No abstract

The thixotropic substances can be found in different industrial sectors, such as chemical, biomedical, manufacturing and oil. These substances show a rheological time-dependent behavior, dependent of their structural level. Generally, a constitutive model for the thixotropic substances is composed by a pair of coupled equations: the constitutive equation (based on viscoelastic models) and the rate equation (that describes the structural evolution). In many works presented in the specialized literature, the shear modulus and viscosity dependencies with the structural nature are not formally considered in the dynamical principles from that the constitutive equation is originated. In the present work, a new, thermodynamically consistent, constitutive model for thixotropic substances, where such dependences are considered, is presented and some rheological tests are analyzed in a numerical simulation point of view (code developed in MATLAB). The constitutive model is based on Jeffreys’ model and the coagulation theory of Smoluchowsky.

No abstract

The numerical simulation is widely used, in now days, to verify the viability and to optimize structural mechanic designs. The numerical approach of elastoplastic materials can found some problems related to ill-conditioning of matrices (from FEM systems), associated to the critical points from the snap through or snap back shape of the equilibrium curve. Aiming to overcome this misfortune it is proposed a strategy via Tikhonov regularization method in association with L-curve technique to determine the regularization parameter. This strategy can be used in many numerical applications for structural analysis. The theoretical development about these Some numerical examples are presented to attest the efficiency of this proposed approach.

No abstract