Semi-implicit finite strain constitutive integration and mixed strain/stress control based on intermediate configurations

A new semi-implicit stress integration algorithm for finite strain plasticity (compatible with hyperelas- ticity) is introduced. Its most distinctive feature is the use of different parameterizations of equilibrium and reference configurations. Rotation terms (nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the reference configuration. In contrast, relative Green–Lagrange strains (which are quadratic in terms of displacements) represent the equilibrium configuration implicitly. In addition, the adequacy of several objective stress rates in the semi-implicit context is studied. We para- metrize both reference and equilibrium configurations, in contrast with the so-called objective stress integration algorithms which use coinciding configurations. A single constitutive framework provides quantities needed by common discretization schemes. This is computationally convenient and robust, as all elements only need to provide pre-established quantities irrespectively of the constitutive model. In this work, mixed strain/stress control is used, as well as our smoothing algorithm for the complemen- tarity condition. Exceptional time-step robustness is achieved in elasto-plastic problems: often fewer than one-tenth of the typical number of time increments can be used with a quantifiable effect in accuracy. The proposed algorithm is general: all hyperelastic models and all classical elasto-plastic models can be employed. Plane-stress, Shell and 3D examples are used to illustrate the new algorithm. Both isotropic and anisotropic behavior is presented in elasto-plastic and hyperelastic examples.

Species richness and composition of butterfly assemblages (Lepidoptera:Rhopalocera) along the altitudinal gradient of Serra da Estrela

Os gradientes altitudinais são importantes modelos em ecologia pois permitem, numa escala reduzida, estudar a influência da variação de diversas variáveis ambientais nos padrões de biodiversidade existentes. Estes padrões são influenciados por diversos factores, desde variáveis climáticas às relacionadas com a perturbação humana. Nesta tese é estudada a variação na composição das comunidades de borboletas ao longo do gradiente altitudinal na Serra da Estrela e são testadas duas hipóteses sobre os padrões de riqueza específica ao longo do gradiente altitudinal: a regra de Rapoport e o “Mid Domain Effect” (MDE). Foram assinaladas 70 espécies de borboletas neste estudo e constatou-se que a variação na riqueza de espécies de borboletas apresenta um padrão “mid peak” apoiando o MDE. Verificou-se também que as comunidades de borboletas do mesmo nível altitudinal são mais semelhantes entre si independentemente da vertente em que se encontram e são também mais semelhantes com as comunidades dos níveis altitudinais adjacentes. Finalmente, a análise da distribuição de algumas espécies ameaçadas de borboletas torna evidente a necessidade de realização de mais estudos sobre a biologia da conservação deste grupo de animais em Portugal; Abstract: Altitudinal gradients are important ecological models because they allow us to study the influence of diverse environmental variables in the existing biodiversity patterns. These patterns are influenced by various factors, from climatic variables to variables related to human disturbance. In this thesis we studied the variations in the composition of the butterfly assemblages along the altitudinal gradient of Serra da Estrela and we tested two hypotheses regarding the species richness patterns along the altitudinal gradient: Rapoport’s rule and the Mid Domain Effect (MDE). In this study 70 butterfly species were marked recorded and it was observed that the butterfly species richness presents a mid-peak pattern supporting the MDE. It was also noted that the butterfly assemblages in the same altitudinal level show more similarity within themselves regardless of the slope they are found in, and are also more similar to the assemblages present in the adjacent altitudinal levels. Finally, the distribution of some threatened butterfly species was analyzed and it became evident the need to do more studies regarding the conservation biology of this animal group in Portugal.