Determining Material Parameter of Solder Alloys by Nanoindentation

Environmental awareness motivates the replacement of traditional plumbiferous solder joints in microelectronic devices by new material alloys. In our group mechanical properties of some lead-free alloys are determined by nanoindentation experiments. We use a Microsystems-Nanoindenter Machine with Berkovich tip and apply standard techniques to extract the material properties from the measured load-displacement curves. To assess the quality of our experimental results we model and analyze the setup by finite element computations. By comparing the real (input) material data with the results determined from the load-displacement curves we analyze the obtained data in dependence of strength and stiffness of the materials under consideration. For low-strength material we point out deviations. By inverse analysis we adapt numerically elastic modulus and yield stress to experimentally measured load-displacement curves. To obtain information on the material's work hardening we suggest the use of a blunt indenter tip, e.g., a spherical indenter. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Microscopic model for a cell-seeded material

The aim of the present paper is to account for the growth of fiber which is observed in a cell-seeded material stimulated in a bioreactor. For this purpose, the change of mass is considered in the balance laws, and the deformation energy is assumed to be a function of varying mass and the Helmholtz free-energy. Fiber growth at the microscopic level causes a macroscopic change of the material's mechanical properties. The study is a first approach towards a micromechanical model accounting for remodelling in cartilage replacement materials. In so doing, constitutive equations for renewable soft tissues are proposed. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computational characterization of ferroelectric solids with a 3D Preisach model based on an orientation distribution function

Ferroelectric or ferromagnetic materials show an interaction between mechanical deformations and polarization or magnetization. A few multiferroic materials possess both ferroic properties and exhibit a magneto-electric (ME) coupling. These ME properties can be achieved in two-phase composites, which combine ferroelectric and ferromagnetic characteristics. To predict a realistic material behavior and a more precise ME coefficient, the application of suitable material models which describe the nonlinear hysteretic behavior is of particular importance. In the present contribution we focus on the characterization of a nonlinear ferroelectric material behavior, in terms of a 3D Preisach model based on an orientation distribution function. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Topology and material orientation optimization based on evolution equations

Many modern high-performance materials have inherent anisotropic elastic properties and its local material orientation can be considered to be an additional design variable for the topology optimization [1–3]. We extend our previous model for topology optimization with variational controlled growth [4–6] for linear elastic anisotropic materials, for which the material orientation is introduced as an additional design variable. We solve the optimization problem purely with the principles of thermodynamics by minimizing the Gibbs energy. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An examination of tissue engineered scaffolds in a bioreactor

Replacement tissues, designed to fill in articular cartilage defects, should exhibit the same properties as the native material. The aim of this study is to foster the understanding of, firstly, the mechanical behavior of the material itself and, secondly, the influence of cultivation parameters on cell seeded implants as well as on cell migration into acellular implants. In this study, acellular cartilage replacement material is theoretically, numerically and experimentally investigated regarding its viscoelastic properties, where a phenomenological model for practical applications is developed. Furthermore, remodeling and cell migration are investigated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling the hydrogen material interaction as parametric instability of the continuum

The hydrogen is contained in any material. Its concentration inside the materials leads to mechanical properties degradation. The two-continuum model of solid allows one to describe the influence of small concentration of hydrogen on the mechanical properties of materials in terms of changing the bonding energy of the second continuum, the latter being responsible for the hydrogen concentration. The application of this model to fatigue task give the hydrogen concentration that are critical for material destruction. Such fatigue destruction has a nature of parametric instability during the cyclic redistribution of the hydrogen under the cyclic loading. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于变体积约束的阻尼材料微结构拓扑优化研究北大核心CSCD

阻尼复合结构的抑振性能取决于材料布局和阻尼材料特性.该文提出了一种变体积约束的阻尼材料微结构拓扑优化方法,旨在以最小的材料用量获得具有期望性能的阻尼材料微结构.基于均匀化方法,建立阻尼材料三维微结构有限元模型,得到阻尼材料的等效弹性矩阵.逆用Hashin-Shtrikman界限理论,估计对应于期望等效模量的阻尼材料体积分数限,并构建阻尼材料体积约束限的移动准则.将获得阻尼材料微结构期望性能的优化问题转化为体积约束下最大化等效模量的优化问题,建立阻尼材料微结构的拓扑优化模型.利用优化准则法更新设计变量,实现最小材料用量下的阻尼材料微结构最优拓扑设计.通过典型数值算例验证了该方法的可行性和有效性,并讨论了初始微构型、网格依赖性和弹性模量等对阻尼材料微结构的影响.     

Relaxation model of piezoelectric materials

Polarization switching inside grains is time dependent. When external applied loading is not quasi-static, macroscopic properties of piezoelectric materials changes with the rate of loading. In this paper, a 2-D micromechanical model is proposed in order to simulate the rate dependent properties of certain perovskite type tetragonal piezoelectric materials based on linear constitutive, nonlinear domain switching, intergranular effects and kinetics models. The material is electrically loaded with an alternating voltage of various frequencies. For the onset of domain switching, energy equation is implemented. Propagation of the domain wall during domain switching in grains is modeled by means of exponential kinetics relation after domain nucleation. Mechanical strain butterfly loops under different frequencies (0.01Hz–1Hz) are simulated. The model gives important insights into the rate dependency of the piezoelectric materials that have been observed in some experiments reported in the literature. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mechanical modelling and experimental validation of meniscus replacement material

In the present study a condensed collagen gel is investigated for its application as a cartilage replacement material. For this reason, the strength and damping properties are examined experimentally and a theoretical model for predicting specimen deformations and stresses is proposed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiscale simulations of concrete mechanical tests

In civil engineering, computational modeling is widely used in the design process at the structural level. In contrast to that, an automated support for the selection or design of construction materials is currently not available. Specification of material properties and model parameters has a strong influence on the results. Therefore, an uncoupled two-step approach is employed to provide relatively quick and reliable simulations of concrete (mortar) tests. First, the Mori–Tanaka method is utilized to include the majority of small aggregates and air voids. The strain incremental form of MT approach serves for the prediction of material properties subsequently used in the finite element simulations of mechanical tests.     

Homogenization of fibre composites using X-FEM

A successful material design process for novel textile reinforced composites requires an integrated simulation of the material behaviour and the estimation of the effective properties used in a macroscopic structural analysis. In this context the Extended Finite Element Method (X-FEM) is used to model the behavior of materials that show a complex structure on the mesoscale efficiently. A homogenization technique is applied to compute effective macroscopic stiffness parameters. This contribution gives an outline of the implementation of the X-FEM for complex multi-material structures. A modelling procedure is presented that allows for the automated generation of an extended finite element model for a specific representative volume element. Furthermore, the problem of branching material interfaces arising from complex textile reinforcement architectures in combination with high fibre volume fractions will be addressed and an appropriate solution is proposed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Biomechanical modelling of cellular articular cartilage replacement tissues

The aim of the present study is to investigate the strength and damping properties of cellular articular cartilage replacement material. For this purpose, a viscoelastic-diffusion model for the acellular water-saturated condensed collagen gel type I is proposed and validated experimentally. Moreover, a remodelling law for the cell seeded collagen gel is introduced. For an experimental study of the interaction between fibre growth and mechanical stimulation, bioreactors are developed and histological investigations are carried out. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Measuring and modeling the thermal conductivities of three-dimensionally woven fabric composites

The effect of a three-dimensional fiber reinforcement on the out-of-plane thermal conductivity of composite materials is investigated. Composite preforms with different fibers in the thickness direction were fabricated. After in fusion by using a vacuum-assisted resin transfer molding process, their through-thickness thermal conductivities were evaluated. The measured thermal conductivities showed a significant increase compared with those of a typical laminated composite. Although the through-thickness thermal conductivity of the samples increased with through-thickness fiber volume fraction, its values did not match those predicted by the simple rule of mixtures. By using finite-element models to better under stand the behavior of the composite material, improvements in an existing analytical model were performed to predict the effective thermal conductivity as a function of material properties and in-contact thermal properties of the composite. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 241–254, March–April, 2009.     

Applying Cauchy-Born rule for converting atomistic model to continuum model

The Cauchy-Born rule has been applied in the Quasicontinuum method to derive continuum material properties based on underlying atomistic model in a physically consistent way. In this short work, the procedure is demonstrated, where the resulted materials constants are compared with experimental data found in literature. Moreover, the condition for applying the Cauchy-Born rule is discussed, with an intuitive explanation for why it can be only applied to crystalline materials with perfect structure. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An anisotropic viscoelastic soft tissue model at large strains

Soft biological tissues represent complex inhomogeneous, and as a rule multiphase materials subjected to large strains under in vivo mechanical conditions. Apart from a number of other structural-related features they are characterized by a ratedependent material behavior which is attributed to fluid-solid interactions as well as intrinsic viscoelastic properties of the solid matrix. The authors propose to model rate-dependent phenomena of the solid phase of soft biological tissues within the context of a thermodynamically consistent phenomenological material approach resulting from an overstress concept. Due to the presence of directed fibrous constituents soft tissues should be considered as anisotropic materials. Therefore, the viscous overstress model has been completed by a transversely isotropic approach. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical analysis of quenching – Heat conduction in metallic materials

Metallic materials present a complex behavior during heat treatment processes. In a certain temperature range, change of temperature induces a phase transformation of metallic structure, which alters physical properties of the material. Indeed, measurements of specific heat and conductivity show strong temperature-dependence during processes such as quenching of steel. Several mathematical models, as solid mixtures and thermal–mechanical coupling, for problems of heat conduction in metallic materials, have been proposed. In this work, we take a simpler approach without thermal–mechanical coupling of deformation, by considering the nonlinear temperature-dependence of thermal parameters as the sole effect due to those complex behaviors. The above discussion of phase transformation of metallic materials serves only as a motivation for the strong temperature-dependence as material properties. In general, thermal properties of materials do depend on the temperature, and the present formulation of heat conduction problem may be served as a mathematical model when the temperature-dependence of material parameters becomes important. For this mathematical model we present the error estimate using the finite element method for the continuous-time case.     

Existence and uniqueness of a classical solution for the coupled heat and mass transfer during the freezing of high‐water content materials

A recent model for the coupled problem of heat and mass transfer during the solidification of high‐water content materials like soils, foods, tissues and phase‐change materials was developed. This model takes into account the role played by material properties and process variables on the advance of freezing and sublimation fronts, temperature and water vapour profiles and weight loss. The goal of this paper is to determine the existence of a unique local classical solution for the corresponding two‐phase coupled free boundary problem in an adequate functional space. Copyright © 2011 John Wiley & Sons, Ltd.     

A homogenization method for heterogeneous materials using a multi-scale technique

For modern microelectronics solders lifetime and stability predictions are important. To perform such an analysis material properties are required. As electronic devices and the corresponding amount of matter used become smaller, the influence of a changing microstructure on mechanical properties must be considered. First some analytical methods were conducted for upper and lower bounds ignoring the exact geometric distribution of the solder phases. Second, analytical equations derived for geometries such as laminate structures were applied to examine the influence of the geometry on homogenized properties. Third, a multi-scale approach for periodic media was presented allowing for a more general analysis of structures. We assume that the solder material is composed of periodic cells, which represent the properties of the whole structure. Composite materials with periodic structures can be investigated by using at least two scales. A global scale is related to the whole piece of material whereas a local scale is related to the periodic cell only. The constitutive equations are stated and a homogenization technique for the elastic properties of arbitrary structures is derived. The resulting equations are solved numerically and results are presented. Again, for layered materials closed-form formulas are derived and compared to the numerical results. The method is also used to obtain effective mechanical properties for materials with linear hardening. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)