Obtaining Cosserat material parameters by homogenization of a Cauchy continuum

An increasing importance of composites with sandwich architecture and fibre-reinforced components is recognizable especially in aerospace and light weight industry. Due to the inner structure such materials often exhibit a complex behavior. If the ratio of micro- and macroscopic length scales, l and L, violates the condition l/L ≪ 1, a higher order continuum should be used to describe the macroscopic material behavior correctly. The numerical simulation requires reliable material constants, for which the experimental determination is laborious and sometimes impossible. Alternatively homogenization methods can be used for the numerical identification of overall material parameters. A short introduction to the linear Cosserat theory is followed by an extended homogenization procedure to derive the macroscopic material constants of a linear Cosserat continuum. The parameters obtained with a heterogeneous cell are used to simulate different bending load cases. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flexural Properties of Fiber-Reinforced Composites

To describe the macroscopic mechanical behavior of composite materials with biaxial weft-knitted fabric reinforcement, a difference between the flexural and tensile stiffness must be taken into account. Due to the periodic structure of the composite, the material behavior can be investigated on a unit cell. A homogenization technique based on the Hill-Mandel energy balance is used to replace a heterogenous Boltzmann medium by a homogenous COSSERAT continuum. To simulate the material behavior, this homogenization method is applied to the Binary Model. Tensile, shear and bending tests were performed to verify the simulation results. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Polycrystal vs. Classical Continuum Models for Structures

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

Investigation of Cosserat material parameters obtained by homogenization of a Cauchy continuum

If a higher order continuum theory is used in a numerical simulation, the material parameters have to be derived. The experimental determination is laborious and sometimes impossible. Alternatively homogenization methods can be used for the numerical identification of overall material parameters. A short introduction to the micropolar continuum and the homogenization approach is followed by the discussion of the identified properties. Therefore some parameter studies are presented. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-dimensional cell model analysis of ductile damage under dynamic loading condition

The paper deals with the damage and fracture behavior of ductile metals under dynamic loading conditions. The in [1–3] presented phenomenological continuum damage and fracture model, which takes into account the rate- and temperature-dependence of the material, provides reasonable results of experiments with high strain rates while the identification of the corresponding material parameters results difficult from the available experimental data. This lack of information can be resolved by micro-mechanical numerical simulations of void containing unit-cells. In this context results of dynamic micro-mechanical simulations are presented which can be used to study the damage effects on the micro-scale and to validate the rate-dependent continuum damage model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Damage and fracture behavior in dynamic tension tests: Modelling and numerical simulations

The continuum damage model is based on a general thermodynamic framework for the modeling of rate and temperature dependent behavior of anisotropically damaged elastic-plastic materials subjected to fast deformation. The introduction of damaged and fictitious undamaged configurations allows the definition of damage tensors and the corresponding free energy functions lead to material laws affected by damage and temperature. The damage condition and the corresponding damage rule strongly depend on stress triaxiality. Furthermore, the rate and temperature dependence is reflected in a multiplicative decomposition of the plastic hardening and damage softening functions. The macro crack behavior is characterized by a triaxiality dependent fracture criterion. The continuum damage model is implemented into LS-DYNA as user defined material model. Corresponding numerical simulations of unnotched and notched tension tests with high strain rates demonstrate the plastic and damage processes during the deformation leading to final fracture numerically predicted by an element erosion technique. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of a viscoplastic material model on a combined quasi-static-electromagnetic forming process

The prediction and simulation of material behavior by finite element methods has become indispensable. Furthermore, various phenomena in forming processes lead to highly differing results. In this work, we have investigated the process chain on a cross-shaped cup in cooperation between the Institute of Applied Mechanics (IFAM) of the RWTH Aachen and the Institute of Forming Technology and Lightweight Construction (IUL) of the TU Dortmund. A viscoplastic material model based on the multiplicative decomposition of the deformation gradient in the context of hyperelasticity has been used [1,2]. The finite strain constitutive model combines nonlinear kinematic and isotropic hardening and is derived in a thermodynamically consistent setting. This anisotropic viscoplastic model is based on the multiplicative decomposition of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong-Frederick kinematic hardening. The constitutive equations of the material model are integrated in an explicit manner and implemented as a user material subroutine in the commercial finite element package LS-DYNA with the electromagnetical module. The aim of the work is to show the increasing formability of the sheet by combining quasi-static deep drawing processes with high speed electromagnetic forming. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Textile Drape as Mechanical Phenomenon

The paper copes with the based on the continuum mechanics simulation of the textile drape. A textile surface is treated as linear elastic two‐dimensional Cosserat continuum with independent in plane and out of plane material properties. Bending stiffness and in plane shearing stiffness measured with the Kawabata Evaluation System for Fabrics (KES‐F) are used in the calculations. Other necessary material constants in the model, which are not measurable in a direct way with the KES‐F and which are introduced in the model, are assumed. To solve the equilibrium equations of the system the Finite Element Method (FEM) is used. An implementation of the arc‐length algorithm makes the tracing of the full equilibrium path (pre‐buckling, critical and post‐buckling behaviour) possible. The paper proves that the simulation of the textile drape with the methods of continuum mechanics can be done regarding measured material mechanical properties and carrying out a stability analysis. By now, the stability analysis has not been examined by the FE textile researchers. Therefore neither critical and post‐buckling phenomena nor the ambiguity of the textile behaviour have been described or explained sufficiently.     

Modeling of large deformation frictional contact in powder compaction processes

In this paper, the computational aspects of large deformation frictional contact are presented in powder forming processes. The influence of powder–tool friction on the mechanical properties of the final product is investigated in pressing metal powders. A general formulation of continuum model is developed for frictional contact and the computational algorithm is presented for analyzing the phenomena. It is particularly concerned with the numerical modeling of frictional contact between a rigid tool and a deformable material. The finite element approach adopted is characterized by the use of penalty approach in which a plasticity theory of friction is incorporated to simulate sliding resistance at the powder–tool interface. The constitutive relations for friction are derived from a Coulomb friction law. The frictional contact formulation is performed within the framework of large FE deformation in order to predict the non-uniform relative density distribution during large deformation of powder die pressing. A double-surface cap plasticity model is employed together with the nonlinear contact friction behavior in numerical simulation of powder material. Finally, the numerical schemes are examined for efficiency and accuracy in modeling of several powder compaction processes.     

Finite element simulation for material accumulation and welding processes including a free melt surface

A modeling and simulation approach for problems with solid-liquid-solid phase transitions and a free surface, feasible for material accumulation processes based on laser-based free form heading and welding processes for joining different metallic materials is presented. Both named processes are modeled within the framework of continuum mechanics by coupling the Stefan problem with the Navier-Stokes equations including a free capillary surface. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A finite element framework for the numerical implementation of boundary potentials

This contribution deals with the implications of boundary potential energies on deformational mechanics in the framework of the finite element method at finite strains. The common material models in continuum mechanics are taking the bulk into account, nevertheless, neglecting the boundary. However, boundary effects sometimes play a dominant role in the material behavior, e.g. surface tension in fluids. The boundary potentials, in general, are allowed to depend not only on the boundary deformation gradient but also on the spatial surface–normal / curve–tangent, as well. For the finite element implementation, a suitable curvilinear coordinate system attached to the boundary is defined and corresponding geometrical and kinematical derivations are carried out. Afterwards, the discretization of the generalized weak formulation, including boundary potentials, is carried out and finally numerical examples are presented to demonstrate the boundary effects due to the different proposed material behavior. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

FE-simulation of spatially graded gelation during adhesive's curing

In this contribution main aspects of material characterization and modelling of a curing adhesive are denoted. It is pointed out how to deal with the exothermic heat generation during curing, both, how to obtain it experimentally as well as how to account for it in the continuum mechanical an FE-modelling framework. Furthermore, a strategy to simulate spatially graded gelation processes in ANSYS® is presented. An academic simulation example completes this work. By the help of this simulation tool a better understanding of a novel manufacturing process of smart semi-finished light weight structures is ensured. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dispersion of elastic waves in a micropolar metamaterial plate with periodical arranged resonators

The wave propagation in a micropolar elastic metamaterial is investigated in this paper. The elastic metamaterial is composed of the micropolar elastic host material and the periodically arranged local resonators. Compared with the classical elastic metamaterial, the micropolar elastic metamaterial has more material parameters that can be elaborately designed to manipulate the elastic wave propagation. By introducing additional displacement fields, a multi-displacement continuum model of the micropolar elastic metamaterial is presented to characterize the resonance behavior of the resonators and the microstructure effects of the unit cell. According to this continuum model, two independent wave systems exist: one is a longitudinal system and the other is a shear and rotation coupled transversal system. The dispersive curves and band gaps of the longitudinal and transversal systems are numerically discussed and the influences of the resonators are mainly considered.     

Failure of granular materials at different scales - microscale approach

In recent years there has been an increase of interest in packed granular and discontinuous media. Due to the properties of such materials, a simple continuum approach is not appropriate to describe the material behavior. Breaking and forming of new contacts between grains, distinguishing for granular media, cannot be captured. We apply a computational homogenization method [6] which is based on a two scale concept to complete the task of modeling packed granular materials. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On effects of discretization and the selection of constitutive equations on stability of continua

In classical continuum mechanics the set of basic equations consists of the equation of motion, the kinematic equation and the constitutive equations. The study concentrates on constitutive modeling and the effects of discretization on stability problems. The method of investigation is analytic, the spectra of linear mapping operators of continuous and discrete dynamical systems are studied. As results cases are found, when a hidden incursive nature of a material model leads to unstable behavior of the continuum. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of particle size on the fracture toughness of a PP-based particulate composite

The main focus of this paper is a numerical investigation of the fracture behavior of a particulate composite (CaCO₃-PP). The composite is modeled as a three-phase continuum and simulated numerically on a microscale by using finite elements. The propagation of a microcrack in a matrix filled with rigid particles covered by an interphase is analyzed. The stress distribution is determined for a variety of particle sizes and material properties of the interphase. The final results, in agreement with experimental data, confirm that the microcrack behavior depends on particle sizes. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 411-418, May-June, 2009.     

Modeling of microscopic failure in heterogeneous materials

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