Elasto-plastic Material Law Research Articles

Suction Bucket Foundations under Cyclic Tensile Loading—Physical and Numerical Modeling

Abstract Although suction buckets are believed to be a promising alternative for multipod foundations of offshore wind turbines, the economic and ecological advantages are still limited because of a lack of knowledge regarding the tensile bearing behavior. Major uncertainties exist in terms of the response under cyclic loading and the assessment of the partially drained loading condition, where negative differential pressure beneath the suction bucket’s lid contributes to the total tensile resistance. This article presents findings from 1-g model tests of suction buckets in sand subjected to various cyclic tensile loads. The suction bucket was installed via negative differential pressure (suction). The results show a strong effect of the applied load magnitude on the evolution of displacement, plug heave, and suction induced. Greater displacement accumulation is observed for the smaller considered frequency. Monotonic tests with varying displacement rates supplement the cyclic tests and serve for the verification of a hydraulic-mechanic coupled finite element model, which is afterward utilized for the back-calculation of cyclic model tests. Although a rather simple elasto-plastic material law was used for the sand, good agreement was found, indicating that the bearing behavior is mainly governed by the hydraulic conditions and only subordinately by the soil mechanics.

Analytical methodology for the verification of buried steel pipelines with flexible joints crossing strike-slip faults

The use of “flexible joints” to enhance the performance of buried pipelines at large PGD areas is a novel design approach with promising results. This paper presents an analytical methodology for the preliminary stress-strain analysis of buried steel pipelines with flexible joints crossing strike-slip faults. The analytical predictions are verified against results from parametric numerical analyses performed with a commercial numerical code. The pipeline is simulated with pipe elements following an elastoplastic material law, while the soil is simulated with non-linear winkler springs. The numerical analyses have been performed for a wide variety of PGD magnitudes, fault crossing angles, flexible joint distance and crossing position. For the sake of simplicity, the mathematics of the new methodology and the verification are presented only for joints with rotation capacity. Μinor modifications required in order to account for the effect of joint extension are stated in the concluding remarks.

Modeling of mechanical behavior in additive manufacturing at part scale

Laser Beam Melting is actually capable of producing parts with reliable mechanical properties. However, efficient production still remains a challenge and high quality numerical simulation is required in order to understand the physical mechanisms involved. Consequently, a macroscopic numerical model at part scale is actually under development for understanding the relationship between different process and material parameters with the mechanical state of final parts such as distortion and residual stress. Classical finite element method is used to solve the coupled thermo-mechanical problem on the whole domain defined by the workpiece, the baseplate and the support structures. At this scale, powder packing is neglected as well as the hydrodynamics behavior within the melt pool. Homogeneous equivalent heat source is used and imposed until several layers below the current deposited layer. Elastoplastic constitutive material law with temperature dependent parameters has been developed.

On process-step parallel computability and linear superposition of mechanical responses in additive manufacturing process simulation

We study linearity assumptions in the transient macroscale mechanical aspect of additive manufacturing (AM) process simulation. Linearity assumptions are often resorted to in combination with calibrated inelastic deformation components to arrive at computationally tractable yet reasonably accurate AM process models. We point out that linearity assumptions permit the independent computation of the response increment in each step of the AM process, and the total mechanical response is the superposition of all the process-step increments. In effect, process-step increments are computed with respect to the stress-free reference configuration in each step. The implication is that the mechanical response increment in each linearised AM process step may be computed in parallel. Trivial process-step-wise parallel computability breaks down, however, if nonlinearity (i.e. geometric or material) is modelled. In our investigation the influence of geometric nonlinearity on part distortion is small (but this is of course part-geometry specific), and more realistic stresses are obtained by imposing a nonlinear elastoplastic material law after the parallel computation and superposition of the linear AM response increments. It is demonstrated that simulation wall-clock time is reduced by exploiting process-step parallel computability in the linear regime. Moreover, numerical experiments suggest that process-step parallelization scales better (in wall-clock time) than conventional parallelization in the sequential computation of each response increment.

Modeling the rubbing contact in honeycomb seals

Metallic honeycomb labyrinth seals are commonly used as sealing systems in gas turbine engines. Because of their capability to withstand high thermo-mechanical loads and oxidation, polycrystalline nickel-based superalloys, such as Hastelloy X and Haynes 214, are used as sealing material. In addition, these materials must exhibit a tolerance against rubbing between the rotating part and the stationary seal component. The tolerance of the sealing material against rubbing preserves the integrity of the rotating part. In this article, the rubbing behavior at the rotor–stator interface is considered numerically. A simulation model is incorporated into the commercial finite element code ABAQUS/explicit and is utilized to simulate a simplified rubbing process. A user-defined interaction routine between the contact surfaces accounts for the thermal and mechanical interfacial behavior. Furthermore, an elasto-plastic constitutive material law captures the extreme temperature conditions and the damage behavior of the alloys. To validate the model, representative quantities of the rubbing process are determined and compared with experimental data from the literature. The simulation results correctly reproduce the observations made on a test rig with a reference stainless steel material (AISI 304). A parametric study using the nickel-based superalloys reveals a clear dependency of the rubbing behavior on the sliding and incursion velocity. Compared to each other, the two superalloys studied exhibit a different rubbing behavior.

Numerical analysis of contact stress and strain distributions for greased and ungreased high loaded oscillating bearings

Nowadays rolling bearings are subject to extreme operating conditions due to the increasing of the transmitted power and the optimized design. Consequently, the reduction of the bearing dimensions can lead to a reduction of the contact area and an increasing of the power transmitted per unit of contact area. Some special applications as space engineering, robotics, aeronautics and wind energy require rolling bearings subjected to high contact pressure while the movement is governed by an oscillating motion; such extreme conditions can lead to degradation and failure scenarios which are not linked to classical contact fatigue and are not completely understood yet. The aim of this work is to investigate the contact stress and strain distribution of rolling bearings under high loaded oscillating motion, i.e. high contact pressure and deformation. 3D finite element simulations with elasto-plastic material law have been carried out and a comparison of the results with the classical elastic law is presented. The effect of the friction coefficient, the radial load and the surface conformity have been investigated. The numerical results have been compared with the tribological observations of the degraded bearings under the same load conditions. The presented results contribute to the tribological and physical interpretation of the degradation scenario, for greased and ungreased bearings, by a mechanical point of view.

An interface finite element based on a frictional contact formulation with an associative plasticity model for the tangential interaction

SummaryIn this contribution, a three‐dimensional frictional contact formulation in the form of an interface solid finite element is discussed. The interface element incorporates normal as well as tangential contact conditions and aims at the modeling of phenomena occurring in engineering problems on the interface between different materials. The focus of this work lies on the description of the tangential interaction of bodies on their contact interface. Instead of the widely used Coulomb friction law, a simple elastoplastic material law is applied in order to model the interaction mechanism on the tangent plane. Appropriate local coordinate systems are introduced on the surface and point of contact, and all contact operations are performed in these coordinate systems by adopting a fully covariant description. In this way, we derive a symmetric element stiffness matrix not only for the case of sticking but also for sliding. Exploiting the advantages of the covariant description, we show that the fact that the derived stiffness matrix discretely consists of constitutive and geometrical parts enables us to introduce rather straightforwardly new appropriate interface laws describing the tangential interaction of the contacting bodies. The presented numerical results show very good correlation of the developed approach with ‘pull‐out’ experiments. Copyright © 2016 John Wiley & Sons, Ltd.

Stress field sensitivity analysis in a sedimentary sequence of the Alpine foreland, northern Switzerland

Abstract. The stress field at depth is a relevant parameter for the design of subsurface constructions and reservoir management. Yet the distortion of the regional stress field due to local-scale features such as sedimentary and tectonic structures or topography is often poorly constrained. We conduct a stress sensitivity analysis using 3-D numerical geomechanical modelling with an elasto-plastic material law to explore the impact of such site-specific features on the stress field in a sedimentary sequence of the Swiss Alpine foreland. The model's dimensions are 14 × 14 × 3 km3 and it contains 10 units with different mechanical properties, intersected by two regional fault zones. An initial stress state is established involving a semi-empirical relationship between the ratio of horizontal to vertical stress and the overconsolidation ratio of argillaceous sediments. The model results indicate that local topography can affect the stress field significantly to depths greater than the relief contrasts at the surface, especially in conjunction with horizontal tectonic loading. The complexity and frictional properties of faults are also relevant. The greatest variability of the stress field arises across the different sedimentary units. Stress magnitudes and stress anisotropy are much larger in stiffer formations such as massive limestones than in softer argillaceous formations. The stiffer formations essentially carry the load of the far-field forces and are therefore more sensitive to changes of the boundary conditions. This general characteristic of stress distribution in the stiff and soft formations is broadly maintained also with progressive loading towards the plastic limit. The stress field in argillaceous sediments within a stack of formations with strongly contrasting mechanical properties like in the Alpine foreland appears to be relatively insensitive to changes in the tectonic boundary conditions and is largely controlled by the maximum stiffness contrast with respect to the load-bearing formations.

Critical Plane Orientation Under Biaxial Fatigue Loading Conditions

The thermal loadings in the pipe wall of the residual heat removal systems in pressurized water reactors can be generally regarded as biaxial fatigue loadings, which may lead to multidirectional thermal fatigue cracks on the inner surface of the pipe wall. In this paper, the orientation of the critical plane defined by maximum damage under biaxial fatigue loading conditions are investigated by analytical and computational approaches. The analytical solutions of the critical plane orientation for the Matake's and Fatemi–Socie's criteria are first derived using an elastic material law. The computational results obtained from Code_Aster are used to validate the analytical solutions. The analytical solutions of the critical plane orientation using an elastic material law appear to be consistent with the computational results obtained from Code_Aster by using an elastic material law or a Chaboche-type elasto-plastic material law. An analytical derivation is performed to investigate the effect of the plasticity on the critical plane orientation by using a simple elasto-plastic material law with one linear isotropic hardening term. It is concluded that for the loading path of applied biaxial stress considered in this study where the maximum and minimum stresses in both directions are reached simultaneously, the critical plane orientation is not effected by the plasticity within the considered elasto-plastic material laws.

Calibration of Hyperelastic Material Properties of the Human Lumbar Intervertebral Disc under Fast Dynamic Compressive Loads

Under fast dynamic loading conditions (e.g. high-energy impact), the load rate dependency of the intervertebral disc (IVD) material properties may play a crucial role in the biomechanics of spinal trauma. However, most finite element models (FEM) of dynamic spinal trauma uses material properties derived from quasi-static experiments, thus neglecting this load rate dependency. The aim of this study was to identify hyperelastic material properties that ensure a more biofidelic simulation of the IVD under a fast dynamic compressive load. A hyperelastic material law based on a first-order Mooney-Rivlin formulation was implemented in a detailed FEM of a L2-L3 functional spinal unit (FSU) to represent the mechanical behavior of the IVD. Bony structures were modeled using an elasto-plastic Johnson-Cook material law that simulates bone fracture while ligaments were governed by a viscoelastic material law. To mimic experimental studies performed in fast dynamic compression, a compressive loading velocity of 1 m/s was applied to the superior half of L2, while the inferior half of L3 was fixed. An exploratory technique was used to simulate dynamic compression of the FSU using 34 sets of hyperelastic material constants randomly selected using an optimal Latin hypercube algorithm and a set of material constants derived from quasi-static experiments. Selection or rejection of the sets of material constants was based on compressive stiffness and failure parameters criteria measured experimentally. The two simulations performed with calibrated hyperelastic constants resulted in nonlinear load-displacement curves with compressive stiffness (7335 and 7079 N/mm), load (12,488 and 12,473 N), displacement (1.95 and 2.09 mm) and energy at failure (13.5 and 14.7 J) in agreement with experimental results (6551 ± 2017 N/mm, 12,411 ± 829 N, 2.1 ± 0.2 mm and 13.0 ± 1.5 J respectively). The fracture pattern and location also agreed with experimental results. The simulation performed with constants derived from quasi-static experiments showed a failure energy (13.2 J) and a fracture pattern and location in agreement with experimental results, but a compressive stiffness (1580 N/mm), a failure load (5976 N) and a displacement to failure (4.8 mm) outside the experimental corridors. The proposed method offers an innovative way to calibrate the hyperelastic material properties of the IVD and to offer a more realistic simulation of the FSU in fast dynamic compression.

Impact of the thermal load on the farfield and galleries of a HLW-repository

Due to the thermal impact by high level waste placed in a repository, the repository and its surroundings are subject to additional thermal load. This load may have an impact on the repository structures and buildings as well as on the surrounding geological rock formations. Two particular points are considered here: the lining of the galleries and tunnels and the long term behaviour of the geological formations at large scale. As the temperature load on the rock and the construction elements like lining and reinforcements is expected to be non-negligible in comparison to in situ conditions at construction time, its influence has to be studied to predict the repository behaviour. The thermal effects have been addressed using a thermo-mechanically coupled FE-code with classic elasto-plastic material laws. It is found that the thermal impact leads to deformation in the rock mass above the repository up to the ground surface. Furthermore, the loading on the galleries lining is important already during a relatively early stage after waste emplacement and has to be considered for dimensioning of the structures.

Identification and estimation of constitutive parameters for material laws in elastoplasticity

AbstractThe paper summarizes the comprehensive experience of the authors in the numerical identification and estimation of parameters for anisotropic elastoplastic material laws analyzing inhomogeneous mechanical fields. Generally, the constitutive model under consideration represents a system of differential and algebraic equations. It distinguishes itself by a strictly thermodynamically consistent foundation, and an identical structure in case of small as well as finite deformations. Different rules for the evolution of internal variables describing various hardening effects are proposed. The nonlinear inverse problem of the identification of material parameters is solved with deterministic optimization methods. Basically, the least squares type objective function contains several local and global variables for the comparison of experimental and numerical data. Within this context, the numerical values of the comparative quantities are calculated either using the local integration of the initial value problem at suitably chosen material points or analyzing the entire initial‐boundary value problem (e.g. with the Finite Element Method). In order to obtain the gradient of the objective function within the framework of a sensitivity analysis a semianalytical approach based on the implicit differentiation of the equilibrium conditions and the discretized constitutive relations is presented. The numerical algorithms for the direct as well as the inverse problem are implemented into in‐house Finite Element codes. Some examples based on real and numerical experiments analyzing selected constitutive approaches are presented. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Study of the Strain Rate Effect on Cold-Reduced Carbon Steel and Aluminium Alloy with Numerical Simulations

In this paper, the effect of strain rate has been considered in the simulation of forming process with a simple form combined into the material law. Quite a few researchers have proposed various hardening laws and strain rate functions to describe the material tensile curve. In this study, the strain rate model Cowper-Symonds is used with anisotropic elasto-plastic material law in the simulation process. The strain path evolution of certain elements, when the strain rate is considered and not, is compared. Two sheet materials, Cold-reduced Carbon Steel (SPCC) JIS G3141 and Aluminum alloy 6112 are used in this study. Two yield criteria, Hill 48 and Hill 90, are applied respectively to improve the accuracy of simulation result. They show different performance when strain rate effect is considered. Strain path of the elements in the fracture risk area of SPCC (JIS G3141) varies much when the strain rate material law is used. There is only little difference of the strain distribution of Al 6112 when the strain rate effect is included and excluded in the material law. The simulation results of material SPCC under two conditions indicate that the strain rate should be considered if the material is the rate-sensitive material, which provides more accurate simulation results.

On internal dissipation inequalities and finite strain inelastic constitutive laws: Theoretical and numerical comparisons

Internal dissipation always occurs in irreversible inelastic deformation processes of materials. The internal dissipation inequalities (specific mathematical forms of the second law of thermodynamics) determine the evolution direction of inelastic processes. Based on different internal dissipation inequalities several finite strain inelastic constitutive laws have been formulated for instance by Simo [Simo, J.C., 1992. Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Computer Methods in Applied Mechanics and Engineering 99, 61–112]; Simo and Miehe [Simo, J.C., Miehe, C., 1992. Associative coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation. Computer Methods in Applied Mechanics and Engineering 98, 41–104]; Lion [Lion, A., 1997. A physically based method to represent the thermo-mechanical behavior of elastomers. Acta Mechanica 123, 1–25]; Reese and Govindjee [Reese, S., Govindjee, S., 1998. A theory of finite viscoelasticity and numerical aspects. International Journal of Solids and Structures 35, 3455–3482]; Lin and Schomburg [Lin, R.C., Schomburg, U., 2003. A finite elastic–viscoelastic–elastoplastic material law with damage: theoretical and numerical aspects. Computer Methods in Applied Mechanics and Engineering 192, 1591–1627]; Lin and Brocks [Lin, R.C., Brocks, W., 2004. On a finite strain viscoplastic theory based on a new internal dissipation inequality. International Journal of Plasticity 20, 1281–1311]; and Lin and Brocks [Lin, R.C., Brocks, W., 2005. An extended Chaboche’s viscoplastic law at finite strains: theoretical and numerical aspects. Journal of Materials Science and Technology 21, 145–147]. These constitutive laws are consistent with the second law of thermodynamics. As the internal dissipation inequalities are described in different configurations or coordinate systems, the related constitutive laws are also formulated in the corresponding configurations or coordinate systems. Mathematically, these constitutive laws have very different formulations. Now, a question is whether the constitutive laws provide identical constitutive responses for the same inelastic constitutive problems. In the present work, four types of finite strain viscoelastic and endochronically plastic laws as well as three types of J 2-plasticity laws are formulated based on four types of dissipation inequalities. Then, they are numerically compared for several problems of homogeneous or complex finite deformations. It is demonstrated that for the same inelastic constitutive problem the stress responses are identical for deformation processes without rotations. In the simple shear deformation process with large rotation, the presented viscoelastic and endochronically plastic laws also show almost identical stress responses up to a shear strain of about 100%. The three laws of J 2-plasticity also produce the same shear stresses up to a shear strain of 100%, while different normal stresses are generated even at infinitesimal shear strains. The three J 2-plasticity laws are also compared at three complex finite deformation processes: billet upsetting, cylinder necking and channel forming. For the first two deformation processes similar constitutive responses are obtained, whereas for the third deformation process (with large global rotations) significant differences of constitutive responses can be observed.

Constitutive restrictions for a hyperelastic material, based upon strain invariants yielding orthogonal stress response terms

Internal dissipation always occurs in irreversible inelastic deformation processes of materials. The internal dissipation inequalities (specific mathematical forms of the second law of thermodynamics) determine the evolution direction of inelastic processes. Based on different internal dissipation inequalities several finite strain inelastic constitutive laws have been formulated for instance by Simo [Simo, J.C., 1992. Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Computer Methods in Applied Mechanics and Engineering 99, 61–112]; Simo and Miehe [Simo, J.C., Miehe, C., 1992. Associative coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation. Computer Methods in Applied Mechanics and Engineering 98, 41–104]; Lion [Lion, A., 1997. A physically based method to represent the thermo-mechanical behavior of elastomers. Acta Mechanica 123, 1–25]; Reese and Govindjee [Reese, S., Govindjee, S., 1998. A theory of finite viscoelasticity and numerical aspects. International Journal of Solids and Structures 35, 3455–3482]; Lin and Schomburg [Lin, R.C., Schomburg, U., 2003. A finite elastic–viscoelastic–elastoplastic material law with damage: theoretical and numerical aspects. Computer Methods in Applied Mechanics and Engineering 192, 1591–1627]; Lin and Brocks [Lin, R.C., Brocks, W., 2004. On a finite strain viscoplastic theory based on a new internal dissipation inequality. International Journal of Plasticity 20, 1281–1311]; and Lin and Brocks [Lin, R.C., Brocks, W., 2005. An extended Chaboche’s viscoplastic law at finite strains: theoretical and numerical aspects. Journal of Materials Science and Technology 21, 145–147]. These constitutive laws are consistent with the second law of thermodynamics. As the internal dissipation inequalities are described in different configurations or coordinate systems, the related constitutive laws are also formulated in the corresponding configurations or coordinate systems. Mathematically, these constitutive laws have very different formulations. Now, a question is whether the constitutive laws provide identical constitutive responses for the same inelastic constitutive problems. In the present work, four types of finite strain viscoelastic and endochronically plastic laws as well as three types of J2-plasticity laws are formulated based on four types of dissipation inequalities. Then, they are numerically compared for several problems of homogeneous or complex finite deformations. It is demonstrated that for the same inelastic constitutive problem the stress responses are identical for deformation processes without rotations. In the simple shear deformation process with large rotation, the presented viscoelastic and endochronically plastic laws also show almost identical stress responses up to a shear strain of about 100%. The three laws of J2-plasticity also produce the same shear stresses up to a shear strain of 100%, while different normal stresses are generated even at infinitesimal shear strains. The three J2-plasticity laws are also compared at three complex finite deformation processes: billet upsetting, cylinder necking and channel forming. For the first two deformation processes similar constitutive responses are obtained, whereas for the third deformation process (with large global rotations) significant differences of constitutive responses can be observed.

A simple model for viscous regularization of elasto‐plastic constitutive laws with softening

AbstractAn overlay‐type rheological model is presented, which is used to introduce viscosity in inviscid elasto‐plastic material laws with softening, in order to reduce the mesh‐dependency of Finite Element solutions. This model is intended to be an alternative to the well‐known visco‐plastic formulations of Perzyna and Duvaut–Lions. A time integration algorithm for the visco‐elastic model component is presented, being demonstrated in the paper, that it is unconditionally stable and oscillation‐free. The algorithm is tested in a problem with slip driven softening (von Mises material) and in a problem with decohesion driven softening (Cam‐Clay model). Figures showing the capability of the algorithm to regularize the solution are presented. Copyright © 2004 John Wiley & Sons, Ltd.

Outwards pointing hysteresis operators and asymptotic behaviour of evolution equations

The paper deals with the long-time behaviour of evolution systems described by ODEs and PDEs with hysteresis operators. The analysis is based on two concepts. The first one is the outward pointing property of the involved hysteresis operators which implies uniform a priori bounds for solutions, the second one is related to the hysteresis modelling itself and consists in introducing a class of thermodynamically consistent generalized Prandtl–Ishlinskii operators as a model for a nonlinear elastoplastic material law. A stability result for solutions in one-dimensional visco-elasto-plasticity is derived as an illustration of the theory.

A finite elastic–viscoelastic–elastoplastic material law with damage: theoretical and numerical aspects

The present work is concerned with the theoretical formulation and numerical implementation of a new isotropic finite elastic–viscoelastic–elastoplastic material law with Mullins’ damage for rubber-like materials based on a set of dissipation inequalities published recently by the first author. A phenomenological model consisting of an elastic, an elastoplastic branch and N viscoelastic branches connected in parallel is exploited. The total free energy and the total stress are additively decomposed into three parts corresponding to the three types of branches. The damage effect is assumed to act on the three types of branches homogeneously and isotropically. According to the dissipation inequalities the evolution equations of the viscoelastic and elastoplastic branches are directly formulated in terms of the corotational rates of the internal elastic logarithmic strains. It is proved that in the present constitutive setting the internal elastic logarithmic strains are coaxial to the total and trial elastic logarithmic strains. The present theoretical and algorithmic formulations provide an alternative geometric representation of the same constitutive model outlined in [J. Mech. Phys. Solids 48 (2000) 323]. The numerical simulations show that the present material law gives predictions agreeing quite well with the experimental observations and numerical simulations issued in (loc. cit.).

Springer handbook of enzymes, 2nd edn

Internal dissipation always occurs in irreversible inelastic deformation processes of materials. The internal dissipation inequalities (specific mathematical forms of the second law of thermodynamics) determine the evolution direction of inelastic processes. Based on different internal dissipation inequalities several finite strain inelastic constitutive laws have been formulated for instance by Simo [Simo, J.C., 1992. Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Computer Methods in Applied Mechanics and Engineering 99, 61–112]; Simo and Miehe [Simo, J.C., Miehe, C., 1992. Associative coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation. Computer Methods in Applied Mechanics and Engineering 98, 41–104]; Lion [Lion, A., 1997. A physically based method to represent the thermo-mechanical behavior of elastomers. Acta Mechanica 123, 1–25]; Reese and Govindjee [Reese, S., Govindjee, S., 1998. A theory of finite viscoelasticity and numerical aspects. International Journal of Solids and Structures 35, 3455–3482]; Lin and Schomburg [Lin, R.C., Schomburg, U., 2003. A finite elastic–viscoelastic–elastoplastic material law with damage: theoretical and numerical aspects. Computer Methods in Applied Mechanics and Engineering 192, 1591–1627]; Lin and Brocks [Lin, R.C., Brocks, W., 2004. On a finite strain viscoplastic theory based on a new internal dissipation inequality. International Journal of Plasticity 20, 1281–1311]; and Lin and Brocks [Lin, R.C., Brocks, W., 2005. An extended Chaboche’s viscoplastic law at finite strains: theoretical and numerical aspects. Journal of Materials Science and Technology 21, 145–147]. These constitutive laws are consistent with the second law of thermodynamics. As the internal dissipation inequalities are described in different configurations or coordinate systems, the related constitutive laws are also formulated in the corresponding configurations or coordinate systems. Mathematically, these constitutive laws have very different formulations. Now, a question is whether the constitutive laws provide identical constitutive responses for the same inelastic constitutive problems. In the present work, four types of finite strain viscoelastic and endochronically plastic laws as well as three types of J2-plasticity laws are formulated based on four types of dissipation inequalities. Then, they are numerically compared for several problems of homogeneous or complex finite deformations. It is demonstrated that for the same inelastic constitutive problem the stress responses are identical for deformation processes without rotations. In the simple shear deformation process with large rotation, the presented viscoelastic and endochronically plastic laws also show almost identical stress responses up to a shear strain of about 100%. The three laws of J2-plasticity also produce the same shear stresses up to a shear strain of 100%, while different normal stresses are generated even at infinitesimal shear strains. The three J2-plasticity laws are also compared at three complex finite deformation processes: billet upsetting, cylinder necking and channel forming. For the first two deformation processes similar constitutive responses are obtained, whereas for the third deformation process (with large global rotations) significant differences of constitutive responses can be observed.

Extension of the ?solid-shell? concept for application to large elastic and large elastoplastic deformations

In the present contribution we extend a previously proposed so-called solid–shell concept which incorporates only displacement degrees of freedom to the simulation of large elastic and large elastoplastic deformations of shells. Therefore, the modifications necessary for hyper-elastic or elastoplastic material laws are discussed. These modifications concern the right Cauchy–Green tensor for large elastic deformations, respectively, the deformation gradient for elastoplasticity which then are consistent to the modified Green–Lagrange strains that are necessary for transverse shear and membrane locking free solid–shell element formulations. However, in addition to the locking mentioned above especially in the range of plasticity incompressibility locking becomes important. Thus, the second major aspect of this contribution is the discussion of several ways to avoid incompressibility locking also including the investigation of eigenmodes. Finally, a selective reduced integration scheme with reduced integration for the volumetric term is employed and described in detail, although it is limited to material laws which allow the decomposition into a volumetric and a deviatoric part. Some numerical examples show the range of application for the proposed elements. Copyright © 2000 John Wiley & Sons, Ltd.