Inelastic Material Behavior Research Articles

Plastic-damage smeared crack model to simulate the behaviour of structures made by cement based materials

This work proposes a constitutive model to simulate nonlinear behaviour of cement based materials subjected to different loading paths. The model incorporates a multidirectional fixed smeared crack approach to simulate crack initiation and propagation, whereas the inelastic behaviour of material between cracks is treated by a numerical strategy that combines plasticity and damage theories. For capturing more realistically the shear stress transfer between the crack surfaces, a softening diagram is assumed for modelling the crack shear stress versus crack shear strain. The plastic-damage model is based on the yield function, flow rule and evolution law for hardening variable, and includes an explicit isotropic damage law to simulate the stiffness degradation and the softening behaviour of cement based materials in compression. This model was implemented into the FEMIX computer program, and experimental tests at material scale were simulated to appraise the predictive performance of this constitutive model. The applicability of the model for simulating the behaviour of reinforced concrete shear wall panels submitted to biaxial loading conditions, and RC beams failing in shear is investigated.

Modelling and Assessment of Shear Wall–Flat Slab Joint Region in Tall Structures

This paper explains the investigation carried out to study the seismic behaviour of shear wall–flat slab connections with various reinforcement detailing at the joint region. The modelling and assessment of scaled down exterior wall–slab connection sub-assemblages subjected to static reverse cyclic loading is presented. Three-dimensional nonlinear finite element models with different reinforcement detailing at the joint region were developed using ABAQUS/CAE software. The concrete damage plasticity model was used to model the inelastic behaviour of the concrete material under cyclic loading. Moreover, three specimens with overall dimensions of 1.375 m (height) × 0.625 m (width) were tested under the same seismic-type loading. The validation of the numerical results against the experimental results has shown that the adopted models could predict the joint capacity. This research also confirms the viability of using the proposed type of joint detailing system in construction.

Numerical Modeling of Mechanical Behavior for Buried Steel Pipelines Crossing Subsidence Strata.

This paper addresses the mechanical behavior of buried steel pipeline crossing subsidence strata. The investigation is based on numerical simulation of the nonlinear response of the pipeline-soil system through finite element method, considering large strain and displacement, inelastic material behavior of buried pipeline and the surrounding soil, as well as contact and friction on the pipeline-soil interface. Effects of key parameters on the mechanical behavior of buried pipeline were investigated, such as strata subsidence, diameter-thickness ratio, buried depth, internal pressure, friction coefficient and soil properties. The results show that the maximum strain appears on the outer transition subsidence section of the pipeline, and its cross section is concave shaped. With the increasing of strata subsidence and diameter-thickness ratio, the out of roundness, longitudinal strain and equivalent plastic strain increase gradually. With the buried depth increasing, the deflection, out of roundness and strain of the pipeline decrease. Internal pressure and friction coefficient have little effect on the deflection of buried pipeline. Out of roundness is reduced and the strain is increased gradually with the increasing of internal pressure. The physical properties of soil have a great influence on the mechanical properties of buried pipeline. The results from the present study can be used for the development of optimization design and preventive maintenance for buried steel pipelines.

An elastic molecular model for rubber inelasticity

Rubber materials are characterized by a variety of inelasticities such as softening behavior, hysteresis loops and permanent set. In order to calculate the inelastic material behavior, constitutive models, that describe rubber as a homogeneous continuum, have to make use of damping or friction elements.On the nanoscale, there is no need to adopt such rheological models. Inelastic material behavior can be explained and simulated by a continuous rearrangement of bonds, in particular, the van der Waals interactions, and by the polymer chains transitioning between cis and trans equilibrium torsion angles. The discrete molecular dynamics simulations presented in this paper are performed in an explicit FEM environment using nonlinear but elastic force field potentials. From a structural mechanics point of view, topological changes of the polymer network can be interpreted as a sequence of local material instability problems due to negative tangential bond stiffnesses.In order to obtain representative results within reasonable computational time, the model is optimized with respect to the number of atoms and the loading velocity. It is shown that by increasing the model size, the stress–strain curves become independent of both the atoms initial state and the strain amplitudes.

Bending Behavior of Reinforced Thermoplastic Pipe

Reinforced thermoplastic pipe (RTP) is a composite thermoplastic pipe, which is increasingly being used in oil and gas industry. In practical applications, RTPs inevitably experience bending during reeling process and offshore installation. The ovalization instability of RTP under pure bending was investigated. Several fundamental assumptions of RTP were proposed from the engineering application point of view. Then, based on nonlinear ring theory initially proposed by Kyriakides et al., the effect of transverse deformation through the thickness was introduced, and the ovalization growth of cross section during bending was studied according to nonlinear kinematics. The formulation was based on the principle of virtual work and was solved by a numerical solution. Inelastic material behavior of high density polyethylene (HDPE) was included, and a simplified method was proposed to simulate the behavior of fiber reinforced layer. A detailed Abaqus model was established using solid and truss elements to simulate the HDPE layer and reinforced fiber, respectively. The results obtained from the theoretical method were compared with Abaqus simulation results and test data of verification bending experiment and the results show excellent agreement. The proposed methods are helpful for RTP's engineering applications.

A phenomenological explanation of the pressure–area relationship for the indentation of ice: Two size effects in spherical indentation experiments

Indentation tests provide a simple means to study the inelastic behavior of ice and other materials when loaded under a compressive stress state. Such tests provide force–time plots which are often converted to pressure–area (PA) curves. For ice, PA curves are widely used in the design of ships and offshore structures. Despite their usage, and despite many attempts to relate empirical results to theory, the mechanics underlying PA curves is not clearly understood. In this paper, it is shown that by taking into account the strain-softening behavior of ice when rapidly deformed beyond terminal failure within the regime of brittle behavior, two effects can be explained: the decrease in pressure with increasing area, termed the indentation size effect; and, for a given area, the increase in pressure with increasing radius of indenter, termed the indenter radius effect. The analysis is supported using published data on freshwater, polycrystalline ice that have been obtained using spherically shaped indenters. The indentation size effect for ice reflects a similar effect found in ceramics and rock, but is opposite to the effect found in metals where, owing to strain hardening, indentation pressure or hardness increases with increasing area.

Variational multiscale enrichment method with mixed boundary conditions for elasto-viscoplastic problems

This manuscript presents the formulation and implementation of the variational multiscale enrichment (VME) method for the analysis of elasto-viscoplastic problems. VME is a global---local approach that allows accurate fine scale representation at small subdomains, where important physical phenomena are likely to occur. The response within far-fields is idealized using a coarse scale representation. The fine scale representation not only approximates the coarse grid residual, but also accounts for the material heterogeneity. A one-parameter family of mixed boundary conditions that range from Dirichlet to Neumann is employed to study the effect of the choice of the boundary conditions at the fine scale on accuracy. The inelastic material behavior is modeled using Perzyna type viscoplasticity coupled with flow stress evolution idealized by the Johnson---Cook model. Numerical verifications are performed to assess the performance of the proposed approach against the direct finite element simulations. The results of verification studies demonstrate that VME with proper boundary conditions accurately model the inelastic response accounting for material heterogeneity.

Pipe–soil interaction and pipeline performance under strike–slip fault movements

The performance of pipelines subjected to permanent strike–slip fault movement is investigated by combining detailed numerical simulations and closed-form solutions. First a closed-form solution for the force–displacement relationship of a buried pipeline subjected to tension is presented for pipelines of finite and infinite lengths. Subsequently the solution is used in the form of nonlinear springs at the two ends of the pipeline in a refined finite element model, allowing an efficient nonlinear analysis of the pipe–soil system at large strike–slip fault movements. The analysis accounts for large strains, inelastic material behavior of the pipeline and the surrounding soil, as well as contact and friction conditions on the soil–pipe interface. The numerical models consider infinite and finite length of the pipeline corresponding to various angles β between the pipeline axis and the normal to the fault plane. Using the proposed closed-form nonlinear force–displacement relationship for buried pipelines of finite and infinite length, axial strains are in excellent agreement with results obtained from detailed finite element models that employ beam elements and distributed springs along the pipeline length. Appropriate performance criteria of the steel pipeline are adopted and monitored throughout the analysis. It is shown that the end conditions of the pipeline have a significant influence on pipeline performance. For a strike–slip fault normal to the pipeline axis, local buckling occurs at relatively small fault displacements. As the angle between the fault normal and the pipeline axis increases, local buckling can be avoided due to longitudinal stretching, but the pipeline may fail due to excessive axial tensile strains or cross sectional flattening. Finally a simplified analytical model introduced elsewhere, is enhanced to account for end effects and illustrates the formation of local buckling for relative small values of crossing angle.

Modeling of microscopic failure in heterogeneous materials

AbstractThe proper modeling of state‐of‐the‐art engineering materials requires a profound understanding of the nonlinear macroscopic material behavior. Especially for heterogeneous materials the effective macroscopic response is amongst others driven by damage effects and the inelastic material behavior of the individual constituents [1]. Since the macroscopic length scale of such materials is significantly larger than the fine‐scale structure, a direct modeling of the local structure in a component model is not convenient. Multiscale techniques can be used to predict the effective material behavior. To this end, the authors developed a modeling technique based on representative volume elements (RVE) to predict the effective material behavior on different length scales. The extended finite element method (XFEM) is used to model discontinuities within the material structure independent of the underlying FE mesh. A dual enrichment strategy allows for the combined modeling of kinks (material interfaces) and jumps (cracks) within the displacement field [2]. The gradual degradation of the interface is thereby controlled by a cohesive zone model. In addition to interface failure, a non‐local strain driven continuum damage model has been formulated to efficiently detect localization zones within the material phases. An integral formulation introduces a characteristic length scale and assures the convergence of the approach upon mesh refinement [3]. The proposed method allows for an efficient modeling of substantial failure mechanisms within a heterogeneous structure without the need of remeshing or element substitution. Due to the generality of the approach it can be used on different length scales. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Mini-Workshop: Inelastic and Non-equilibrium Material Behavior: from Atomistic Structure to Macroscopic Constitutive Relations

The workshop brought together 15 scientists, which included leaders in the fields of mathematics (partial differential equations, statistical mechanics and calculus of variations) and mechanics (continuum mechanics, computational mechanics, microstructure and material science) as well as mid- and early-career participants. We addressed the themes of modeling crystal plasticity, crystallization and fracture, and non-equilibrium thermodynamics.

Dynamic and Pushover Analysis of 8 Storey Building (G+8) Using ETAB Nonlinear

Nonlinear Dynamic analysis can be done by direct integration of the equations of motion by step by step procedures. Direct integration provides the most powerful and informative analysis for any given earthquake motion. A time dependent forcing function (earthquake accelerogram) is applied and the corresponding response-history of the structure during the earthquake is computed. That is, the moment and force diagrams at each of a series of prescribed intervals throughout the applied motion can be found. Computer programs have been written for both linear elastic and non-linear inelastic material behaviour using step-by-step integration procedures. One such program is ETAB in which three-dimensional non-linear analyses can be carried out taking as input the three orthogonal accelerogram components from a given earthquake, and applying them simultaneously to the structure.

Application of a large deformation nonlinear-viscoelastic viscoplastic viscodamage constitutive model to polymers and their composites

Based on the effective stress concept in continuum damage mechanics and the large deformation theory, a viscodamage model, coupled with Schapery-type nonlinear-viscoelasticity and Perzyna-type viscoplasticity constitutive models, is used in order to simulate and predict the inelastic and time-dependent damage behavior of polymeric materials and their composites. The thermo-viscodamage model is presented as a function of temperature, total effective strain, damage history, and a damage-driving force expressed in terms of the deviatoric stress invariants in the undamaged configuration. This expression for the damage force allows for the distinction between the influence of compression and extension loading conditions on damage nucleation and growth. Also, the ability of the constitutive model for predicting the tertiary creep, which shows the nonlinear behavior of polymers during damage growth and nucleation, is presented. The numerical algorithm for integrating the coupled constitutive model is implemented in the finite element software Abaqus via the user-material subroutine UMAT. The model capability in predicting the nonlinear-viscoelastic, viscoplastic, and damage behavior of polymers is demonstrated through comparison of model predictions with experimental measurements in different loading conditions including creep tests and constant strain rate tests over a range of stress levels, strain rates, and temperatures. Also, a general thermodynamic framework for deriving a coupled viscoelastic–viscoplastic–viscodamage constitutive model is presented.

A frictional mortar contact approach for the analysis of large inelastic deformation problems

A multibody frictional mortar contact formulation (Gitterle et al., 2010) is extended for the simulation of solids undergoing finite strains with inelastic material behavior. The framework includes the modeling of finite strain inelastic deformation, the numerical treatment of frictional contact conditions and specific finite element technology. Several well-established and recent models are employed for each of these building blocks to capture the distinct physical aspects of the deformation behavior. The approach is based on a mortar formulation and the enforcement of contact constraints is realized with dual Lagrange multipliers. The introduction of nonlinear complementarity functions into the frictional contact conditions combined with the global equilibrium leads to a system of nonlinear equations, which is solved in terms of the semi-smooth Newton method. The resulting method can be interpreted as a primal–dual active set strategy (PDASS) which deals with contact nonlinearities, material and geometrical nonlinearities in one iterative scheme. The consistent linearization of all building blocks of the framework yields a robust and highly efficient approach for the analysis of metal forming problems. The effect of finite inelastic strains on the solution behavior of the PDASS method is examined in detail based on the complementarity parameters. A comprehensive set of numerical examples is presented to demonstrate the accuracy and efficiency of the approach against the traditional node-to-segment penalty contact formulation.

New 2D-Experiments and Numerical Simulations on Stress-state-dependence of Ductile Damage and Failure

The paper deals with a series of new experiments and corresponding numerical simulations to be able to study the effect of stress state on damage and failure behavior of ductile metals. The material behavior is modeled by a continuum approach based on free energy functions defined in damaged and corresponding fictitious undamaged configurations leading to elastic material laws which are affected by damage. Inelastic behavior of ductile materials is modeled by continuum plasticity and continuum damage model, respectively. The present approach takes into account the effect of stress state on damage and failure conditions expressed in terms of the stress intensity, the stress triaxiality and the Lode parameter. Previous studies have shown that it will not be possible to propose the stress-state-dependent functions for damage and failure criteria only based on tests with uniaxially loaded specimens. Therefore, new experiments with carefully designed and two-dimensionally loaded specimens have been developed. Corresponding numerical simulations of these tests show that they cover a wide range of stress states allowing validation of stress-state-dependent functions for the damage criterion and evolution laws for the damage strains.

Material Forces in Consideration of Phase Transformation in TRIP-steel

The phase transformation in austenitic TRIP-steels contributes to favourable mechanical properties and may affect their fracture behavior. Therefore, the influence of the phase transformation on the crack driving force is investigated. The concept of material forces is applied to a casted CrMnNi TRIP-steel by incorporating inelastic material and transformation behavior via the material model. The resultant material force expression for the near tip crack driving force is presented and evaluated by summing up nodal material forces. The advantage of this method is the separated calculation of material forces due to dissipation by plastic deformation and phase transformation as well as the material force acting directly at the crack tip. The TRIP-effect implies a considerable contribution to the material forces, i.e. the driving force for crack propagation is reduced, which indicates a shielding effect.

Endochronic model of plasticity generalizing Sanders theory

The Sanders’s theory of plasticity and quasi-statistical variant of incremental plastic theory with isotropic and kinematic hardening in Novozhilov’s version are generalized in the frameworks of the endochronic approach. The constitutive equations of endochronic theory of inelasticity including the ideas of Sanders, Novozhilov and Valanis are formulated. The relations for the calculation of stresses and strains in uniaxial active and reversible material loadings are proposed. The formulas are obtained by using the elementary average principle of local values and by the simplest set of material constants and functions. Two types of initial conditions are considered in the calculations. The results of numerical modeling of inelastic material behavior under uniaxial active and cyclic loadings are presented. The results are compared with each other and with original Sanders’s theory. The similarity and differences between the generalized endochronic theory and the Sanders’s version are demonstrated. Several unusual manifestations of inelastic material behavior that require further theoretical analysis, calculations on the complex loading paths and the experimental verification are noted.

Polycrystal vs. Classical Continuum Models for Structures

AbstractIn this work a comparison of polycrystal and classical continuum models illustrated by examples of full structures is investigated. The general idea is to represent the averaged distribution of displacement, stress and strain fields for statistically randomized realizations of discrete structures. A technique for averaging fields in the FEM program ABAQUS is proposed and implemented. To improve the computation efficiency mesh dependence was investigated. Results of simulation are given for a rectangular plate and for the Kirsch's problem for both examples elastic as well as inelastic material behavior. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On Configurational‐Force‐Driven Crack Propagation and Adaptive Mesh Refinement in Finite Inelasticity

AbstractWe introduce a consistent variational framework for inelasticity at finite strains, yielding dual balances in physical and material space as the Euler equations. The formulation is employed for the simultaneous usage of configurational forces as both driving forces for crack propagation as well as h‐adaptive mesh refinement. The theoretical basis builds upon a global balance of internal and external power, where the mechanical response is exclusively governed by two scalar functions, the free energy function and a dissipation potential. The resulting variational structure is exploited in the context of fracture mechanics and yields evolution equations for internal variables. In the discrete setting, we present a geometry model fully separated from the finite element mesh structure that represents structural changes of the material configuration due to crack propagation. Advanced meshing algorithms provide an optimal discretization at the crack tip. Local and global criteria are obtained via error estimators based on configurational forces being interpreted as indicators of an energetic misfit due to an insufficient discretization. The numerical handling is decomposed into a staggered algorithm scheme for the dual set of equilibrium equations in material and physical space and efficient mesh generation tools. Exemplary numerical examples are considered to illustrate the method and to underline the effects of inelastic material behaviour in the presented context. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

속도 의존적인 폴리머 거동에 대한 구성적 모델

Abstract Solid polymers exhibit rate-dependent deformation behavior such as nonlinear strain rate sensitivity and stress relaxation like metallic materials. Despite the different microstructures of polymeric and metallic materials, they have common properties with respect to inelastic deformation. Unlike most metallic materials, solid polymers and shape memory alloys (SMAs) exhibit highly nonlinear stress-strain behavior upon unloading. The present work employs the viscoplasticity theory [K. Ho, 2011, Trans. Mater. Process. 20, 350-356] developed for the pseudoelastic behavior of SMAs, which is based on unified state variable theory for the rate-dependent inelastic deformation behavior of typical metallic materials, to depict the curved unloading behavior of polyphenylene oxide (PPO). The constitutive equations are characterized by the evolution laws of two state variables that are related to the elastic modulus and the back stress. The simulation results are compared with the experimental data obtained by Krempl and Khan [2003, Int. J. Plasticity 19, 1069-1095].

Damage of plates due to impact, dynamic pressure and explosive loads

It is the purpose of this article to present design equations which can be used to predict the damage of ductile plating when subjected to mass impact, dynamic pressure or impulsive loadings. The external loadings are sufficiently severe to produce inelastic material behaviour and produce finite transverse displacement, or geometry change, effects. The damage is characterised as the final or permanent transverse displacement of a plate. The theoretical method predicts values for the maximum permanent transverse displacements which agree reasonably well with the corresponding experimental results generated on aluminium alloy circular, square and rectangular plates. Thus, the equations presented in this article are valuable for preliminary design purposes and for forensic studies, while the experimental data can be used for validating numerical schemes.