Numerical integration of the incrementally non-linear, zero elastic range, bounding surface plasticity model for sand

SANISAND-Z is a recently developed plasticity model for sands with zero purely elastic range in stress space within the framework of Bounding Surface (BS) plasticity. As a consequence of zero elastic range the plastic strain increment direction, and consequently the elastic-plastic moduli fourth order tensor depends on the direction of the stress increment, rendering the model incrementally non-linear and intrinsically implicit. An iterative algorithm based on the Backward Euler method is presented to solve the non-linear system of ordinary differential equations. A non-traditional consistency condition based on the plastic multiplier is introduced as a core element of the system. A thorough analysis of the stability and accuracy of the algorithm is presented based on error estimation. The proposed integration scheme allows the use of SANISAND-Z framework in Finite Element Analysis

Solid Flow Fields and Growth of Soft Solid Mass

Recent work on growth of actin gel, and earlier studies on radial plastic forming processes, while seemingly distinct have in fact much in common by adopting the underlying view of source flow of solid materials. That conceptual framework, of Eulerian formulation of solid flow fields, is examined in the present contribution. We focus on radial patterns, with spherical symmetry in steady state conditions, to model kinematics of growth on a spherical bead. Constitutive response includes the Blatz-Ko hyperelastic solid, the Cauchy-Hookean elastic solid and a simple hypoelastic incompressible material. Useful analytical relations are derived for radial velocity profile, stretches and strains. High circumferential stresses at the external layer, in agreement with findings reported by Dafalias et al. using different constitutive models, can possibly induce symmetry breakdown. Growth driving parameters are discussed, including a thermodynamic growth driving force, and thin shell asymptotic formulae are given. Keywords: Finite elasticity, Growth condition, Actin Ge

Cyclic Loading Response of Cohesive Soils Using A Bounding Surface Plasticity Model

The concept of the bounding surface in plasticity theory has been used to develop a general three-dimensional constitutive model for cohesive soils within the framework of critical state soil mechanics. The present work focuses on the response of the above model under cyclic loading conditions. It is shown mainly qualitatively and partially quantitatively, that the model predicts in detailed form a material response which does agree with observed experimental behavior under undrained and drained loading conditions at any overconsolidation ratio and for different cyclic deviatoric stress amplitudes

A constitutive model for unsaturated cemented soils under cyclic loading

On the basis of plastic bounding surface model, the damage theory for structured soils and unsaturated soil mechanics, an elastoplastic model for unsaturated loessic soils under cyclic loading has been elaborated. Firstly, the description of bond degradation in a damage framework is given, linking the damage of soil's structure to the accumulated strain. The Barcelona Basic Model (BBM) was considered for the suction effects. The elastoplastic model is then integrated into a bounding surface plasticity framework in order to model strain accumulation along cyclic loading, even under small stress levels. The validation of the proposed model is conducted by comparing its predictions with the experimental results from multi-level cyclic triaxial tests performed on a natural loess sampled beside the Northern French railway for high speed train and about 140 km far from Paris. The comparisons show the capabilities of the model to describe the behaviour of unsaturated cemented soils under cyclic loading

An Approach to Elastoplasticity at Large Deformations

Finite plasticity theories are still a subject of controversy and lively discussions. Among the approaches to finite elastoplasticity two became especially popular. The first, implemented in the commercial finite element codes, is based on the introduction of a hypoelastic constitutive law and the additive elastic-plastic decomposition of the deformation rate tensor. Unfortunately, the use of hypoelasticity may lead to a nonphysical creation or dissipation of energy in a closed deformation cycle. In order to replace hypoelasticity with hyperelasticity the second popular approach based on the multiplicative elastic-plastic decomposition of the deformation gradient tensor was developed. Unluckily, the latter theory is not perfect as well because it introduces intermediate plastic configurations, which are geometrically incompatible, non-unique, and, consequently, fictitious physically. In the present work, an attempt is made to combine strengths of the described approaches avoiding their drawbacks. Particularly, a tensor of the plastic deformation rate is introduced in the additive elastic-plastic decomposition of the velocity gradient. This tensor is used in the flow rule defined by the generalized isotropic Reiner-Rivlin fluid. The tensor of the plastic deformation rate is also used in an evolution equation that allows calculating an elastic strain tensor which, in its turn, is used in the hyperelastic constitutive law. Thus, the present approach employs hyperelasticity and the additive decomposition of the velocity gradient avoiding nonphysical hypoelasticity and the multiplicative decomposition of the deformation gradient associated with incompatible plastic configurations. The developed finite elastoplasticity framework for isotropic materials is specified to extend the classical -theory of metal plasticity to large deformations and the simple shear deformation is analyzed

A fatigue damage model for seismic response of RC structures

Numerous damage models have been developed in order to analyze seismic behavior. Among the different possibilities existing in the literature, it is very clear that models developed along the lines of continuum damage mechanics are more consistent with the definition of damage as a phenomenon with mechanical consequences because they include explicitly the coupling between damage and mechanical behavior. On the other hand, for seismic processes, phenomena such as low cycle fatigue may have a pronounced effect on the overall behavior of the frames and, therefore, its consideration turns out to be very important. However, most of existing models evaluate the damage only as a function of the maximum amplitude of cyclic deformation without considering the number of cycles. In this paper, a generalization of the simplified model proposed by Cipollina et al. [Cipollina A, López-Hinojosa A, Flórez-López J. Comput Struct 1995;54:1113–26] is made in order to include the low cycle fatigue. Such a model employs in its formulation irreversible thermodynamics and internal state variable theory

Effects of principal stress rotation on the wave–seabed interactions

This paper simulates the wave–seabed interactions considering the principal stress rotation (PSR) by using the finite element method. The soil model is developed within the framework of kinematic hardening and the bounding surface concept, and it can properly consider the impact of PSR by treating the PSR generating stress rate independently. The simulation results are compared with centrifuge test results. The comparison indicates that the simulation with the soil model considering the PSR can better reproduce the test results on the development of pore water pressure and liquefaction than the soil model without considering the PSR. It indicates that it is important to consider the PSR impact in simulation of wave–seabed soil interactions