Heinz E. Pettermann

A comprehensive unit cell model : a study of coupled effects in piezoelectric 1-3 composites

Abstract A finite element unit cell model for investigation of arbitrary loading conditions is developed for composites with periodic arrangements of continuous aligned fibers. Special emphasis is placed on the formulation of the boundary conditions to allow for simulation of all modes of overall deformation arising from any arbitrary combination of mechanical and electrical loading. The model is applied to piezoelectric composites whereby the overall elastic, dielectric, as well as piezoelectric moduli are fully extracted. The boundary conditions are validated for elastic in-plane shear loading and checked by recourse to comparisons with analytical bounds as well as semianalytical bounds and experimental investigations for piezoelectric composites from the literature. Aspects of fiber arrangement and differences between piezoelectric ceramic as well as polymer matrix composites reinforced with piezoelectric fibers are discussed.

Computational simulation of composites reinforced by planar random fibers : Homogenization and localization by unit cell and mean field approaches

The linear thermoelastic and thermophysical behavior of a short fiber reinforced composite material with planar random fiber arrangement is investigated by advanced numerical and analytical micromechanical methods. On the one hand, finite element based multi-fiber unit cells are introduced that contain 40-50 short fibers in arrangements approximating 2D random orientation distributions. On the other hand, the same fiber arrangements are investigated by an extended Mori-Tanaka mean field approach that can handle both statistical and discrete descriptions of the fiber orientations. Within the Mori-Tanaka scheme average microfields are extracted for individual fibers, and finite-length cylindrical reinforcements are modeled via averaged dilute concentration tensors that are evaluated numerically by finite element analysis. Homogenization and localization are performed for a metal matrix composite consisting of copper, reinforced by 21 vol% of carbon fibers that closely approximate a planar random arrangement. Simulation results on the macroscopic and microscopic linear elastic, thermoelastic, and thermal conductivity responses obtained by the two approaches are compared and excellent agreement is found.

A thermo-elasto-plastic constitutive law for inhomogeneous materials based on an incremental Mori–Tanaka approach

Abstract The behavior of a composite consisting of aligned thermo-elastic reinforcements embedded in a thermo-elasto-plastic matrix is described by an incremental Mori–Tanaka mean field approach. The matrix phase behavior is described by incremental J2 plasticity and the breakdown of isotropy of the matrix phase upon yielding is accounted for. The proposed method is implemented as a constitutive material model for a finite element code incorporating temperature dependent material data. An implicit solution strategy is introduced and special emphasis is put on the appropriate handling of the thermal expansion behavior. The applicability of the method is shown by both material characterization and a structural analysis of a hybrid component.

Computational simulation of internal bone remodeling

SummaryA review of the state of the art in computational modeling and analysis of the mechanical behavior of living bone is given. Particular attention is placed on algorithms for the simulation of the stress or strain induced remodeling processes. A special remodeling algorithm is presented which allow the simulation of internal bone remodeling taking into account not only adaptation of the spatial distribution of the effective mass density, but also the adaptation of the orientation of the material axes and of the orientation dependent stiffness parameters. Such remodeling algorithms require a sound formulation of the constitutive relations of bony material. For this purpose some micro-macro mechanical descriptions of bone in its different microstructural configurations are discussed. In conjunction with the above mentioned remodeling algorithm a new unified material model is derived for describing the linear elastic, orthotropic behavior of bone in the full range of micro-structures of cancellous and cortical bone. The application of the novel remodeling algorithm is demonstrated in an example.

Some direction-dependent properties of matrix-inclusion type composites with given reinforcement orientation distributions

A Mori-Tanaka mean-field approach for predicting the overall thermoelastic properties of multi-phase composites with given orientation distributions of the inclusion phases is used to study the influence of the inclusion orientation distribution on the effective material properties. The aim of this study is primarily to understand the effects of the inclusion orientations in short-fiber-reinforced composites and to identify the basic mechanisms of interaction between the phases which govern the overall thermoelastic behavior. Perfectly aligned discontinuous fibers, various orientation distributions as well as two-dimensional and three-dimensional random orientations of the inclusions are studied. The overall Youngs moduli, shear moduli and coefficients of thermal expansion, as well as the onset of yielding of the matrix phase under thermal and mechanical loading conditions, are calculated. The results are evaluated both in terms of the orientation distributions of the inclusions and in terms of the direction dependences of the predicted overall moduli. From these findings useful information on the appropriate requirements for the design of composite materials and composite structures can be obtained.

A finite element study on the effects of disorder in cellular structures

The susceptibility to deformation localization of simple cubic arrangements of struts, which are a simple approximation of the micro-architecture in cancellous bone, is analyzed. The coherence between structural disorder and the tendency towards deformation localization is investigated and its relevance from a biological point of view is discussed. A systematic study on the spatial deformation distribution of regular and disordered open cell structures is carried out. To this end, finite element models are employed which account for elastic-plastic bulk material and large strain theory, and a methodology for the estimation of the degree of deformation localization is introduced.

Electrical response during indentation of a 1-3 piezoelectric ceramic-polymer composite

The electrical response during indentation of a piezoelectric ceramic-polymer 1-3 composite has been investigated. The current (quasistatic charge increment) induced in the indentor due to the polarized layer on the contact surface increases with load as the contact area increases. Good agreement was found between the measured currents as a function of load with those predicted using an analytical model. In addition, the current increases with increasing indentation velocity and indentor diameter. It uses known analytical results to develop a new tool for characterizing the electrical response of piezoelectric composites. As such, linear elastic indentation with simultaneous measurement of load and electric current is shown to be a new, fast, and nondestructive technique that can be used for quality assurance and to study the effect of aging and development/presence of damage/microcracking in monolithic piezoelectric and 1-3 piezoelectric composites.

Heat conduction of a spheroidal inhomogeneity with imperfectly bonded interface

An analytical approach is presented for solving the steady state thermal conductivity problem for the following configuration. An infinite matrix material contains a single inhomogeneous spheroidal inclusion and a thermal resistance is present at the pertinent interface. The matrix shows isotropic conductivity while the inclusion is transversely isotropic, the principal material axes being aligned with the spheroid. Analytical expressions are derived for the local gradient fields in the matrix and in the inclusion as well as for the temperature mismatch along the interface. An analytical method is developed which enables replacement of the original imperfectly bonded inclusion by a less conductive but perfectly bonded inclusion. For the specific case of confocal distributions of the interface resistance the present approach yields the exact solution, i.e., the replacement operation leaves the matrix fields unchanged. For general spatial distributions of the interface properties (consistent with the sphero...

Numerical simulation of thermal conductivity of MMCs: effect of thermal interface resistance

Abstract The thermal conductivity of metal matrix composites is investigated by computational simulations, in which the effect of a thermal barrier resistance between the constituent phases is explicitly taken into account. A numerical unit cell approach, which is based on the finite element method, an analytical mean field method of the Mori–Tanaka type and bounding techniques are employed. To predict the effective conductivities of fibre composites two different types of unit cell are utilised for the numerical studies. Two dimensional unit cells are developed which allow for investigations of aligned, continuous fibre reinforced composites while three dimensional unit cells are employed to study a large variety of different arrangements of non-staggered and staggered aligned short fibres. In the case of short fibres the thermal barrier resistances of the end faces and of the cylindrical surfaces are modelled independently, which allows one to study both their individual and their combined influences on the overall behaviour. Results are presented for carbon fibre/copper composites and their overall thermal conductivities are investigated in terms of interfacial thermal barriers and microtopologies.

An Incremental Mori-Tanaka Homogenization Scheme for Finite Strain Thermoelastoplasticity of MMCs

The present paper aims at computational simulations of particle reinforced Metal Matrix Composites as well as parts and specimens made thereof. An incremental Mori-Tanaka approach with isotropization of the matrix tangent operator is adopted. It is extended to account for large strains by means of co-rotational Cauchy stresses and logarithmic strains and is implemented into Finite Element Method software as constitutive material law. Periodic unit cell predictions in the finite strain regime are used to verify the analytical approach with respect to non-proportional loading scenarios and assumptions concerning finite strain localization. The response of parts made of Metal Matrix Composites is predicted by a multiscale approach based on these two micromechanical methods. Results for the mesoscopic stress and strain fields as well as the microfields are presented to demonstrate to capabilities of the developed methods.