Modelos estocásticos de crescimento individual e desenvolvimento de software de estimação e previsão

Os modelos de crescimento individual são geralmente adaptações de modelos de crescimento de populações. Inicialmente estes modelos eram apenas determinísticos, isto é, não incorporavam as flutuações aleatórias do ambiente. Com o desenvolvimento da teoria do cálculo estocástico podemos adicionar um termo estocástico, que representa a aleatoriedade ambiental que influencia o processo em estudo. Actualmente, o estudo do crescimento individual em ambiente aleatório é cada vez mais importante, não apenas pela vertente financeira, mas também devido às suas aplicações nas áreas da saúde e da pecuária, entre outras. Problemas como o ajustamento de modelos de crescimento individual, estimação de parâmetros e previsão de tamanhos futuros são tratados neste trabalho. São apresentadas novas aplicações do modelo estocástico monomolecular generalizado e um novo software de aplicação deste e de outros modelos. ABSTRACT: Individual growth models are usually adaptations of growth population models. Initially these models were only deterministic, that is, they did not incorporate the random fluctuations of the environment. With the development of the theory of stochastic calculus, we can add a stochastic term that represents the random environmental influences in the process under study. Currently, the study of individual growth in a random environment is increasingly important, not only by the financial scope but also because of its applications in health care and livestock production, among others. Problems such as adjustment of an individual growth model, estimation of parameters and prediction of future sizes are treated in this work. New applications of the generalized stochastic monomolecular model and a new software applied to this and other models are presented.

Predictions of J integral and tensile strength of clay/epoxy nanocomposites material using phase field model

We predict macroscopic fracture related material parameters of fully exfoliated clay/epoxy nano- composites based on their fine scale features. Fracture is modeled by a phase field approach which is implemented as user subroutines UEL and UMAT in the commercial finite element software Abaqus. The phase field model replaces the sharp discontinuities with a scalar damage field representing the diffuse crack topology through controlling the amount of diffusion by a regularization parameter. Two different constitutive models for the matrix and the clay platelets are used; the nonlinear coupled system con- sisting of the equilibrium equation and a diffusion-type equation governing the phase field evolution are solved via a NewtoneRaphson approach. In order to predict the tensile strength and fracture toughness of the clay/epoxy composites we evaluated the J integral for different specimens with varying cracks. The effect of different geometry and material parameters, such as the clay weight ratio (wt.%) and the aspect ratio of clay platelets are studied.