A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of-reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced-assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of- reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced- assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

Thermoregulatory response in hair sheep and shorn wool sheep

This study’s main goal was to evaluate the thermoregulatory responses velocity through the variation of rectal temperature (RT), related to the thermolytic pathways, respiratory rate (RR) and sweating rate (SR) among different sheep breeds. Ninety female sheep, eighteen of each breed: Santa Ines and Morada Nova (Brazilian hair breeds), Texel, Suffolk and Ile de France (wool breeds) were challenged during three non-consecutive summer days (22◦42′S, 47◦18′W, and 570m of altitude, maximum air temperature of 33.5◦C, average relative humidity of 52±6.9%). The physiological variables were registered at 0800h (T1), 1300 h (T2: after 2 h of shade rest), 1400 h (T3) (after one hour of sun exposure) and in the shade at 1415 h (T4), 1430 h (T5), 1445 h (T6) and 1500 h (T7) and a thermotolerance index (TCI) was calculated as (10-(T7 to T4)-T1). The statistical analysis was performed by a mathematical model including the fixed effects of breeds and time frames, and the interaction between these effects, besides random effects such as animal and day. The Santa Ines breed presented the lowest RT after sun exposure (39.3 ± 0.12 ◦ C; P < 0.05) and it was the only one to recover morning RT 60 min after heat stress (38.7 and 38.9 for 1300 h and 1500 h; P > 0.05). Hair breeds presented RR lower (P < 0.05) than wool breeds. Although thick wool or hair thickness differs among and within hair and wool breeds (P < 0.05), SR did not differ among breeds and time (227.7 ± 16.44 g m−2 h−1 ; P > 0.05). The thermotolerance index did not differ among breeds, but it showed similar response (P > 0.05) 45 min or 1 h of shade after sun exposure. One week post shearing is not enough to wool breeds present to show thermotolerance similar to hair breeds.

fuzzySim: Fuzzy similarity in species distributions

fuzzySim is an R package for calculating fuzzy similarity in species occurrence patterns. It includes functions for data preparation, such as converting species lists (long format) to presence-absence tables (wide format), obtaining unique abbreviations of species names, or transposing (parts of) complex data frames; and sample data sets for providing practical examples. It can convert binary presence-absence to fuzzy occurrence data, using e.g. trend surface analysis, inverse distance interpolation or prevalence-independent environmental favourability modelling, for multiple species simultaneously. It then calculates fuzzy similarity among (fuzzy) species distributions and/or among (fuzzy) regional species compositions. Currently available similarity indices are Jaccard, Sørensen, Simpson, and Baroni-Urbani & Buser.

Finite-strain laminates: Bending-enhanced hexahedron and delamination

With a new finite strain anisotropic framework, we introduce a unified approach for constitutive model- ing and delamination of composites. We describe a finite-strain semi-implicit integration algorithm and the application to assumed-strain hexahedra. In a laminate composite, the laminae are modeled by an anisotropic Kirchhoff/Saint-Venant material and the interfaces are modeled by the exponential cohesive law with intrinsic characteristic length and the criterion by Benzeggagh and Kenane for the equivalent fracture toughness. For the element formulation, a weighted least-squares algorithm is used to calculate the mixed strain. Löwdin frames are used to model orthotropic materials without the added task of per- forming a polar decomposition or empirical frames. To assess the validity of our proposals and inspect step and mesh size dependence, a least-squares based hexahedral element is implemented and tested in depth in both deformation and delamination examples.

Least-squares finite strain hexahedral element/constitutive coupling based on parametrized configurations and the Löwdin frame

Two novelties are introduced: (i) a finite-strain semi-implicit integration algorithm compatible with current element technologies and (ii) the application to assumed-strain hexahedra. The Löwdin algo- rithm is adopted to obtain evolving frames applicable to finite strain anisotropy and a weighted least- squares algorithm is used to determine the mixed strain. Löwdin frames are very convenient to model anisotropic materials. Weighted least-squares circumvent the use of internal degrees-of-freedom. Het- erogeneity of element technologies introduce apparently incompatible constitutive requirements. Assumed-strain and enhanced strain elements can be either formulated in terms of the deformation gradient or the Green–Lagrange strain, many of the high-performance shell formulations are corotational and constitutive constraints (such as incompressibility, plane stress and zero normal stress in shells) also depend on specific element formulations. We propose a unified integration algorithm compatible with possibly all element technologies. To assess its validity, a least-squares based hexahedral element is implemented and tested in depth. Basic linear problems as well as 5 finite-strain examples are inspected for correctness and competitive accuracy.