Inelastic Material Behavior Research Articles

Non-isothermal energy–momentum time integrations with drilling degrees of freedom of composites with viscoelastic fiber bundles and curvature–twist stiffness

3D fiber-reinforced composites demand for a special simulation technique, because they consist of fiber bundles. Therefore, in the corresponding representative volume element of these metamaterials, secondary effects as a micro inertia and a curvature–twist stiffness have to bear in mind. The latter increases the strength-to-weight ratio of thin-walled lightweight structures due to a separate twisting and bending stiffness of the fiber bundles. In this paper, these secondary effects are introduced in a continuum formulation by means of independent drilling degrees of freedom. The resulting non-isothermal constrained micropolar continuum is derived by a principle of virtual power, which simultaneously generates in the discrete setting a mixed B-bar method and a Galerkin-based energy–momentum scheme of higher order. This work also takes into account viscoelastic material behavior in the fiber bundles, which arises from a mixture of organic and inorganic fibers. Here, the viscous evolution equation is solved elementwise by using a mixed field as viscous internal variable. Representative numerical examples demonstrate the inelastic material behavior, the effect of micro inertia on the physical properties of the continuum as well as on its space and time discretization and, finally, the twisting and bending stiffness of the fiber bundles. Further, non-standard boundary conditions are applied in the dynamic simulations performed by higher order energy–momentum schemes.

Blast response of one-way arching masonry walls

The dynamic response of arching unreinforced masonry walls subjected to blast loads combines a spectrum of complex physical phenomena including opening and closing of cracks, unloading and reloading, accumulation of damage, rocking, coupling of in-plane and out-of-plane responses, and time variation of the arching force. These aspects contribute to the complexity of the dynamic behavior of the masonry wall and make the dynamic analysis challenging. This study develops a new model that integrates the aforementioned characteristics of the wall behavior and presents a quantitative tool for the assessment of the complex response. The model assumes one-way flexural action of an unreinforced masonry wall and takes the form of a multi-degree-of-freedom system, where the response is described by the displacements and rotations of the masonry units. The formulation employs variational principles and accounts for equilibrium conditions, cracking, geometrically nonlinear kinematics, and nonlinear and inelastic constitutive laws. The masonry units are assumed rigid bodies, whereas the flexural longitudinal and shear deformations of the wall are due to the mortar strains only. The mortar joints and the interfaces between adjacent masonry units are represented by arrays of nonlinear longitudinal and shear springs that introduce the normal, shear, and contact interactions between blocks. The model is examined and compared against experimental results taken from the literature. The investigated features include the cracking process, the inelastic behavior of the mortar material, and its effect on the wall response. The results demonstrate the capabilities of the analysis and throw light on the dynamic nonlinear response of the arching masonry wall under blast loads.

Artificial neural networks in structural dynamics

AbstractThe aim of the present study is to investigate how structural models with inelastic material behaviour can be enhanced by means of artificial intelligence. To this end, artificial neural networks are proposed to replace continuum mechanical models in structural dynamics. This concerns predictions of shock wave‐loaded plates and finite element simulations with neural network enhanced material modelling. By comparison to experiments, the accuracy and the computational effort of the new approach is investigated.

Towards the incorporation of damage into solid‐shells based on reduced integration

AbstractSome years ago, a family of continuum finite elements based on reduced integration [1], [2], [3] was investigated. Many structural components with different kinds of elastic and inelastic material behaviour were considered and these elements showed accurate results while beeing more efficient than similar three‐dimensional formulations based on full integration. The objective of the present contribution is to extend the analysis to damage and fracture. To this end, we present the incorporation of a modified version of a gradient‐extended damage model [4] based on the micromorphic approach [5] into solids with only a single integration point. Due to the analogy to fully‐coupled thermomechanical problems, we adapt the derivation of a consistent hourglass stabilization from an earlier contribution for multi‐field problems [6]. A numerical benchmark problem of quasi‐brittle fracture reveals the accuracy and efficiency of the proposed approach. Besides the ability to deliver mesh‐independent results, the framework is especially suitable for highly constrained situations in which conventional low‐order finite elements suffer from well known locking phenomena.

Out-of-plane response of arching masonry walls to static loads

This paper aims at characterizing the response of arching masonry walls to out-of-plane static loading. An analytical multi-degree-of-freedom model is presented aiming at modeling the nonlinear out-of-plane behavior of arching masonry walls. The model combines physical modeling tools with a formulation that applies variational principles and equilibrium conditions, boundary and continuity conditions, geometrically nonlinear kinematics, and nonlinear constitutive laws. The latter take into account the nonlinear response in compression and in tension, including cracking and inelastic response of the joints. The model refers to one-way flexural action of unreinforced masonry walls. The masonry units are modeled as rigid bodies, whereas the mortar joints are represented by arrays of springs with nonlinear kinematics and nonlinear constitutive behavior. A series of numerical examples that explore the capabilities of the model, reveal various aspects of its physical behavior and compare the analysis with experimental results reported in the literature are presented. The examined aspects include the cracking process, the development of the arching mechanism, and the effect of inelastic behavior of the mortar material on the response. The combination of the above provides a deeper look into the unique and complex physical behavior of arching walls and sets a modeling approach for its quantitative assessment.

Thermal in-plane stability of concrete-filled steel tubular arches

This paper analytically and numerically investigates the pre-buckling response and in-plane stability boundaries of circular concrete-filled steel tubular (CFST) arches subjected to combined thermal and mechanical loading. The governing non-linear equations of equilibrium are obtained using energy methods and both elastic and inelastic material behaviour is considered. A novel mechanically derived non-discretisation numerical method is proposed for the pre-buckling analysis. The stress-strain relation of the confining steel tube is described using a bi-linear plasticity model, and an inelastic material model is adopted for the concrete core which considers the effects of confinement and transient thermal strain. The result is a system of first-order differential equations which can be numerically solved with known boundary conditions including fixed ends, pinned ends or crowned-pinned cases. Closed-form solutions are presented for the elastic anti-symmetric bifurcation loads, whilst the inelastic anti-symmetric buckling strength was studied using finite element (FE) analysis. The FE model is verified by comparison to the derived analytical and numerical models which show a high level of agreement. Additionally, a sensitivity analysis is conducted which explores the influence of the constitutive material law for the concrete core and contact model for the steel-concrete interface on critical buckling loads.

Inelastic Ultimate Load Analysis of Steel Frames Considering Lateral Torsional Buckling Under Distributed Loads

Contemporary structural design approaches necessitates ways to determine realistic behavior of structures. For this purpose, inelastic ultimate load analysis methods are used widely since strength and stability of whole structure can be represented. In this study, a numerical method is proposed for determining inelastic ultimate load capacity of steel frames considering lateral torsional buckling behavior under distributed loads. In the analyses, inelastic material behavior, second-order effects and residual stresses of the structural frame system and its members are taken into account. Additionally, lateral torsional buckling behavior is considered in the analysis using finite difference method and it is used for determining the structural load carrying capacity of steel frames. Consequently, the problem associated with flexural capacity decreases due to lateral torsional buckling is precisely considered in the load increment steps of inelastic ultimate load analysis. In order to validate the proposed method, numerical examples from the literature are calculated considering the proposed method, AISC 360-16 design specification equations and approaches from the literature. Results of the numerical examples show that lateral torsional buckling is a key issue in determining structural load carrying capacity. Thus, proposed analysis method is shown to be an efficient and consistent tool for inelastic ultimate load analysis.

Low-Cycle-Fatigue (LCF) behavior and cyclic plasticity modeling of E250A mild steel

A series of strain-controlled fully-reversed uni-axial tension-compression Low-Cycle-Fatigue (LCF) tests are carried out on IS 2062:E250A (Fe410W-A) mild steel specimens with strain amplitudes upto ±1.2%, to study the cyclic in-elastic material behavior. Accordingly, parameters of Cyclic-Stress-Strain (CSS) and Basquin-Coffin-Manson relationships are derived using the LCF test results. Further, the calibration of Non-Linear Combined (isotropic-kinematic) Hardening Material (NLCHM) model of cyclic plasticity is illustrated based on the experimental hysteresis response data. Finally, the efficiency of the calibrated NLCHM model parameters is substantiated by accurately simulating the material response from the tests conducted, using a non-linear FE software, Abaqus.

On the application of SPH to solid mechanics

We analyze the applicability of the smooth particle hydrodynamics (SPH) to the solution of boundary value problems involving large deformation of solids. The main focus is set on such issues as the reduction of artificial edge effects by implementing corrected kernels and their gradients, accurate and efficient computation of the deformation gradient tensor, evaluation of the internal forces from the given stress field. For demonstration purposes, a hyperelastic body of neo-Hookean type and a visco-elastic body of Maxwell type are considered; the formulation of the Maxwell material is based on the approach of Simo and Miehe (1992). For the implementation of constitutive relations efficient and robust numerical schemes are used. A solution for a series of test problems is presented. The performance of the implemented algorithms is assessed by checking the preservation of the total energy of the system. As a result, a functional combination of SPH-techniques is identified, which is suitable for problems involving large strains, rotations and displacements coupled to inelastic material behaviour. The accuracy of the SPH-computations is assessed using nonlinear FEM as a benchmark.

Constitutive modeling of plastic deformation behavior of open-cell foam structures using neural networks

This article presents an approach to use neural networks as a constitutive model for the inelastic deformation behavior of open-cell foams or other porous materials. The inelastic deformation behavior of highly porous materials can be very complex and makes the formulation of a closed form constitutive model a very challenging or even impossible task. The presented methods include the creation of a periodic representative volume element (RVE) of the porous structure, the supply of training data by means of finite element simulations using the RVE and the use of trained neural networks within a user material routine (UMAT) for the finite element code ABAQUS. As a proof of concept this approach is applied to relatively simple two dimensional porous structures, where both the homogenized material behavior and a fully resolved porous structure are simulated and compared. The computational effort for simulating a simple foam structure can be reduced by a factor of more than 10,000 using the proposed homogenization approach.

Geo-structural nonlinear analysis of piles for infrastructure design

Pile foundations are utilized to support a variety of important infrastructure that are subjected to static and/or dynamic lateral loads due to lateral earth pressure, vessel impacts, traffic, waves, wind, and earthquakes. The pile lateral behavior under extreme lateral loading is governed by two main factors: the interaction between the pile and surrounding soil and the material inelasticity of the pile itself. This presentation covers the state of the art of modeling the nonlinear response of piles. In addition, it describes the recent development of an efficient and robust approach for the analysis of piles based on the beam on nonlinear Winkler (BNWF). In this work, a general cyclic BNWF model is developed to account for the important features of soil–pile-interaction problem including lateral load characteristics, soil cave-in, soil–pile side shear, gap formation, and strength and stiffness hardening/degradation. The inelastic behavior of pile material is also modeled effectively by implementing the advanced fiber technique. The capability of the developed model in predicting the response of piles under lateral static, cyclic and seismic loading is validated by comparing the computed results with experimental data.

Convergence of $$\text{ dG(1) }$$ dG(1) in elastoplastic evolution

The discontinuous Galerkin (dG) methodology provides a hierarchy of time discretization schemes for evolutionary problems such as elastoplasticity with the Prandtl-Reus flow rule. A dG time discretization has been proposed for a variational inequality in the context of rate-independent inelastic material behaviour in Alberty and Carstensen in (CMME 191:4949–4968, 2002) with the help of duality in convex analysis to justify certain jump terms. This paper establishes the first a priori error analysis for the dG(1) scheme with discontinuous piecewise linear polynomials in the temporal and lowest-order finite elements for the spatial discretization. Compared to a generalized mid-point rule, the dG(1) formulation distributes the action of the material law in the form of the variational inequality in time and so it introduces an error in the material law. This may result in a suboptimal convergence rate for the dG(1) scheme and this paper shows that the stress error in the $$L^\infty (L^2)$$ norm is merely $$O(h+k^{3/2})$$ based on a seemingly sharp error analysis. The numerical investigation for a benchmark problem with known analytic solution provides empirical evidence of a higher convergence rate of the dG(1) scheme compared to dG(0).

Square block foundation resting on an unbounded soil layer: Long-term prediction of vertical displacement using a time homogenization technique for dynamic loading

In this contribution, the structural long-term response of a square block foundation resting on a soil layer over rigid bedrock is investigated in the time domain. To efficiently predict the vertical displacement of the square block foundation at periodic loading, a time homogenization technique is employed to deal with different time scales in the response of the soil-foundation system and its long-term evolution due to the foundation's inelastic and nonlinear material behavior (continuous damage, discontinuous damage, viscoelastic, elastoplastic). To correctly represent the laterally unbounded soil layer over rigid bedrock, the stiffness of the linear elastic soil is first computed in the frequency domain via the modified scaled boundary finite element method. The soil stiffness in the frequency domain is then transferred to the time domain via a lumped-parameter model representation. Subsequently, the time homogenization technique including dynamic effects is developed and applied to obtain the response of the foundation-soil system in the time domain. Consolidation of the soil layer (linear elastic) is not addressed in this contribution.

Kinetic approach to the development of computational dynamic models for brittle solids

The paper presents an approach to developing the mathematical formalism of the discrete element method to numerically study the inelastic behavior and fracture of brittle materials under dynamic loading. The approach adopts the basic principles of the kinetic theory of strength which postulate the finite time of nucleation of discontinuities and relaxation of local stresses in the material. A general methodology is proposed for constructing dynamic (kinetic) models of the mechanical behavior of a discrete element based on quasi-static models and using three dynamic material parameters (time parameters). The physical meaning of these parameters is discussed, and a method is proposed for estimating the magnitude of the parameters for a considered material using standard experimental data on its mechanical characteristics. The approach is verified by a dynamic formulation of two-parameter models of inelasticity and strength of brittle materials within the method of simply deformable discrete elements. The proposed way to the dynamic generalization of conventional quasi-static mechanical models is applicable to various Lagrangian numerical methods and makes it possible to numerically study the dynamic behavior features and to predict the mechanical characteristics of brittle materials at different strain rates (up to strain rates 103 s−1) and different types of stress state.

On The Stiffness Prediction of GFRP Pipes Subjected to Transverse Loading

The main objective of this study is to predict the stiffness of GFRP pipes subjected to compressive transverse loading. An experimental study is performed to measure the stiffness of a composite pipe with a core layer of sand/resin composites. Then, a simple analytical modeling constructed on the basis of solid mechanics is used to estimate the stiffness of the investigated pipe as the back-of-envelope technique widely used by industrial sectors. The simulation of stiffness test is conducted using finite element modeling wherein both large deformation and inelastic behavior of material is taken into account as the sources of nonlinearity. The results reveal that a very good estimation with high level of accuracy can be reached by proper selection of the element and performing nonlinear analysis.

Interaction between ductile damage and texture evolution in finite polycrystalline elastoplasticity

In this paper, a multiscale model of ductile damage and its effects on the inelastic behavior of face centered cubic polycrystalline metallic materials, such as the evolution of their crystallographic textures, are investigated. The constitutive equations are written in the framework of rate-dependent polycrystalline plasticity at the microscopic scale. Plasticity and damage are coupled through a ductile damage variable introduced at the scale of the crystallographic slip systems of each grain. When homogenized to the macro-scale, this becomes an approximate phenomenological measure of the macroscopic ductile damage which can describe the material degradation by initiation, growth, and coalescence of micro-defects. In this paper, thermally activated intergranular (or creep) damage is not taken into account. Both theoretical and numerical aspects of the model are presented. The model is implemented into a general-purpose finite element code in order to analyze the effects of texture evolution and ductile damage initiation in the grains with favorably oriented slip systems. The capability of the proposed model to predict the plastic strain localization and the induced textural evolution, as well as the effects of the ductile damage and its evolution up to the final macroscopic failure are studied for a classical tensile loading path, applied to a representative volume element and to a 3D tensile specimen on which a parametric study has been carried out.

Eurofer97 Creep-Fatigue assessment tool for ANSYS APDL and workbench

For the design of future fusion reactors the ferritic-martensitic steel Eurofer97 is the main candidate for in-vessel structural application to be able to withstand harsh environment like irradiation and cyclic loading under elevated temperatures. In case of high temperatures, not only fatigue but also creep damage becomes significant and has to be considered. In the past a so called Creep-Fatigue Assessment (CFA) tool has been developed for Finite Element software ANSYS APDL as post-processor within the frame of Engineering Data & Design Integration (EDDI) in EUROfusion. This tool was initially based on the elastic Creep-Fatigue rules of ASME Boiler Pressure Vessel Code (BPVC) Section III Division 1 Subsection NH Appendix T.Nowadays the tool is able to automatically identify the critical region regarding Creep-Fatigue damage in ANSYS APDL and Workbench using local stress, maximum elastic strain range and temperature from elastic thermo-mechanical Finite Element analysis. The use of stress linearization in elastic analysis allows the calculation of a modified equivalent strain range including inelastic effects to finally determine the allowable number of cycles, creep and fatigue damage fraction. For Creep-Fatigue Assessment (CFA) post-processing design fatigue curves, creep stress versus time to rupture curves, monotonic and isochronous stress versus strain curves have been used in the combination with Creep-Fatigue damage interaction diagram to describe the Creep-Fatigue behavior of Eurofer97.As it is well known that Eurofer97 shows cyclic softening, a modified Creep-Fatigue rule has been implemented in CFA tool to improve the underestimation of creep damage. This modified rule uses for calculation of creep damage the stress versus strain and design creep curves of cyclic softened material for some fraction of lifetime and an improved Creep-Fatigue damage interaction diagram of Eurofer97.In cases where the elastic analysis of ASME BPVC is too conservative, inelastic analysis can be used to calculate total strain directly instead of the prediction used in the elastic analysis. This inelastic approach for Creep-Fatigue Assessment is less complicated compared to the elastic route because only few steps according to ASME BPVC are necessary. Nevertheless more efforts for Finite Element simulation including inelastic material behavior are required.In Summary, this CFA tool can be used for fast Creep-Fatigue evaluation. It simply allows the fast identification of Creep-Fatigue damage for a structural component which is made of Eurofer97.

Geometrically nonlinear inelastic analysis of steel–concrete composite beams with partial interaction using a higher-order beam theory

A comprehensive finite element model based on a higher-order beam theory (HBT) is developed for an accurate prediction of the response of steel–concrete composite beams with partial shear interaction. The formulation of the proposed one dimensional finite element model incorporated nonlinearities due to large deformations of the beam as well as inelastic material behaviour of its constituent components. The higher-order beam model is achieved by taking a third order variation of the longitudinal displacement over the beam depth for the steel and concrete layers separately. The deformable shear studs used for connecting the concrete slab with the steel girder are modelled as distributed shear springs along the interface between these two material layers. The Green–Lagrange strain vector is used to capture the effect of geometric nonlinearity due to large deflections. The von Mises plasticity theory with an isotropic hardening rule and a damage mechanics model are incorporated within the proposed finite element model for simulating the inelastic response of the beam materials. The nonlinear governing equations are solved by an incremental-iterative technique following the Newton–Raphson method. A dissipation based arc-length method is employed to capture the post peak response of these beams successfully. The capability of the proposed model is assessed through its validation and verification using existing experimental results and numerical results produced by detailed finite element modelling of these beams.

A model for coupled inelastic deformation and anisotropic damage behaviour of concrete

AbstractThe present paper describes a simplified model for isotropic damage developed on continuum damage theory. The model characterizes the distinct behaviour of concrete in tension and compression using a unified equivalent strain, which governs the growth of damage. In reality, concrete exhibits distributed micro‐cracking pattern under multi‐directional loads. Therefore, the model is extended to incorporate damage induced anisotropy inherently for a reliable representation of damage, and captures the direction of possible damage evolution. Moreover, the model takes the inelastic behaviour of material into account based on the extended version of Lubliner failure criterion. The model is validated with experimental data. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling the Damage Characteristics of Concrete Subjected to Cyclic Loadings

Various damage formulations have been used to simulate the inelastic behavior of granular composite materials, e.g., concrete, under cyclic loadings, but the results obtained differ from experimental data. The aim of this study is to develop general nonlinear damage formulations, with calibration capabilities, on the basis of two nonlinear indices, namely the tension and compression states, covering all cyclic loading conditions, including partial and complete unloading/reloading ones. Using verification procedures, the efficiency of calibration ability of the formulations, especially for computer programming, is illustrated.