Fully Lagrangian Method For Shear Band Capturing

<p>KeyWords: FEM, Legandre element, plasticity, localization, shear band</p><p> </p><p>The phenomenon of strain localization is widespread and can reveal both during the geodynamic sliding</p><p>of plates at macro scale length and at scales, character to a wells and mining. Herein we propose</p><p>accurate way to solve problems based on the spectral Legendre element with incremental formulation,</p><p>elastoplastic deformations, a consistent linearized matrix for governing relations. Two models of materials</p><p>are taken into account: the Drucker-Prager (pressure dependent) model and the Mises (pressure</p><p>insensitive) model. This report presents a qualitative and quantitative analysis of the kinematic pattern of</p><p>the lines of plastic deformations at different characteristic scales and types of stress states. It is shown for</p><p>general case pressure dependent Drucker-Prager model, in contrast to Mises model, solution can not possess</p><p>symmetric and continuous values: both radial and hoop stresses in the case of thick-walled cylinder</p><p>under compression can have periodic symmetry, but are discontinuous along the thickness.</p>

Nonlinear effects in 4D-Var

The ability of a data assimilation system to deal effectively with nonlinearities arising from the prognostic model or the relationship between the control variables and the available observations has received a lot of attention in theoretical studies based on very simplified test models. Less work has been done to quantify the importance of nonlinearities in operational, state-of-the-art global data assimilation systems. In this paper we analyse the nonlinear effects present in ECMWF 4D-Var and evaluate the ability of the incremental formulation to solve the nonlinear assimilation problem in a realistic NWP environment. We find that nonlinearities have increased over the years due to a combination of increased model resolution and the ever-growing importance of observations that are nonlinearly related to the state. Incremental 4D-Var is well suited for dealing with these nonlinear effects, but at the cost of increasing the number of outer loop relinearisations. We then discuss strategies for accommodating the increasing number of sequential outer loops in the tight schedules of operational global NWP.

Elasto-Plastic Modeling of Low-Velocity Impact on Functionally Graded Circular Plates

Low-velocity impact of elasto-plastic functionally graded material (FGM) plates is first investigated in this paper based on Mori–Tanaka model to underline micromechanics and locally determine the effective FGM properties and self-consistent method of Suquet for the homogenization of the stress-field. The elasto-plastic behavior of the particle reinforced metal matrix FGM plate is assumed to follow Ludwik hardening law. An incremental formulation of the elasto-plastic constitutive relation is developed to predict the tangent operator. The homogenization formulation and numerical algorithms are implemented into ABAQUS/Standard via a user material subroutine (UMAT) and USDFLD subroutine. The effect of the power-law index on low-velocity impact parameters like contact force, deflection, permanent indentation, velocity distribution and the kinetic energy are examined using the proposed method. With the aim of demonstrating the accuracy and efficiency of the present method, current numerical results are compared to experimental and theoretical results from the literature and show very good agreement.

Nonlinear effects in 4D-Var

The ability of a data assimilation system to deal effectively with nonlinearities arising from the prognostic model or the relationship between the control variables and the available observations has received a lot of attention in theoretical studies based on very simplified test models. Less work has been done to quantify the importance of nonlinearities in operational, state-of-the-art global data assimilation systems. In this paper we analyse the nonlinear effects present in ECMWF 4D-Var and evaluate the ability of the incremental formulation to solve the nonlinear assimilation problem in a realistic NWP environment. We find that nonlinearities have increased over the years due to a combination of increased model resolution and the ever-growing importance of observations that are nonlinearly related to the state. Incremental 4D-Var is well suited for dealing with these nonlinear effects, but at the cost of increasing the number of outer loop relinearisations. We then discuss strategies for accommodating the increasing number of sequential outer loops in the tight schedules of operational global NWP.

Multi scale numerical approach for micro-cracked viscoelastic masonry

A multi-scale numerical method for viscoelastic micro-cracked masonry is proposed. Firstly, the effective viscoelastic properties of the masonry are modelled by a periodic homogenization approach. The Modified Maxwell (MM) model is chosen for the creep. Secondly, an incremental procedure is proposed. Thirdly, an incremental formulation is used to get the overall viscoelastic behaviour of the two dimensional periodic cell. Finally, the result of the method is validated against analytical solution.

Incremental Formulation of Concrete Creep under Stress History

An incremental format of the age-dependent constitutive equation was derived by expanding the total form of the constitutive equation by using the first-order Taylor series to describe the persistent change in the creep-causing stress state as well as drying shrinkage and the development of the elastic modulus. The resulting incremental constitutive equation was defined by three basic equations for basic creep, drying shrinkage, and the development of the elastic modulus. Three types of laboratory experiments were carried out to validate the performance of the presented age-dependent constitutive equation; these included cylindrical concrete specimen tests with and without axial reinforcements and reinforced beam specimen tests. The performance of the creep model was compared with those calculated by the other age-dependent constitutive equations.