jaumann�s derivative). Only the linear part has been used from the general form of the law which depends on scalar functions. The calculations lead to relationships depending on five parameters which are identified according to experimental data. A numerical simulation of the stress-strain evolution during the simple compression of a diepressed powder sample is made; the numerical simulation has been validated by the experimental results.

Analyses of Textile Composite Reinforcement Compaction at the Mesoscopic Scale

Mesoscopic simulations of the transverse compression of textile preforms are presented in this paper. They are based on 3D FE models of each yarn in contact with friction with its neighbours. The mesoscopic simulations can be used as virtual compression tests. In addition they determine the internal geometry of the reinforcement after compaction. The internal geometry can be used to compute the permeability of the deformed reinforcement and to calculate the homogenised mechanical properties of the final composite part. A hypoelastic model based on the fibre rotation depicts the mechanical behaviour of the yarn. The compression responses of several layer stacks with parallel or different orientations are computed. The numerical simulations show good agreement when compared to compaction experiments.

Eulerian Framework for Inelasticity Based on the Jaumann Rate and a Hyperelastic Constitutive Relation—Part I: Rate-Form Hyperelasticity

An integrable Eulerian rate formulation of finite deformation elasticity is developed, which relates the Jaumann or other objective corotational rate of the Kirchhoff stress with material spin to the same rate of the left Cauchy–Green deformation measure through a deformation dependent constitutive tensor. The proposed constitutive relationship can be written in terms of the rate of deformation tensor in the form of a hypoelastic material model. Integrability conditions, under which the proposed formulation yields (a) a Cauchy elastic and (b) a Green elastic material model are derived for the isotropic case. These determine the deformation dependent instantaneous elasticity tensor of the material. In particular, when the Cauchy integrability criterion is applied to the stress-strain relationship of a hyperelastic material model, an Eulerian rate formulation of hyperelasticity is obtained. This formulation proves crucial for the Eulerian finite strain elastoplastic model developed in part II of this work. The proposed model is formulated and integrated in the fixed background and extends the notion of an integrable hypoelastic model to arbitrary corotational objective rates and coordinates. Integrability was previously shown for the grade-zero hypoelastic model with use of the logarithmic (D) rate, the spin of which is formulated in principal coordinates. Uniform deformation examples of rectilinear shear, closed path four-step loading, and cyclic elliptical loading are presented. Contrary to classical grade-zero hypoelasticity, no shear oscillation, elastic dissipation, or ratcheting under cyclic load is observed when the simple Zaremba–Jaumann rate of stress is employed.

At-Rest Earth Pressure Coefficient from Hypoelastic Model

At-rest earth pressure codfficient,K0,is very important in geotechnical engineering design and finite element analysis. At present, it’s treated as a constant usually for given soil in FEM analysis. However recent test results indicate that K0of both clay and sand varies with pressure increasing nonlinearly. It’s shown that Duncan-Chang model, a kind of hypoelastic model widely used, can reproduce K0varying with pressure. The calculating procedure of K0derived from Duncan-Chang’s E-B model is proposed, and then influence of model parameters on calculated K0is explored. Studies show that cohesionless soil’s calculated K0decreases with pressure increasing, while cohesive soil’s calculated K0increases with pressure increasing. Three of the seven model parameters, m, Kband Rf, have a positive correlation with calculated K0, and there is a negative correlation between the residual parameters and calculated K0.The influence of seven model parameters on the calculated K0decreases gradually in the following order: m ,n, Rf, φ, c, K, Kb.

A Hypoelastic Model for Computing the Stresses in Center-Wound Rolls of Magnetic Tape

A hypoelastic finite element model for the calculation of continuous internal stress and deformation distributions in wound rolls used in center winding is presented. The stress problem is formulated as an initial boundary value problem and its solution satisfies continuity of deformation as one rewinds more layers on the growing roll. Hypoelasticity is shown to be a natural way to account for the growing body nature of a magnetic tape during winding. Several cases are examined with constant and radial stress dependent radial elastic modulus. The agreement with Hakiel’s model and experimental data obtained through the sandwiched pull strip method is very good. The results for the static linear and nonlinear cases examined found to be weakly dependent on the winding speed. The present analysis is more versatile than previous models in simulating the growing nature of the tape pack and it can naturally be extended to include nonlinear time and history-dependent phenomena.