Non-associated Plastic Potential Research Articles

A non-associative macroelement model for vertical plate anchors in clay

This work proposes a new plastic-hardening, non-associative macroelement model to predict the behaviour of anchors in clay for floating offshore structures during keying and up to the peak load. Building on available models for anchors, a non-associated plastic potential is introduced to improve prediction of anchor trajectory and loss of embedment at peak conditions for a large range of padeye offsets and different pull-out directions. The proposed model also includes a displacement-hardening rule to simulate the force and displacement mobilisation at the early stages of the keying process. The model is challenged and validated against different sets of numerical and centrifuge data. This extensive validation process revealed that two of the four newly introduced model parameters assume a constant value for the range of simulated cases. This suggests that only two of the newly introduced parameters may need to be calibrated for the use of the proposed macroelement model in practice.

Macro-element modelling of suction-embedded plate anchors for floating offshore structures

This work presents a new macro-element model to predict the behaviour of Suction Embedded Plate Anchors (SEPLAs) for floating offshore structures during keying and loading stages. Differently from previously published models for anchors, this new model is characterised by (i) a non-associated plastic potential with the aim of improving the prediction of anchor trajectory for the whole displacement domain and for a large range of padeye offsets; and (ii) by a strain-hardening rule enabling to predict the force and displacement mobilisation from the early stages of the keying process. The model was calibrated against LDFE analyses and compared with a broad set of LDFE and centrifuge tests results. The model proves capable of reproducing anchor rotation and displacement with good accuracy for a wide range of padeye offsets and distinct studies from the literature.

Viscoelasticplastic–Fracture Modeling of Asphalt Mixtures Under Monotonic and Repeated Loads

Rutting and cracking occur simultaneously in asphalt mixtures as observed in the field and in the laboratory. Existing mechanical models have not properly addressed viscoelastic and viscoplastic deformation together with cracking attributable to model deficiencies, parameter calibration, and numerical inefficiency. This study developed viscoelasticplastic–fracture (VEPF) models for the characterization of viscoelasticity by Prony model and viscoplasticity by Perzyna’s flow rule with a generalized Drucker–Prager yield surface and a nonassociated plastic potential. Viscofracture damage was modeled by a viscoelastic Griffith criterion and a pseudo J-integral Paris’s law for crack initiation and propagation, respectively. The VEPF models were implemented in a finite element program by using a weak form partial differential equation modeling technique without the need for programming user-defined material subroutines. Model parameters were derived from fundamental material properties by using dynamic modulus, strength, and repeated load tests. Simulations indicated that the viscoelastic–viscoplastic–viscofracture characteristics were effectively modeled by the VEPF models for asphalt mixtures at different confinements and temperatures. An asphalt mixture under monotonic compressive loads exhibited a sequenced process including a pure viscoelastic deformation stage, a coupled viscoelastic–viscoplastic deformation stage, a viscoelastic–viscoplastic deformation coupled with a viscofracture initiation and a propagation stage, and then a viscoelastic–viscofracture rupture stage with saturated viscoplastic deformation. The asphalt mixture under repeated loads yielded an increasing viscoplastic strain at an increasing rate during the first half of the haversine load, while the increment of the viscoplastic strain (per load cycle) decreased with load cycles. The finite element program, which is based on a partial differential equation, effectively modeled the coupled viscoelastic–viscoplastic–viscofracture behaviors of the asphalt mixtures.

An incremental micro-macro model for porous geomaterials with double porosity and inclusion

This paper is devoted to micro-mechanical analysis of heterogeneous rock-like materials with two populations of pores as well as mineral inclusions. This work is an extension of the previous works devoted to materials with a single population of pores in (Shen et al., 2012, 2013a,b). A three-step homogenization procedure is developed. During the first step, the effective plastic yield function is determined in an analytical form for a porous medium constituted of Drucker-Prager solid matrix and microscopic pores. An analytical effective plastic yield function is then obtained by the second homogenization step for a porous materials containing a porous matrix and mesoscopic pores. During the last step, the macroscopic plastic behavior of heterogeneous materials is determined by considering effects of mineral grains and by using an incremental approach. In parallel, the effective elastic properties of heterogeneous materials are also estimated by the three-step homogenization procedure with a Mori-Tanaka scheme by considering effects of two populations of pores and inclusions. A non-associated plastic potential is also postulated. The proposed model is applied to two typical heterogeneous rock-like materials, claystone and mortar. Comparisons between numerical results and experimental data show that the micro-mechanical model is able to capture main features of a class of rock-like materials with complex micro-structures.

Micromechanical modeling of the elasto-viscoplastic behavior of granite

We present in this paper a micromechanics-based elasto-viscoplastic approach for modeling the time-dependent deformation of granite. Inspired by the polycrystalline theory of metallic materials, the sliding behavior in an individual grain is regarded as the sole source of plastic deformation, which is characterized by a Mohr–Coulomb-type yield criterion and a non-associated plastic potential. The micro–macro transition is realized within the framework of Hill's self-consistent approach. The performance of the proposed model is evaluated by several case studies and by reproducing experimental data.

Modeling of viscoplastic deformation in geomaterials with a polycrystalline approach

A micromechanical model is proposed to describe the viscoplastic deformation of cohesive frictional geomaterials with a granular texture. Inspired by the widely used polycrystalline theory, the macroscopic viscoplastic deformation is attributed to the subcritical sliding along a number of oriented weakness planes, which are assimilated to the crystallographic planes in single crystals. Main features of geomaterials, such as pressure sensitivity and plastic compressibility/dilatancy, are taken into account by introducing an appropriate yield criterion and a non-associated plastic potential for each weakness plane. A simple interaction law is adopted to relate the local stress and strain fields to the macroscopic ones of the representative elementary volume. Computational aspects about the implementation of constitutive equations of both single crystal and polycrystal are discussed in detail. The performance of proposed model is checked through the comparisons between numerical results and experimental data on both triaxial compression tests and creep tests performed on a typical rock - granite.

Experimental and Numerical Investigations on Strength and Deformation Behavior of Cataclastic Sandstone

This work is devoted to characterization of the deformation and strength properties of cataclastic sandstones. Before conducting mechanical tests, the physical properties were first examined. These sandstones are characterized by a loose damaged microstructure and poorly cemented contacts. Then, a series of mechanical tests including hydrostatic, uniaxial, and triaxial compression tests were performed to study the mechanical strength and deformation of the sandstones. The results obtained show nonlinear stress–strain responses. The initial microcracks are closed at hydrostatic stress of 2.6 MPa, and the uniaxial compressive strength is about 0.98 MPa. Under triaxial compression, there is a clear transition from volumetric compressibility to dilatancy and a strong dependency on confining pressure. Based on the experimental evidence, an elastoplastic model is proposed using a linear yield function and a nonassociated plastic potential. There is good agreement between numerical results and experimental data.

A hyperbolic augmented elasto-plastic model for pressure-dependent yield

A three-dimensional elasto-plastic model for the deformation and flow of granular materials which generalises the plastic potential model and contains an additional term analogous to that appearing in the double-shearing model is presented. It is shown that for planar flows the resulting system of first-order partial differential equations is hyperbolic. This is in distinct contrast to both the non-associated plastic potential and double-shearing models, which fail to be hyperbolic. The ill-posedness of the Cauchy problem for the planar double-shearing model is due to the presence of the rotation rate of the principal axes of stress while that of the non-associated plastic potential model is due to distinct quasi-static spatial stress and velocity characteristics. The present model attains well-posedness by replacing the planar rotation rate of the principal stress axes by the vector intrinsic spin of a Cosserat continuum and using it to ensure identical spatial stress and velocity characteristics. Flows in which the intrinsic spin vector is constant in both space and time correspond to flows in an ordinary continuum. The model governing such flows is embedded into a Cosserat model in such a way that the characteristic structure is preserved.

Multiscale modeling of cohesive geomaterials with a polycrystalline approach

The main objective of this paper is to investigate the macroscopic elastic–plastic behaviors of a class of cohesive geomaterials with the aid of classical polycrystalline schemes. Specific local constitutive equations are proposed to describe the typical features of geomaterials. The local yield criterion for crystallographic sliding systems takes into account the pressure sensitivity and a non-associated plastic potential is introduced to properly describe the plastic dilatancy. Consequently, the concentration law is also modified in order to establish the relationship between the macroscopic stress tensor and the local stress tensor in each mineral grain. Computational aspects associated with the numerical implementation of polycrystalline model are revisited and discussed. The proposed model is applied to a typical polycrystalline rock, granite. After the identification of material parameters, its validity is verified through comparisons between model’s predictions and experimental data on both conventional and true triaxial compression tests.

Double shearing and double rotation: A generalisation of the plastic potential model in the mechanics of granular materials

Two important models for rigid-plastic flows of granular materials are the non-associated plastic potential flow rule and the double shearing model. Both models generalise the equations governing metal plasticity and both, unlike the well-posed metal plasticity equations, are ill-posed in the sense that solutions to initial value problems do not depend continuously on the initial data. For the non-associated plastic potential model ill-posedness is a consequence of the non-coincidence of the velocity and stress characteristics, whereas for the double shearing model the presence of the material time rate of change of the inclination of the major principal axis of stress gives rise to a spatially elliptic system. A recently proposed model represents a generalisation of both the plastic potential and double shearing model and which incorporates a non-coaxial term in which the stress rotation rate of the double shearing model is replaced by a Cosserat intrinsic spin. The new model preserves the characteristic structure of metal plasticity, i.e. the characteristics exist and the non-coaxial term can be chosen so as to give rise to coincident stress and velocity characteristics.