Stability of Plates Made of a Granular Composite with Damageable Components

The stability problem is solved for a plate made of a granular composite material with microdamageable components. Microdamages are simulated by randomly dispersed pores filled with a damaged material. The problem is formulated using the concept of continuous load     

Dispersed Damages in Stability Problems for Doubly Curved Shells of Revolution

An approach is expounded to the study of the bifurcation stability of doubly curved shells of revolution. The microdamage of an isotropic material is considered as empty spherical pores randomly dispersed over the volume, their concentration increasing with load. A damaged inhomogeneous material is modeled by a continuous physically nonlinear medium whose nonlinear deformation depends on how the material fails and the microstrength is distributed. A bifurcation stability problem is formulated based on the concept of continuous loading within the framework of the Kirchhoff–Love hypotheses. As an example, a solution is given to the stability problem on shells of positive Gaussian curvature under external uniform pressure     

Exact Results for the Homogenization of Elastic Fiber-Reinforced Solids at Finite Strain

This work is concerned with the homogenization of solids reinforced by aligned parallel continuous fibers or weakened by aligned parallel cylindrical pores and undergoing large deformations. By alternatively exploiting the nominal and material formulations of the corresponding homogenization problem and by applying the implicit function theorem, it is shown that locally homogeneous deformations can be produced in such inhomogeneous materials and form a differentiable manifold. For every macroscopic strain associated to a locally homogeneous deformation field, the effective nominal or material stress–strain relation is exactly determined and connections are also exactly established between the effective nominal and material elastic tangent moduli. These results are microstructure-independent in the sense that they hold irrespectively of the transverse geometry and distribution of the fibers or pores. A porous medium consisting of a compressible Mooney–Rivlin material with cylindrical pores is studied in detail to illustrate the general results. This work was the first time presented at the Euromech Colloqium 464 on “Fiber-reinforced Solids: Constitutive Laws and Instabilities”, September 28–October 1, 2004, Cantabria, Spain.     

考虑孔洞影响的铸造镁合金ZM6疲劳寿命预估方法

铸造镁合金ZM6是一种应用于直升机减速器机匣制造的典型材料。然而,在铸造过程中产生的内部缺陷对材料的疲劳性能有显著影响。本文研究了含内部孔洞缺陷ZM6材料的疲劳损伤模型和寿命预估方法。首先,采用X射线断层扫描技术,对三个批次毛坯料制成的试验件进行扫描观察,获得了试验件内部孔洞的分布特征。进而,对48件试验件进行了两种应力比下多级应力水平的疲劳试验,获得了各批次试验件寿命结果,并通过观察与分析,得出了孔隙率和近表面较大孔洞为影响试验件疲劳寿命的两个关键因素。然后,基于损伤力学理论提出了通过材料初始弹性模量和等效孔洞局部应力应变场来分别反映孔隙率和近表面较大孔洞影响的疲劳损伤模型和寿命计算方法,并结合ABAQUS软件平台实现了含孔洞试验件的疲劳损伤计算和寿命计算。最后,采用所提理论模型和计算方法给出了试验件的疲劳寿命预测结果,并与试验结果进行了不同维度的对比,验证了所提模型与方法的有效性和适用性。     

Development and experimental validation of a continuum micromechanics model for the elasticity of wood

This contribution covers the development and validation of a microelastic model for wood, based on a four-step homogenization scheme. At a length scale of several tens of nanometers, hemicellulose, lignin, and water are intimately mixed, and build up a polymer (polycrystal-type) network. At a length scale of around one micron, fiberlike aggregates of crystalline and amorphous cellulose are embedded in an contiguous polymer matrix, constituting the so-called cell wall material. At a length scale of about one hundred microns, the material softwood is defined, comprising cylindrical pores (lumen) in the cell wall material of the preceding homogenization step. Finally, at a length scale of several millimeters, hardwood comprises larger cylindrical pores (vessels) embedded in the softwood-type material homogenized before. Model validation rests on statistically and physically independent experiments: The macroscopic stiffness values (of hardwood or softwood) predicted by the micromechanical model on the basis of tissue-independent (‘universal’) phase stiffness properties of hemicellulose, amorphous cellulose, crystalline cellulose, lignin, and water (experimental set I) for tissue-specific composition data (experimental set IIb) are compared to corresponding experimentally determined tissue-specific stiffness values (experimental set IIa).     

The Micromechanics of Short-Term Damageability of Fibrolaminar Composites

A theory of microdamageability is constructed for fibrous laminated composites consisting of transversally isotropic fibers and a microdamaged isotropic porous binder. Microdamages in the binder are simulated by pores filled with compression-resisting particles of the destroyed material. Damage in a microvolume of the binder is described by the Schleicher–Nadai strength criterion, which allows for the difference between the ultimate tensile and compressive loads. The ultimate strength is a random function of coordinates with the Weibull distribution. The stress–strain state and effective characteristics of the material are determined by solving the stochastic equations of elastic theory for a fibrous laminated composite with a porous binder. The equations of deformation and microdamageability are closed by the equations of porosity balance in the binder. Nonlinear diagrams of the concurrent processes of deformation of the fibrous laminated material and microdamage of the matrix for various physical and geometrical parameters are constructed     

Theory of Short-Term Microdamageability of Granular Composite Materials

The theory of microdamageability of granular composites is outlined through the simulation of microdamages in the components by pores filled with compression-resisting particles of a destroyed material. The damage criterion for a microvolume of a component is taken in the Schleicher–Nadai form, which allows for the difference between the ultimate tensile and compressive loads. The ultimate strength is a random function of Weibull-distributed coordinates. The stress–strain state and the efficient properties of the material are determined from the stochastic equations of elastic theory for a granular composite with porous components. The equations of deformation and microdamage are closed by the equations of porosity balance in the components. Nonlinear diagrams of the concurrent processes of deformation in the granular material and microdamage in the matrix are plotted. The effect of the physical and geometrical parameters on them is studied     

Revisiting poromechanics in the context of microporous materials

Poromechanics offers a consistent theoretical framework for describing the mechanical response of porous solids, fully or partially saturated with a fluid phase. When dealing with fully saturated microporous materials, which exhibit pores of the nanometre size, aside from the fluid pressure acting on the pore walls additional effects due to adsorption and confinement of the fluid molecules in the smallest pores must be accounted for. From the mechanical point of view, these phenomena result into volumetric deformations of the porous solid: the so-called “swelling” phenomenon. The present work investigates how the poromechanical theory should be refined in order to describe adsorption and confinement induced swelling in microporous solids. Firstly, we report molecular simulation results that show that the pressure and density of the fluid in the smallest pores are responsible for the volumetric deformation of the material. Secondly, poromechanics is revisited in the context of a microporous material with a continuous pore size distribution. Accounting for the thermodynamic equilibrium of the fluid phase in the overall pore space, the new formulation introduces an apparent porosity and an interaction free energy. We use a prototype constitutive relation relating these two quantities to the Gibbs adsorption isotherm, and then calculate the induced deformation of the solid matrix. Agreement with experimental data found in the literature is observed. As an illustrating example, we show the predicted strains in the case of adsorption of methane on activated carbon.     

Simulation of the Short-Term Microdamageability of Laminated Composites

The theory of microdamageability of multicomponent laminated composites is outlined through the simulation of microdamages in the components by pores filled with compression-resisting particles of the destroyed material. The damage criterion for a microvolume of a component is taken in the Schleicher–Nadai form, which allows for the difference between the ultimate tensile and compressive loads. The ultimate strength is a random function of Weibull-distributed coordinates. The stress–strain state and the efficient properties of the material are determined from the stochastic equations of the elastic theory for a laminated composite with porous components. The equations of deformation and microdamage are closed by the equations of porosity balance in the components. Nonlinear diagrams of the concurrent processes of deformation in the laminated material and microdamage in the matrix are plotted. The effect of the physical and geometrical parameters on them is studied     

A Note on the Theory of Short-Term Microdamageability of Granular Composites under Thermal Actions

The theory of microdamageability of granular composites is stated with allowance made for the thermal effect. Microdamages in the components are modeled by pores, hollow or filled with particles of the destroyed material that resist compression. The fracture criterion is assumed to have the Schleicher–Nadai form, which takes into account the difference between the tensile and compressive ultimate loads, with the ultimate strength being a random function with a power or Weibull distribution. The stress–strain state and effective properties of the material are determined from the stochastic thermoelastic equations for granular composites with porous components. The equations of deformation and microdamage are closed by the equation of porosity balance corrected for the thermal effect. Nonlinear diagrams are plotted for the concurrent processes of deformation of a granular material and microdamage of the matrix as functions of macrostrains and temperature. The influence of the physical and geometrical parameters on the processes is analyzed.