Richard A. Regueiro

Strain localization in frictional materials exhibiting displacement jumps

Abstract This paper presents a mathematical model for analyzing strain localization in frictional solids exhibiting displacement jumps. Precise conditions for the appearance of slip lines, including their initiation and evolution, are outlined for a rate-independent, strain-softening Drucker–Prager model, and explicit analytical expressions are used to describe the orientation of the slip line. A stress–displacement relation obtained through the consistency condition is also formulated to describe the quasi-static response in the post-localization regime. The mathematical model, which is cast within the framework of finite element analysis employing the assumed enhanced strain method, circumvents mesh-dependence issues often associated with rate-independent plasticity models. It is shown that the enhancement equation is nothing else but the consistency condition imposed on the band. Numerical examples involving plane strain compression are described to demonstrate objectivity with respect to mesh refinement and insensitivity to mesh alignment of finite element solutions.

Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity

Numerical simulations of localized deformation in solids should capture the structural phenomenon of localization and associated loss of material body strength in a manner independent of spatial discretization. Many regularization techniques have been proposed to address the ill posedness associated with rate-independent softening plasticity that leads to mesh-dependent numerical simulations. One approach to alleviating mesh dependence is the strong discontinuity approach, which represents localized deformation as a slip surface within a plasticity model; a strong discontinuity is a discontinuous displacement field. This approach is used in this paper to formulate a plane strain, pressure sensitive, nonassociative plasticity model with strong discontinuity and to implement the model, along with an enhanced bilinear quadrilateral element, via an assumed enhanced strain method. Numerical examples demonstrate mesh independence of the method for pressure sensitive materials.

A finite element model of localized deformation in frictional materials taking a strong discontinuity approach

Abstract A finite element model of localized deformation in frictional materials taking a strong discontinuity approach is presented. A rate-independent, non-associated, strain-softening Drucker–Prager plasticity model is formulated in the context of strong discontinuities and implemented along with an enhanced quadrilateral element within the framework of an assumed enhanced strain finite element method. For simple model problems such as uniform compression, the strong discontinuity approach has been shown to lead to mesh-independent finite element solutions when localized deformation is present. In this paper, a finite element analysis of localized deformation occurring in a more complex model problem of slope stability is conducted in a nearly mesh-independent manner. The effect of dilatancy on the orientation of slip lines is demonstrated for the slope stability problem.

A Nonlocal Phenomenological Anisotropic Finite Deformation Plasticity Model Accounting for Dislocation Defects

A phenomenological, polycrystalline version of a nonlocal crystal plasticity model is formulated. The presence of geometrically necessary dislocations (GNDs) at, or near, grain boundaries is modeled as elastic lattice curvature through a curl of the elastic part of the deformation gradient. This spatial gradient of an internal state variable introduces a length scale, turning the local form of the model, an ordinary differential equation (ODE), into a nonlocal form, a partial differential equation (PDE) requiring boundary conditions. Small lattice elastic stretching results from the presence of dislocations and from macroscopic external loading. Finite deformation results from large plastic slip and large rotations. The thermodynamics and constitutive assumptions are written in the intermediate configuration in order to place the plasticity equations in the proper configuration for finite deformation analysis.

Three‐dimensional ellipsoidal discrete element modeling of granular materials and its coupling with finite element facets

Purpose – The purpose of this paper is to develop a discrete element (DE) and multiscale modeling methodology to represent granular media at their particle scale as they interface solid deformable bodies, such as soil‐tool, tire, penetrometer, pile, etc., interfaces.Design/methodology/approach – A three‐dimensional ellipsoidal discrete element method (DEM) is developed to more physically represent particle shape in granular media while retaining the efficiency of smooth contact interface conditions for computation. DE coupling to finite element (FE) facets is presented to demonstrate initially the development of overlapping bridging scale methods for concurrent multiscale modeling of granular media.Findings – A closed‐form solution of ellipsoidal particle contact resolution and stiffness is presented and demonstrated for two particle, and many particle contact simulations, during gravity deposition, and quasi‐static oedometer, triaxial compression, and pile penetration. The DE‐FE facet coupling demonstrat...

Coupled Axisymmetric Thermo-Poro-Mechanical Finite Element Analysis of Energy Foundation Centrifuge Experiments in Partially Saturated Silt

The paper presents an axisymmetric, small strain, fully-coupled, thermo-poro-mechanical (TPM) finite element analysis (FEA) of soil–structure interaction (SSI) between energy foundations and partially saturated silt. To account for the coupled processes involving the mechanical response, gas flow, water species flow, and heat flow, nonlinear governing equations are obtained from the fundamental laws of continuum mechanics, based on mixture theory of porous media at small strain. Constitutive relations consist of the effective stress concept, Fourier’s law for heat conduction, Darcy’s law and Fick’s law for pore liquid and gas flow, and an elasto-plastic constitutive model for the soil solid skeleton based on a critical state soil mechanics framework. The constitutive parameters employed in the thermo-poro-mechanical FEA are mostly fitted with experimental data. To validate the TPM model, the modeling results are compared with the observations of centrifuge-scale tests on semi-floating energy foundations in compacted silt. Variables measured include the thermal axial strains and temperature in the foundations, surface settlements, and volumetric water contents in the surrounding soil. Good agreement is obtained between the experimental and modeling results. Thermally-induced liquid water and water vapor flow inside the soil were found to have an impact on SSI. With further improvements (including interface elements at the foundation-soil interface), FEA with the validated TPM model can be used to predict performance and SSI mechanisms for energy foundations.

Concurrent Multiscale Computational Modeling for Dense Dry Granular Materials Interfacing Deformable Solid Bodies

A method for concurrent multiscale computational modeling of interfacial mechanics between granular materials and deformable solid bodies is presented. It involves two main features: (1) coupling discrete element and higher order continuum finite element regions via an overlapping region; and (2) implementation of a finite strain micromorphic pressure sensitive plasticity model as the higher order continuum model in the overlap region. The third main feature, adaptivity, is not currently addressed, but is considered for future work. Single phase (solid grains) and dense conditions are limitations of the current modeling. Extensions to multiple phases (solid grains, pore liquid and gas) are part of future work. Applications include fundamental grain-scale modeling of interfacial mechanics between granular soil and tire, tool, or penetrometer, while properly representing far field boundary conditions for quasi-static and dynamic simulation.

Prediction of Final Material State in Multi‐Stage Forging Processes

Multi‐stage forging processes are used to manufacture reservoirs for high pressure hydrogen and tritium storage. The warm‐forging process is required to produce required macro and microscale forged material properties of 304 and 21‐6‐9 stainless steel. Strict requirements on the forged material strength, grain size and grain flow are necessitated to inhibit the diffusion of gas which inevitably leads to material embrittlement. Accurate prediction of the final material state requires modeling of each of the forging stages and tracking the material state evolution through each deformation and reheating stage. An internal state variable constitutive model, capable of predicting the high strain rate, temperature dependent material behavior, is developed to predict final material strength and microstructure. History dependent, internal state variables are used to model the isotropic and kinematic hardening, grain size and recrystallization. Numerical methodologies were developed to track and remap material sta...

On the formulation, parameter identification and numerical integration of the EMMI model :plasticity and isotropic damage.

In this report we present the formulation of the physically-based Evolving Microstructural Model of Inelasticity (EMMI) . The specific version of the model treated here describes the plasticity and isotropic damage of metals as being currently applied to model the ductile failure process in structural components of the W80 program . The formulation of the EMMI constitutive equations is framed in the context of the large deformation kinematics of solids and the thermodynamics of internal state variables . This formulation is focused first on developing the plasticity equations in both the relaxed (unloaded) and current configurations. The equations in the current configuration, expressed in non-dimensional form, are used to devise the identification procedure for the plasticity parameters. The model is then extended to include a porosity-based isotropic damage state variable to describe the progressive deterioration of the strength and mechanical properties of metals induced by deformation . The numerical treatment of these coupled plasticity-damage constitutive equations is explained in detail. A number of examples are solved to validate the numerical implementation of the model.

ONR MURI project on soil blast modeling and simulation

Current computational modeling methods for simulating blast and ejecta in soils resulting from the detonation of buried explosives rely heavily on continuum approaches such as Arbitrary Lagrangian-Eulerian (ALE) and pure Eulerian shock-physics techniques. These methods approximate the soil as a Lagrangian solid continuum when deforming (but not flowing) or an Eulerian non-Newtonian fluid continuum when deforming and flowing at high strain rates. These two extremes do not properly account for the transition from solid to fluid-like behavior and vice versa in soil, nor properly address advection of internal state variables and fabric tensors in the Eulerian approaches. To address these deficiencies on the modeling side, we are developing a multiscale multiphase hybrid Lagrangian particle-continuum computational approach, in conjunction with coordinated laboratory experiments for parameter calibration and model validation. This paper provides an overview of the research approach and current progress for this Office of Naval Research (ONR) Multidisciplinary University Research Initiative (MURI) project.