Microplane modeling of cyclic behavior of concrete: a gradient plasticity-damage formulation

A microplane model is developed to simulate the behavior of concrete under cyclic loading conditions. Pure damage mechanics or pure plasticity models yield satisfactory results for concrete under monotonic loading but cannot capture correctly the unloading and reloading response. Therefore, coupling damage and plasticity is necessary for accurate constitutive modeling of concrete. The microplane model offers a straightforward approach to simulate induced anisotropy by formulating the material laws on many randomly oriented planes. Distinguishing between compression and tension response using the proper plastic yield function and damage laws is considered. Furthermore, gradient enhancement is employed to handle the pathological mesh sensitivity related to strain softening. The new formulation is implemented within a 3D finite element code and a numerical example is simulated and compared to experiments in order to evaluate the capabilities of the model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical aspects of microplane constitutive models for concrete

This paper presents a comprehensive study on the numerical aspects of a class of microplane constitutive models for concrete, with emphasis on the most popular one, i.e., the model M4 developed by Bažant and co-workers. The effect of the computational procedures for the microplane shear stress components, the strain increment magnitude, the integration scheme and the loading direction on the model responses are investigated in detail. Several problems in the responses of the model, from the computational point of view, are detected and discussed. Some procedures to enhance the numerical performance of the model are then proposed. These include a removal of the tensile volumetric stress boundary in the original formulation, the introduction of a novel semi-explicit numerical algorithm for the microplane volumetric and deviatoric stresses, and a method to minimise the sensitivity of the model responses to the loading direction through a simple meshing-based integration scheme. Finally, some practical considerations for the choice of numerical integration scheme in the finite element calculations of large-scale concrete structures with the microplane model M4 are presented.     

Comparison of dilatant plasticity models in application to rubber-toughened polymers

The overall deformation behavior of rubber-toughened polymers (e.g. PC/ABS blends) exhibits a pronounced plastic dilatancy. As this volume increase results from diverse micromechanisms the appropriate structure of a macroscopic model is not obvious. In this contribution, different material models featuring plastic dilatancy are compared with regard to their ability to capture the deformation behavior of PC/ABS in different loading situations. All models are calibrated to match experimental data under uniaxial tension in terms of true stress-strain curves and the evolution of volume strain. Afterwards they are employed in finite element (FE) simulations of single-edge-notch-tensile (SENT) tests. Patterns of plastic deformation computed from the different material models are compared to experimental findings. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Constitutive modeling of ferromagnetic and ferroelectric behaviors and application to multiferroic composites

In this paper, the constitutive modeling of nonlinear multifield behavior as well as the finite element implementation are presented. Nonlinear material models describing the magneto-ferroelectric or electro-ferromagnetic behaviors are presented. Both physically and phenomenologically motivated constitutive models have been developed for the numerical calculation of principally different nonlinear magnetostrictive behaviors. Further, the nonlinear ferroelectric behavior is based on a physically motivated constitutive model. On this basis, the polarization in the ferroelectric and magnetization in the ferromagnetic and magnetostrictive phases, respectively, are simulated and the resulting effects analyzed. Numerical simulations focus on the calculation of magnetoelectric coupling and on the prediction of local domain orientations going along with the poling process, thus supplying information on favorable electric-magnetic loading sequences. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of the effective viscoelastic material behavior of textile reinforced composites using a multi-scale approach

The increasing importance of constructive lightweight in modern engineering science involves the use of advanced materials like textile reinforced composites. In order to reduce development costs, efficient numerical simulations are needed to model the macroscopic behavior of the final product. Focussing on long term phenomena, which are important when parts made of composites with rate-dependent material behavior are assembled by bolted or screwed joints, a two-step homogenization procedure is used to obtain an effective homogeneous equivalent material at the macroscopic scale. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Well-posedness Results for Models of Elastomers

Existence and uniqueness of weak solutions are shown for different models of the dynamic behavior of elastomers. The models are based on a nonlinear stress-strain relationship (satisfying a locally Lipschitz and affine domination property) and incorporate hysteretic effects as well. The results provide alternatives to previous theories that required monotonicity assumptions on the nonlinearities. Results with a nonlinear constitutive law and nonlinear internal dynamics are presented for the first time.     

Theoretical study and numerical simulation of textiles

We propose a new approach for developing continuum models fit to describe the mechanical behavior of textiles. We develop a physically motivated model, based on the properties of the yarns, which can predict and simulate the textile behavior. The approach relies on the selection of a suitable topological model for the patch of the textile, coupled with constitutive models for the yarn behavior. The textile structural configuration is related to the deformation through an energy functional, which depends on both the macroscopic deformation and the distribution of internal nodes. We determine the equilibrium positions of these latter, constrained to an assigned macroscopic deformation. As a result, we derive a macroscopic strain energy function, which reflects the possibly nonlinear character of the yarns as well as the anisotropy induced by the microscopic topological pattern. By means of both analytical estimates and numerical experiments, we show that our model is well suited for both academic test cases and real industrial textiles, with particular emphasis on the tricot textile.     

Influence of Inertia on the Microscale in Homogenization

When calculating effective dynamical properties of a material, inertia on the microscale is usually neglected. Here, contrary to these approaches, inertia effects are taken into account, leading to a frequency dependent microscopic behavior. Thus, a frequency dependent macroscopic constitutive equation is required. Therefore, a viscoelastic constitutive equation is applied on the macroscale. The material parameters are found using an Evolutionary Strategy. In the 1‐D case, system responses on the micro‐ and macroscale show a good agreement in a frequency range from 0 up to the first eigenfrequency of the microstructure. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On physics-based crystal plasticity models: Application to virtual material testing of sheet metals

It is possible to pursue a multi-scale modeling approach for sheet forming simulations by applying the concept of virtual material testing to determine the yield surface from the microstructure of a given material. Full-field simulations with phenomenological crystal plasticity models are widely used for this kind of investigations. However, recent developments focus on incorporating physical quantities like dislocation density into these models. In this work, a dislocation density based crystal plasticity model is used to investigate the plastic anisotropy of the deep drawing steel DC04. In particular, we focus on the prediction of R-values, which can be used to calibrate macroscopic plasticity models. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A condensed approach to model the constitutive behavior of multiphase ferroelectric and multiferroic materials

Ferroelectric as well as ferromagnetic materials are widely used in smart structures and devices as actuators, sensors etc. Most of the developed models, describing the nonlinear behavior, are implemented within the framework of the Finite Element Method. Most investigations, however, are restricted to simple boundary value problems under uniaxial or biaxial loading and their goal is the calculation of hysteresis loops or to determine e.g. electromechanical coupling coefficients. Regarding these circumstances, the so-called condensed method (CM) is introduced to investigate the macroscopic polycrystalline ferroelectric material behavior at a macroscopic material point without any kind of discretization scheme. In the presented paper, the CM is extended towards multiphase ferroelectric material behavior. Moreover, first numerical results of a multiphase ferroelectric material at the morphotropic phase boundary are presented. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The generalized Masing models for deteriorating hysteresis and cyclic plasticity

The Masing model originally proposed for one-dimensional cyclically stabilized hysteretic behavior is generalized for deteriorating hysteresis and for cyclic plasticity, with system degradation and cyclic hardening effects taken into account. The generalization into the multi-dimensional case is based on the concept of a universal stress–strain curve and the associated effective stress and effective strain. Numerical simulations confirm the validity of the generalized models that are conceptually simple and parametrically parsimonious. The generalization method employed also provides a unifying way of extending 1-D hysteretic models to multi-dimensional constitutive models in cyclic plasticity.     

On the simulation of textile reinforced composites and structures

This paper presents experimental and numerical methods to perform simulations of the mechanical behavior of textile reinforced composites and structures. The first aspect considered refers to the meso-to-macro transition in the framework of the finite element (FE) method. Regarding an effective modelling strategy the Binary Model is used to represent the discretized complex architecture of the composite. To simulate the local response and to compute the macroscopic stress and stiffness undergoing small strain a user routine is developed. The results are transfered to the macroscopic model during the solution process. The second aspect concerns the configuration of the fiber orientation and textile shear deformation in complex structural components. To take these deformations which affect the macroscopic material properties into account they are regarded in a macroscopic FE model. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A class of optimal control problems for piezoelectric frictional contact models

We consider control problems for a mathematical model describing the frictional bilateral contact between a piezoelectric body and a foundation. The material’s behavior is modeled with a linear electro–elastic constitutive law, the process is static and the foundation is assumed to be electrically conductive. Both the friction and the electrical conductivity conditions on the contact surface are described with the Clarke subdifferential boundary conditions. The weak formulation of the problem consists of a system of two hemivariational inequalities. We provide the results on existence and uniqueness of a weak solution to the model and, under additional assumptions, the continuous dependence of a solution on the data. Finally, for a class of optimal control problems and inverse problems, we prove the existence of optimal solutions.     

Numerical investigations on the fixation of cemented and uncemented endoprostheses

In this contribution, a constitutive model adopted from the computational plasticity-models of Drucker-Prager and von Mises is presented. This model captures the material behavior of osseointegration and the curing-process of bone cement. With this basic model, both simulations of bone-ingrowth of uncemented implants and simulations of the curing process of bone cement for cemented implants are carried out in a bone-implant interface. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the effective viscosity of a periodic suspension – analysis of primal and dual formulations for Newtonian and non‐Newtonian solvents

Computer simulations of the injection molding process of fiber‐reinforced plastics critically depend on the accuracy of the constitutive models. Of prime importance for the process simulation is the precise knowledge of the viscosity. Industrial applications generally feature both high shear rates and high fiber volume fractions. Thus, both the shear‐thinning behavior of the melt and the strong anisotropic effects induced by the fibers play a dominant role. Unfortunately, the viscosity cannot be determined experimentally in its full anisotropy, and analytical models cease to be accurate for the high fiber volume fractions in question. Computing the effective viscosity by a simplified homogenization approach serves as a possible remedy. This paper is devoted to the analysis of a cell problem determining the effective viscosity. We provide primal as well as dual formulations and prove corresponding existence and uniqueness theorems for Newtonian and Carreau fluids in suitable Sobolev spaces. In the Newtonian regime, the primal formulation leads to a saddle point problem, whereas a dual formulation can be obtained in terms of a coercive and symmetric bilinear form. This observation has deep implications for numerical formulations. As a by‐product, we obtain the invertibility of the effective viscosity, considered as a function, mapping the macroscopic shear rate to the macroscopic shear stress. Copyright © 2016 John Wiley & Sons, Ltd.     

Kinetic Models for Chemotaxis and their Drift-Diffusion Limits

Kinetic models for chemotaxis, nonlinearly coupled to a Poisson equation for the chemo-attractant density, are considered. Under suitable assumptions on the turning kernel (including models introduced by Othmer, Dunbar and Alt), convergence in the macroscopic limit to a drift-diffusion model is proven. The drift-diffusion models derived in this way include the classical Keller-Segel model. Furthermore, sufficient conditions for kinetic models are given such that finite-time-blow-up does not occur. Examples are given satisfying these conditions, whereas the macroscopic limit problem is known to exhibit finite-time-blow-up. The main analytical tools are entropy techniques for the macroscopic limit as well as results from potential theory for the control of the chemo-attractant density.     

Modelling of thin viscoelastic shell structures under Reissner–Mindlin kinematic assumption

In this paper, we study thin viscoelastic shell structures using a constitutive equation in hereditary integral form. An alternative mathematical formulations for several viscoelastic shell structures under the Reissner–Mindlin kinematical assumptions are obtained. The resulting equations are written as a Volterra equation of the second kind to allow further mathematical analysis. A locking-free finite element formulation, with selective reduced integration is used to approximate the equation. To perform numerical experiments we consider several situations suffering from locking in both cases dynamic and quasi-static. We show the good behavior of the model compared with other models from the literature.