Efficient time stepping for the multiplicative Maxwell fluid including the Mooney-Rivlin hyperelasticity

A popular version of the finite strain Maxwell fluid is considered, which is based on the multiplicative decomposition of the deformation gradient tensor. The model combines Newtonian viscosity with hyperelasticity of Mooney-Rivlin type; it is a special case of the viscoplasticty model proposed by Simo and Miehe (1992). A simple, efficient and robust implicit time stepping procedure is suggested. Lagrangian and Eulerian versions of the algorithm are available, with equivalent properties. The numerical scheme is iteration free, unconditionally stable and first order accurate. It exactly preserves the inelastic incompressibility, symmetry, positive definiteness of the internal variables, and w-invariance. The accuracy of the stress computations is tested using a series of numerical simulations involving a non-proportional loading and large strain increments. In terms of accuracy, the proposed algorithm is equivalent to the modified Euler backward method with exact inelastic incompressibility; the proposed method is also equivalent to the classical integration method based on exponential mapping. Since the new method is iteration free, it is more robust and computationally efficient. The algorithm is implemented into MSC.MARC and a series of initial boundary value problems is solved in order to demonstrate the usability of the numerical procedures.Comment: 28 pages, 5 figures, 6 table

Efficient implicit integration for finite-strain viscoplasticity with a nested multiplicative split

An efficient and reliable stress computation algorithm is presented, which is based on implicit integration of the local evolution equations of multiplicative finite-strain plasticity/viscoplasticity. The algorithm is illustrated by an example involving a combined nonlinear isotropic/kinematic hardening; numerous backstress tensors are employed for a better description of the material behavior. The considered material model exhibits the so-called weak invariance under arbitrary isochoric changes of the reference configuration, and the presented algorithm retains this useful property. Even more: the weak invariance serves as a guide in constructing this algorithm. The constraint of inelastic incompressibility is exactly preserved as well. The proposed method is first-order accurate. Concerning the accuracy of the stress computation, the new algorithm is comparable to the Euler Backward method with a subsequent correction of incompressibility (EBMSC) and the classical exponential method (EM). Regarding the computational efficiency, the new algorithm is superior to the EBMSC and EM. Some accuracy tests are presented using parameters of the aluminum alloy 5754-O and the 42CrMo4 steel. FEM solutions of two boundary value problems using MSC.MARC are presented to show the correctness of the numerical implementation.Comment: 33 pages, 12 figure

Parameter identification in elasto-plasticity: distance between parameters and impact of measurement errors

A special aspect of parameter identification in finite-strain elasto-plasticity is considered. Namely, we analyze the impact of the measurement errors on the resulting set of material parameters. In order to define the sensitivity of parameters with respect to the measurement errors, a mechanics-based distance between two sets of parameters is introduced. Using this distance function, we assess the reliability of certain parameter identification procedures. The assessment involves introduction of artificial noise to the experimental data; the noise can be both correlated and uncorrelated. An analytical procedure to speed up Monte Carlo simulations is presented. As a result, a simple tool for estimating the robustness of parameter identification is obtained. The efficiency of the approach is illustrated using a model of finite-strain elasto-plasticity, which accounts for combined isotropic and kinematic hardening. It is shown that dealing with correlated measurement errors, most stable identification results are obtained for non-diagonal weighting matrix. At the same time, there is a conflict between the stability and accuracy.Comment: 11 pages, 2 figures, 4 table

A viscoplasticity model with an enhanced control of the yield surface distortion

A new model of metal viscoplasticity, which takes combined isotropic, kinematic, and distortional hardening into account, is presented. The basic modeling assumptions are illustrated using a new two-dimensional rheological analogy. This demonstrative rheological model is used as a guideline for the construction of constitutive relations. The nonlinear kinematic hardening is captured using the well-known Armstrong-Frederick approach. The distortion of the yield surface is described with the help of a so-called distortional backstress. A distinctive feature of the model is that any smooth convex saturated form of the yield surface which is symmetric with respect to the loading direction can be captured. In particular, an arbitrary sharpening of the saturated yield locus in the loading direction combined with a flattening on the opposite side can be covered. Moreover, the yield locus evolves smoothly and its convexity is guaranteed at each hardening stage. A strict proof of the thermodynamic consistency is provided. Finally, the predictive capabilities of the material model are verified using the experimental data for a very high work hardening annealed aluminum alloy 1100 Al.Comment: 32 pages, 9 figure

Analysis of some basic approaches to finite strain elasto-plasticity in view of reference change

There is a large variety of concepts used to generalize the classical Prandtl-Reuss relations of infinitesimal elasto-plasticity to finite strains. In this work, some basic approaches are compared in a qualitative way with respect to a certain invariance property. These basic approaches include the additive hypoelasto-plasticity with corotational stress rates, additive plasticity in the logarithmic strain space, and multiplicative hyperelasto-plasticity. The notion of weak invariance is introduced in this study. Roughly speaking, a material model is weakly invariant under a certain transformation of the local reference configuration if this reference change can be neutralized by a suitable transformation of initial conditions, leaving the remaining constitutive relations intact. We analyse the basic models in order to find out if they are weakly invariant under arbitrary volume-preserving transformations of the reference configuration. It is shown that the weak invariance property corresponds to a generalized symmetry which provides insights into underlying constitutive assumptions. This property can be used for a systematic study of different frameworks of finite strain elasto-plasticity. In particular, it can be used as a classification criterion.Comment: 29 pages, 3 figure

Mathematical analysis of fully coupled approach to creep damage

We prove the existence and uniqueness of solution to a classical creep damage problem. We formulate a sufficient condition for the problem to have a unique smooth solution, locally in time. This condition is stated in terms of smoothness of given data, such as solid geometry, boundary conditions, applied loads, and initial conditions. Counterexamples with an arbitrary small lifetime of a structure are also given, showing the mechanical interpretation of imposed smoothness conditions. The proposed theory gives a rigorous framework for a strain localization analysis. The influence of the damage gradient on the strain localization process is characterized within this framework and a measure of the damage localization is proposed.Comment: 21 pages, 1 figur

Simulation of Growth of Graded Bandgap Solid Solutions of GaAsxP1-x at Liquid Phase Electroepitaxy

The possibility of the composition control of the GaAs1-xPx solid solution on the GaAs substrate at liquid phase electroepitaxy from the Ga-As-P solution-melt is theoretically considered. By the simulation it was determined, that under steady-state conditions specifying such parameters of the process as the temperature and/or the thickness of the growth space it is possible to obtain graded bandgap layers of the GaAs1-xPx solid solution with increasing of the content of P towards the surface of the layer that possess the composition gradient from 0.5x10-4 mole fraction/nm to 2.0x10-3 mole fraction/nm. It was also shown that control of the composition of ternary solid solutions at liquid phase electroepitaxy can be realized by use of unsteady state electric field.Comment: 17 pages, 5 figures, 1 tabl

On a dislocation density based two-phase plasticity model: refinement and extension to non-proportional loading

The two-phase composite approach of Estrin et al. (1998) describes an evolving dislocation cell structure. Mckenzie et al. (2007) enhanced the model to capture the effects of hydrostatic pressure and temperature during severe plastic deformation. The goal of the present study is to incorporate this microstructural model into the macroscopic viscoplasticity framework proposed by Shutov and Krei\ss ig (2008a). Thereby, the two-phase composite approach is examined carefully. Both physical and numerical drawbacks are revealed and possible solutions are presented, thus leading to a refined micro model. Moreover, some improvements concerning reliable parameter identification are suggested as well. The material parameters of the refined micro model are identified for an aluminum alloy using TEM cell size measurements. Then, an extension to non-proportional deformation is performed in such a way that the evolution of dislocation densities becomes sensitive to load path changes. Experimental findings suggest that such deformation modes can significantly influence the evolution of microstructure, including the dissolution of cells and the reduction of total dislocation density shortly after the load path change. In order to capture such effects, some tensor-valued state variables are introduced which couple the refined micro model with the macroscopic viscoplasticity model. As a result, a new system of constitutive equations is obtained. In order to demonstrate its capability to respond to load path changes, load cases as typical for Equal Channel Angular Pressing (ECAP) are considered. The obtained evolution of dislocation populations differs signficantly depending on which ECAP route is applied

Radiative recombination through EL2 centers in gallium arsenide single crystals doped by selenium and cadmium

Influence of Cd and Se atoms on the quantum efficiency of photon emission through EL2 defects in gallium arsenide single crystals has been investigated. A comparative technique of impurity diffusion in vacuum and arsenic atmospheres has been used. The change character and extent of the photon emission quantum efficiency have been established to be defined by vacancy structure of crystal that is most likely caused by formation of EL2-dopant complexes.Comment: 5 pages, 3 figure

Simulation of fiber-reinforced viscoelastic structures subjected to finite strains: multiplicative approach

The study is devoted to the geometrically nonlinear simulation of fiber-reinforced composite structures. The applicability of the multiplicative approach to the simulation of viscoelastic properties of a composite material is assessed, certain improvements are suggested. For a greater accuracy in applications involving local compressive fiber buckling, a new family of hyperelastic potentials is introduced. This family allows us to account for the variable critical compressive stress, which depends on the fiber-matrix interaction. For the simulation of viscoelasticity, the well-established Sidoroff decomposition of the deformation gradient is implemented. To account for the viscosity of the matrix material, the model of Simo and Miehe (1992) is used; highly efficient iteration-free algorithms are implemented. The viscosity of the fiber is likewise described by the multiplicative decomposition of the deformation gradient, leading to a scalar differential equation; an efficient iteration-free algorithm is proposed for the implicit time stepping. The accuracy and convergence of the new iteration-free method is tested and compared to that of the standard scheme implementing the Newton iteration. To demonstrate the applicability of the approach, a pressurized multi-layer composite pipe is modelled; the so-called stretch inversion phenomenon is reproduced and explained. The stress distribution is obtained by a semi-analytical procedure; it may serve as a benchmark for FEM computations. Finally, the issue of the parameter identification is addressed.Comment: 17 pages, 13 figures, 3 table