Simulation of microstructural evolution in materials with misfitting precipitates

To predict the behavior of directional coarsening and the temporal evolution of the shape of coherent precipitates in two-phase materials, a dislocation-free model is proposed, based on a combination of statistical mechanics and linear elasticity. This model takes elastic anisotropy and isotropic interfacial energy into account. Based on an example of isolated precipitates under plane strain condition, the influence of particle size, inhomogeneity, direction and sign of external loads on the equilibrium shape will be discussed in terms of a generalized thermodynamic force acting on the interface. To simulate the morphological diffusion process of typical microstructures with several random distributed misfitting inclusions, a computational technique in form of a finite element Monte Carlo simulation is presented. Within this numerical technique, no restrictions on the particle shape or the elastic anisotropy of both phases are made.     

A 3-D micromechanical model for predicting the elastic behaviour of woven laminates

This paper presents an analytical model for the prediction of the elastic behaviour of plain-weave fabric composites. The fabric is a hybrid plain-weave with different materials and undulations in the warp and weft directions. The derivation of the effective material properties is based on classical laminate theory (CLT).The theoretical predictions have been compared with experimental results and predictions using alternative models available in the literature. Composite laminates were manufactured using the resin infusion under flexible tooling (RIFT) process and tested under tension and in-plane shear loading to validate the model. A good correlation between theoretical and experimental results for the prediction of in-plane properties was obtained. The limitations of the existing theoretical models based on classical laminate theory (CLT) for predicting the out-of-plane mechanical properties are presented and discussed.     

Finite element simulations of poly-crystalline shape memory alloys based on a micromechanical model

We present a finite element implementation of a micromechanically motivated model for poly-crystalline shape memory alloys, based on energy minimization principles. The implementation allows simulation of anisotropic material behavior as well as the pseudo-elastic and pseudo-plastic material response of whole samples. The evolving phase distribution over the entire specimen is calculated. The finite element model predicts the material properties for a relatively small number of grains. For different points of interest in the specimen the model can be consistently evaluated with a significantly higher number of grains in a post-processing step, which allows to predict the re-orientation of martensite at different loads. The influence of pre-texture on the material’s properties, due to some previous treatment like rolling, is discussed.     

Finite element analysis of viscoelastic composite structures based on a micromechanical material model

The stress and creep analysis of structures made of micro-heterogeneous composite materials is treated as a two-scale problem, defined as a mechanical investigation on different length scales. Reinforced composites show by definition a heterogeneous texture on the microlevel, determined by the constitutive behaviour of the matrix material and the embedded fibres as well as the characteristics of the bonding properties in the interphase. All these heterogeneities are neglected by the finite element analysis of structural elements on the macroscale, since a ficticious and homogeneous continuum with averaged properties is assumed. Therefore, the constitutive equations of the substitute material should well reflect the mechanical behaviour of the existing micro-heterogeneous composite in an average sense.The paper at hand starts with the brief outline of a micromechanical model, named generalized method of cells (GMC), which provides the macrostress responses due to macrostrain processes as well as the homogenised constitutive tensor of the substitute material. The macroscopic stresses and strains are obtained as volume averages of the corresponding microfields within a representative volume element. The effective material tensor constitutes the mapping between the macro-strains and the macro-stresses. The cells method is used for the homogenisation of the unidirectionally reinforced single layers of laminates made of viscoelastic resins and flexibly embedded elastic fibres. The algorithm for the homogenisation of the constitutive properties runs simultaneously to the finite element analysis at each point of numerical integration and provides the macro-stresses and the homogenised constitutive properties. The validity of the proposed two-scale simulation is investigated by solving boundary value problems and comparing the numerical results for the structures to the experimental data of creep and relaxation tests or analytical solutions.     

基于Preisach理论的形状记忆合金温度-位移迟滞仿真研究

摘 要：智能材料如形状记忆合金(Shape Memory Alloy,SMA)已经广泛应用于驱动器和传感器的设计,实现定位和主动控制目的。然而,受迟滞影响,SMA驱动器的工作精度大大降低,限制了其应用。多数智能材料中,选择Preisach理论成为迟滞建模工具,近年来,也涉及到SMA材料系统。本文,讨论运用Preisach模型描述SMA驱动器系统的迟滞行为,尤其针对驱动器系统的模型建立过程,修正经典Preisach模型的几何解释和数值实现方法。最后,引入Gobert给出的Preisach平面的辨识函数执行仿真计算,数值结果表明该模型能够很好地描述SMA驱动器的迟滞行为。     

Thermo-mechanical optimization of porous building materials based on micromechanical concepts: Application to load-carrying insulation materials

In this paper, a multiscale model for the prediction and, finally, optimization of mechanical (elastic) and thermal (heat conductivity) properties of porous building materials is presented. These technical composites are characterized by the increase of porous space in the respective material system, resulting in a reduction of Young’s modulus, on the one hand, and in an increase of the thermal insulation capacity, on the other hand, yielding either a load-carrying insulation material or a structural material with enhanced resistance to heat transfer. Determination of engineering properties within the proposed multiscale approach departs from the underlying material composition, on the one hand, and the intrinsic properties of the constituents, i.e., the material phases, on the other hand, employing homogenization techniques based on continuum micromechanics.     

A model of cutting cellular elastic materials

A plane model for the cutting of cellular elastic material by a rigid triangular non-slender cutter is developed. The cutter propagates quasi-statically with Coulomb friction at the boundaries causing rupture of the cells in front of the vertex and densification of the material along the cutter's faces. Postulating a wedge-shaped form for the compacted material allows formulating a mixed boundary value problem which is solved exactly by means of Cauchy type integrals. Fracture criteria for rupture and densification processes are applied to adjust the formal solution and to find the cutting regime parameters. The wedging phenomenon with a leading crack and the bearing strain process with a built-up edge are predicted for the cases when cutting is impossible. Numerical examples with graphical illustration are presented.     

A micromechanical constitutive model for dynamic damage and fracture of ductile materials

This paper proposes a detailed theoretical analysis of the development of dynamic damage in plate impact experiments for the case of high-purity tantalum. Our micro-mechanical model of damage is based on physical mechanisms (void nucleation and growth). The model is aimed to be general enough to be applied to a variety of ductile materials subjected to high tensile pressure loading. In this respect, the work of Czarnota et al. (J Mech Phys Solids 56:1624–1650, 2008) has been extended by introducing the concept of nucleation law and by entering a nonlinear formulation of the elastic response based on the Mie-Grüneisen equation of state. This later aspect allows us to consider high impact velocities. All model parameters are directly assessed by experimental measurements to the exception of the nucleation law which is characterized by the way of an inverse identification method using three free-surface velocity profiles (at low, intermediate and high impact velocities). It is shown that the nucleation law can be consistently determined in the range of operating pressures. The nucleation law being identified, the development of internal damage happens to be a natural outcome of the modelling. The model is applied to predict damage development and free-surface velocity profiles for various test conditions. The variety and the quality of results support the physical basis (in particular micro-inertia effects) upon which the proposed model of dynamic damage is based.     

Fracture toughness evaluation by tensile and charpy-type tests based on micromechanical models of materials

With the aim of applying micromechanical approaches to fracture mechanics, we carried out dynamic tensile tests and instrumented impact tests with Charpy-type specimens both with a V-shaped notch and with a crack. We compared two micromechanical strain-rate-dependent models based on a modified Gurson flow function by simulating various dynamically loaded specimens. The results of the tests indicate that the critical void volume fractionf _c and the characteristic lengthl _c are practically independent of the strain rate and the geometry of the specimen. The behavior of the specimens subjected to strains and fracture can be characterized by the parameters determined in tensile tests and impact tests with the Charpy-type specimens. By the three-dimensional analysis based on the strain-rate-dependent Gurson model, we predict the onset of crack growth inside the Charpy specimen.Fraunhofer Institut für Werkstoffmechanic, Freiburg, Deutschland. Published in Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No. 2, pp. 77–84, March–April, 1994.     

Simulation of fracture in heterogeneous elastic materials with cohesive zone models

In brittle composite materials, failure mechanisms like debonding of the matrix-fiber interface or fiber breakage can result in crack deflection and hence in the improvement of the damage tolerance. More generally it is known that high values of fracture energy dissipation lead to toughening of the material. Our aim is to investigate the influence of material parameters and geometrical aspects of fibers on the fracture energy as well as the crack growth for given load scenarios. Concerning simulations of crack growth the cohesive element method in combination with the Discontinuous Galerkin method provides a framework to model the fracture considering strength, stiffness and failure energy in an integrated manner. Cohesive parameters are directly determined by DFT supercell calculations. We perform studies with prescribed crack paths as well as free crack path simulations. In both cases computational results reveal that fracture energy depends on both the material parameters but also the geometry of the fibers. In particular it is shown that the dissipated energy can be increased by appropriate choices of cohesive parameters of the interface and geometrical aspects of the fiber. In conclusion, our results can help to guide the manufacturing process of materials with a high fracture toughness.     

A micromechanical elastic property study of trabecular bone in the human mandible

Micromechanical properties of human mandibular trabecular bone, with particular interest to any site differences were investigated. A mandible was harvested from a 66 year-old female cadaver free from bone disease. It was embedded in PMMA, cut into 2mm sections and polished. Micromechanical property measurements were obtained using the UH3 Scanning Acoustic Microscope (SAM) (Olympus Co., Tokyo, Japan) at 400MHz in the burst mode. 6 vertical slices from the right and 6 horizontal slices from the left were chosen. In each of the 12 samples, 3 points were measured; first in the center, the other 2 from the margins. Data were analyzed statistically by SPSS (SPSS, Inc.) using Student’s t-test. The average value of reflection coefficient r is 0.58±0.079 with the range from 0.46 to 0.64; E=25.0±5.64 GPa. There is no significant difference in properties in the osteonal direction of related cortical bone and those found between the marginal area and center areas. The average value of r from the right side, 0.60±0.07, is statistically higher than the average value of from the left side, 0.56±0.07. Micromechanical properties of both mandibular trabecular and cortical bone have almost the same values.     

Direct simulations of the linear elastic displacements field based on a lattice Boltzmann model

In this paper, a lattice Boltzmann model for simulating linear elastic Lame equation is proposed. Differently from the classic lattice Boltzmann models, this lattice Boltzmann model is based on displacement distribution function in lattice Boltzmann equation. By using the technique of the higher‐order moments of equilibrium distribution functions and a series of partial differential equations in different time scales, we obtain the Lame equation with fourth‐order truncation errors. Based on this model, some problems with small deflection are simulated. The comparisons between the numerical results and the analytical solutions are given in detail. The numerical examples show that the lattice Boltzmann model can be used to solve problems of the linear elastic displacement field with small deflection. Copyright © 2015 John Wiley & Sons, Ltd.     

The effect of slightly weakened interfaces on the overall elastic properties of composite materials

The effect of imperfect interfaces on the overall elastic properties of composites is studied in this paper. The imperfect interface is modeled by a linear spring-layer of vanishing thickness. The Mori-Tanaka estimate and its modification are used to evaluate the effective moduli of composites having slightly weakened interfaces. An interface is said to be slightly weakened, if the compliance of the spring-layer is very small. As an example, a composite consisting of aligned ellipsoidal particles is considered in detail. Explicit expressions of the Mori-Tanaka estimates of the effective moduli are derived when the particles are spherical.

Based on classical minimum energy principles, upper and lower bounds of the effective moduli of composites with imperfect interfaces are also derived.