An Improved Numerical Integration Algorithm For Elastoplastic Constitutive Equations

A simplified methodology is proposed for elastoplastic calculations which holds for associative models. It is based on the representation of the elastoplastic model based on a rotation of the principal stresses and the fact that, in such system of coordinates, the direction that minimizes the square of a distance between a trial stress and the plastic surface has the same direction as the plastic deformation evolution. Such an approach allows for the elastoplastic calculation of complex models to be simpler and more efficient computationally. The proposed methodology is verified by the application to the elastoplastic model of Sandler-DiMaggio.6419Souza Neto, E., Peric, D., Owen, D.R.J., (2008) Computational Methods for Plasticity, , John Wiley & Sons LtdChen, W.F., Han, D.J., (1988) Plasticity for Structural Engineers, , Springer-VerlagDiMaggio, F.L., Sandler, I., Material model for granular soils (1971) Eng Mech Div, 97 (3), pp. 935-950Devloo, P.R.B., PZ: an object oriented environment for scientific programming (1997) Comput Methods Appl Mech Eng, 150 (1-4), pp. 133-153Devloo, P.R.B., Object oriented tools for scientific computing (2000) Eng Comput, 46 (2), pp. 203-214Lainé, E., Vallée, C., Fortuné, D., Nonlinear isotropic constitutive laws: choice of the three invariants, convex potentials and constitutive inequalities (1999) Int J Eng Sci, 37 (15), pp. 1927-1941Borja, R.I., (2012) Plasticity Modeling & Computation, , Springer Science & Business MediaArmero, F., Pérez-Foguet, A., On the formulation of closest-point projection algorithms in elastoplasticity - Part I: The variational structure (2002) Int J Numer Methods Eng, 53 (2), pp. 297-329Armero, F., Pérez-Foguet, A., On the formulation of closest-point projection algorithms in elastoplasticity - Part II: Globally convergent schemes (2002) Int J Numer Methods Eng, 53 (2), pp. 331-374Foster, C.D., Regueiro, R.A., Fossum, A.F., Borja, R.I., Implicit numerical integration of a three-invariant, isotropic/kinematic hardening cap plasticity model for geomaterials (2005) Comput Methods Appl Mech Eng, 194, pp. 5109-5138Fossum, A.F., Fredrich, J.T., Cap plasticity models and compactive and dilatant pre-failure deformation (2000), 4th North American Rock Mechanics Symposium, Seatle, United States of AmericaFossum, A.F., Brannon, R.M., The Sandia Geomodel: Theory and Users Guide (2004), SAND Report, Sandia National LaboratoriesSandler, I.S., Rubin, D., An algorithm and a modular subroutine for the cap model (1979) Int J Numer Anal Methods Geomech, 3 (2), pp. 173-18

Calibração de extratores providos de cápsula porosa para monitoramento da salinidade e da concentração de íons Calibration of porous ceramic cup extractors in monitoring soil salinity and ion concentration

Os resultados satisfatórios obtidos no monitoramento da salinidade e concentração de íons na solução do solo, usando extratores de cápsulas porosas, motivaram a realização deste trabalho, o qual teve como objetivo a obtenção de curvas de calibração para estes extratores monitorarem a condutividade elétrica e a concentração de nitrato e de potássio na solução de dois tipos de solo (Latossolo Vermelho-Amarelo Argissólico franco arenoso, e o outro como Cambissolo Eutrófico), em Mossoró - RN. As concentrações de nitrato utilizadas foram as mesmas nos dois solos (0; 84; 168; 252; 336; 420 e 504 mg L-1); quanto ao potássio, foram utilizadas concentrações diferentes no solo arenoso (0; 117; 234; 351; 468; 585 e 702 mg L-1) e no argiloso (0; 117; 234; 351; 468; 585; 702; 1.170; 1.755; 2.340; 2.925 e 3.510 mg L-1). A condutividade elétrica da solução do solo e a concentração de nitrato e de potássio foram estimadas com precisão satisfatória a partir da solução coletada com extratores providos de cápsulas porosas, sendo necessária uma calibração prévia para cada tipo de solo.<br>The satisfactory results obtained in monitoring soil salinity and ion concentration, by means of porous ceramic cup extractors, motivated the realization of this study, which objective was obtaining calibration curves for these extractors to monitor soil electrical conductivity and concentration of nitrate and potassium in two different soils. The nitrate concentrations tested were the same for the two soils (0; 84; 168; 252; 336; 420 and 504 mg L-1) but, for potassium, different concentrations were used for sandy soil (0; 117; 234; 351; 468; 585 and 702 mg L-1) and clay soil (0; 117; 234; 351; 468; 585; 702; 1,170; 1,755; 2,340; 2,925 and 3,510 mg L-1). Electrical conductivity of soil solution and concentrations of nitrate and potassium were estimated with satisfactory precision from soil solution collected with porous ceramic cup extractors, but this task must be preceded by a calibration for each soil type

Características químicas de solo cultivado com soja e irrigado com água residuária da suinocultura Chemical characteristics of the soil cultivated with soybean and irrigated with swine wastewater

Neste trabalho se avaliou a distribuição "in situ" de fósforo (P), matéria orgânica (MO), potássio (K), cálcio (Ca), magnésio (Mg), capacidade de troca catiônica (T), alumínio (Al), soma de bases (S), saturação por bases (V) e do pH, em um solo cultivado com soja irrigada com água residuária proveniente da suinocultura (ARS), com níveis de concentração de 0, 25, 50 e 75%. Constituiu-se um esquema fatorial a partir dos quatros níveis de concentração da ARS, das profundidades de 20, 40 e 60 cm com cinco repetições. Os resultados encontrados demonstraram diferenças significativas apenas para P, K e T no perfil do solo. Para todas as características na profundidade de 60 cm, os respectivos níveis de concentração estiveram bastante próximos aos níveis iniciais, ou seja, antes da aplicação dos tratamentos.<br>In this work the distribution was evaluated "in situ" of phosphorus (P), organic matter (MO), potassium (K), calcium (Ca), magnesium (Mg), cation exchange capacity (CEC), aluminum (Al), sum of bases (S), base saturation (V) and pH of a soil cultivated with soybean and irrigated with swine wastewater in the 0, 25, 50 and 75% levels. The factorial scheme was constituted by the 20, 40 and 60 cm soil depths and four wastewater levels with five repetitions. The results showed that significant difference occurred only for P, K and CEC in the soil profile. However, in all parameters, the 60 cm soil depth showed that the concentrations levels are similar to before the aplication of treatments