The flora and vegetation of rocky outcrops in three municipalities in the northern region of Ceará, Brazil: phytosociological characterization

This study aims to identify the flora and vegetation of rocky outcrops of low altitude and confined in the municipalities of Sobral, Groaíras and Santa Quitéria (Ceará state, Brazil), to propose a phytosociological classification for the xerophilous communities. We selected five stations in areas with high proportion of bare rock (> 80%), and the field work were conducted in March 2014 and 2015 respectively (3º 56’ S and 40º 23’ W, 4º 01’ S and 40º 05’ W, 4º 07’’ S and 40º 08’ W, 4º 09’ S and 40º 09’ W and 4º 03’ S and 40º 00’ W). Floristic relevés were made following the Braun-Blanquet classic sigmatist method. The minimum areas of the floristic relevés vary between 8 e 16 m². All the plant species growing in cracks, crevices and vegetation "spots" that can be found in these habitats were identified. The classification of the relevés was made through the Twinspan. The floristic list is composed of 89 species, distributed in 61 genera and 29 families. Fabaceae was the most representative in species richness, 20 species, followed by Poaceae (10 spp.), Euphorbiaceae (7 spp.) and Convolvulaceae (6 spp.). 22 Brazilian endemisms have been identified. Based in the phytosociological analysis and in the classification results we identified five groups and two communities can be clearly distinguished: community of Pilosocereus gounellei FA.C.Weber) Byles & Rowley and Encholirium spectabile Mart. ex Schult. & Schult.f. and the community of Crateva tapia L. and Combretum leprosum Mart..

Damage and fracture algorithm using the screened Poisson equation and local remeshing

We propose a crack propagation algorithm which is independent of particular constitutive laws and specific element technology. It consists of a localization limiter in the form of the screened Poisson equation with local mesh refinement. This combination allows the cap- turing of strain localization with good resolution, even in the absence of a sufficiently fine initial mesh. In addition, crack paths are implicitly defined from the localized region, cir- cumventing the need for a specific direction criterion. Observed phenomena such as mul- tiple crack growth and shielding emerge naturally from the algorithm. In contrast with alternative regularization algorithms, curved cracks are correctly represented. A staggered scheme for standard equilibrium and screened equations is used. Element subdivision is based on edge split operations using a given constitutive quantity (either damage or void fraction). To assess the robustness and accuracy of this algorithm, we use both quasi-brittle benchmarks and ductile tests.

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.