Interfacial model for crash resistant adhesives of ductile-modified epoxy resins

Debonding in adhesive joints is modelled and analyzed with the concept of interfacial mechanics. Material equations are presented for the inelastic behaviour of ductile-modified epoxy resins. A two surface function for the onset of yielding is advantageously expressed in terms of the stress vector on the interface. The theory may be extended to material softening due to damage and to rate dependency. This simple constitutive model is not stable in the sense of Drucker's postulate. Therefore, the non-associated flow rule is modified with a quadratic stress-dependent plastic potential. The material parameters are identified by means of the finite-element simulation of the experimental setup for a bluntly glued double steel tube sample. The numerical performance of this modified model is tested at an adhesively bonded joint in the form of a T-intersection. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparative Studies on the Mechanical Properties of a Thermoset Polymer in Tension and Compression

Results of an experimental investigation into the mechanical properties of a polyester resin in tension and compression are reported. Features of the stress-strain curves obtained are discussed. Data on the elastic modulus, Poisson ratio, and volume strains are obtained. The results of creep behavior of the material in tension and compression are also presented. It is found that the time-dependent creep obeys a power law, but the nonlinear stress dependence can be described by using the hyperbolic sine function. The effect of load type (tension or compression) on the nonlinearity of the creep is analyzed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 633–650, September–October, 2005.     

基于非关联流动法则的圆形隧洞滑移线解答

圆形隧洞的滑移线方程早在20世纪中期苏联学者已给出解答,并在国内广泛应用．推导过程中假设滑移线与速度矢量方向夹角为45°-φ/2是错误的,理论上滑移线与速度矢量方向的夹角与采用的流动法则有关．该文分别从关联流动法则和非关联流动法则出发,推导了圆形隧洞的滑移线方程和水平方向破裂体深度的表达式．通过与模型试验结果进行对比,对岩土材料应采用基于非关联流动法则的滑移线解答.     

Interaction of phase-transformations and plasticity – a multi-phase micro-sphere approach

We present an efficient model for the simulation of solid to solid phase-transformations in polycrystalline materials. As a basis, we implement a scalar-valued Gibbs-energy-barrier-based phase-transformation model making use of statistical physics. In this work, we particularly adopt the model for the simulation of phase-transformations between an austenitic parent phase and a martensitic tension and compression phase. The incorporation of plasticity phenomena is established by enhancing the Helmholtz free energy functions of the material phases considered, where the plastic driving forces acting in each phase are derived from the overall free energy potential. The coupled model is embedded into a micro-sphere formulation in order to simulate three-dimensional boundary value problems—a technique well-established in the context of computational inelasticity at small strains. It is shown that the model is capable of reflecting experimentally observed behaviour. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exact analytic solutions to the problem on plane buckling modes of rectangular orthotropic plates with free edges under biaxial loading

A two-dimensional linearized problem on plane buckling modes (BMs) of a rectangular plate with free edges, made of an elastic orthotropic material, underbiaxial tension-compression is considered. With the use of double trigonometric basis functions, displacement functions exactly satisfying all static boundary condition on plate edges are constructed. It is shown that the exact analytic solutions found describe only the pure shear BMs, and if the normal stress in one direction is assumed equal to zero, an analog of the solution given by the kinematic Timoshenko model can be obtained. Upon performing the limit passage to the zero harmonic in the displacement functions of one of the directions, the solution to the problem of biaxial compression can be obtained by equating the Poisson ratio to zero; in the case of uniaxial compression, this solution exactly agrees with that following from the classical Bernoulli-Euler model. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 149–170, March–April, 2007.     

Description of plastic deformation of structural materials in triaxial loading

A model of nonassociated plasticity is put forward for initially isotropic materials deforming with residual changes in volume under the action of triaxial normal stresses. The model is based on novel plastic loading and plastic potential functions, which define closed, convex, every where smooth surfaces in the 6D space of symmetric second-rank stress tensors. By way of example, the plastic deformation of a cylindrical concrete specimen wrapped with a CFRP tape and loaded in axial compression is described. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 183–194, March–April, 2008.     

Modelling the mechanical behaviour of adhesively bonded and sintered hollow-sphere structures

The mechanical properties of periodic hollow-sphere structures are investigated numerically. Young’s modulus and the Poisson ratio are determined in order to describe their linearly elastic behaviour. The initial compressive yield strength is also calculated. The spheres are located at the nodes of a cubic primitive lattice. The cohesion is achieved by an adhesive concentrated in the minimum gap between neighbouring spheres. The geometry of the structure is discretized based on regular hexahedral elements. This approach is much more time-consuming, but it is important in order to achieve a more accurate simulation of the nonlinear behaviour (e.g., plasticity) of such materials. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 803–816, November–December, 2006.     

Effect of viscosity of a thermoplastic prepreg and matrix upon winding of rings

The problem of compression of a unidirectional layer and shear of a polymer interlayer during winding of rings is considered. The equations determining the dependence of the layer thickness and stresses on the parameters entering into the power flow law for a prepreg and polymer matrix and on the basic parameters of the winding process—the initial tension of the prepreg, its placement rate, and the radius of a mandrel—are derived. The ring thickness measurements obtained at various temperatures and initial tension forces of plies confirm the adequacy of the model offered. It is found that the viscous properties of the prepreg and matrix upon winding affect the relative change in the layer thickness to a greater extent than the stresses in these layers. With increase in temperature and tension force upon winding, the effect of viscous deformations of the prepreg and matrix increases. A decrease in viscosity and an increase in the tension force of the tape lead to a higher strength of the ring in tension and interlaminar shear; however, the growing percolation of the polymer melt leads to a greater inhomogeneity of the structure of the composite in the ring and to a lower reinforcing effect of the factors mentioned. Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 419–428, 2000.     

An analysis of contact deformation of auxetic composites

The adaptive mode of frictional interaction has been studied as a self-locking effect upon contact deformation of isotropic and anisotropic auxetic materials with a negative Poisson ratio. This effect manifests itself in the fact that the bearing capacity of the joint rises with increasing shear load. In particular, the parameters of stress state (contact load, tangential stresses, slippage, etc.) were determined for a double-lap joint under conditions of compression with or with out shear. The contact interaction was analyzed by the finite-element method for three profiles of symmetrically located contact elements (plane, cylindrical, and wedge-shaped). The Poisson ratio was varied within the range theoretically admissible for isotropic elastic media. Analogous calculations were also performed for a joint with a deformed element made of an anisotropic auxetic composite, whose reinforcement angle was varied. The maximum loads, tangential stresses, and slippage are obtained as nonlinear functions of Poisson ratio (in the isotropic case) and reinforcement angle of the composite material. The stress concentration and the increased ultimate shear forces are also estimated. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 681–692, September–October, 2006.     

Granular materials: Parameter identification and modelling of localisation problems

The prediction of landsliding requires an exact knowledge of the mechanical behaviour of granular materials. This kind of materials, e. g., sand, have a very complex deformation behaviour, which depend on the stress state and on the loading history. In this work, the deformation behaviour of the solid skeleton is characterised via homogeneous triaxial tests on dry sand specimens. Additionally, an appropriate elasto-plastic material law to describe the solid skeleton in the frame of Theory of Porous Media (TPM) is used, which is implemented in the FE tool PANDAS. Furthermore, a single-surface yield criterion with isotropic hardening, which limits the elastic domain, and a non-associated plastic flow are employed. The determination of the material parameters of the linear elasticity law as well as the single-surface yield criterion are based on test data of triaxial experiments. The material parameters are identified using a derivative-based optimisation method (donlp2), which is coupled with PANDAS. Finally, a simulation of a benchmark test is presented to show shear band localisation effects, where the material behaviour is described by a triphasic porous media model based on the TPM, where the constituents are a deformable solid skeleton and two pore fluids, water and air. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

混凝土材料的粘塑性损伤本构模型

基于不可逆热力学,引入运动硬化、等向硬化和损伤内变量,构造了相应的自由能函数和流动势函数,推导出了混凝土材料的粘塑性损伤本构模型．数值模拟的结果表明,该模型能够避开屈服面和破坏准则的基本假设来描述混凝土材料的以下特性:压缩载荷作用下的体积膨胀现象;应变率敏感性;峰值后由损伤和破坏引起的应力软化和刚度退化现象A·D2由于此模型避开了根据各种变形阶段选择与其相应的本构模型的繁琐计算,因此更便于纳入复杂工况下应力分析有限元程序中．     

Modeling the nonlinear deformation of composite laminates based on plasticity theory

The plasticity theory has been successfully used for describing the nonlinear deformation of laminated composite materials under a monotonically increasing loading. Generally, several tests are needed to determine the parameters of the plastic potential for a laminate. We explore an alternative approach and obtain the plastic potential by using theoretical considerations based on a laminate analysis. The model is shown to provide an accurate prediction for the response of a cross-ply glass/epoxy laminate under uniaxial tensile loading at different angles to the material orthotropy axes. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 3, pp. 309–318, May–June, 2007.     

On Hill's Bipotential

A new formulation of the constitutive law of materials based on the concept of bipotential was introduced by de Saxcé. This concept is able to describe non-associated laws and to suggest robust numerical algorithms. Materials that admit a bipotential to model their behaviour constitute the class of Implicit Standard Materials (ISM). This class contains, as a sub-class, the Generalized Standard Materials (GSM). In this paper, we present a bipotential expressing the coaxiality of two tensors with preservation of the order of the eigenvalues. We call it Hill's bipotential. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parameteridentification of Hostun-Sand and Shear-Band Simulation of Landsliding

The simulation of deformation process of landsliding needs the knowledge of the very complex behaviour of granular materials, e. g., sand. The triax experiments on sand show a highly non-linear elasto-plastic material behaviour. Therefore, it is necessary to use a yield criteria, e. g., single-surface yield criteria with isotropic hardening and non-associated plastic potential, which satisfies adequately the requirements of the material properties. This kind of material behaviour can be described by an elasto-plastic material law in the frame of Theory of Porous Media, which is implemented in the FE tool PANDAS. By means of the data of Hostun-Sand, the material parameters of the singlesurface yield criteria are determined by use of a optimization algorithm, namely Sequential Quadratic Programming (SQP) a gradient based optimization method, which is coupled with PANDAS. Using this optimized material parameters, a simulation of a initial boundary-value problem of landsliding is presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A multi-item production planning model with setup times: algorithms, reformulations, and polyhedral characterizations for a special case

 We study a special case of a structured mixed integer programming model that arises in production planning. For the most general case of the model, called PI, we have earlier identified families of facet–defining valid inequalities: (l, S) inequalities (introduced for the uncapacitated lot–sizing problem by Barany, Van Roy, and Wolsey), cover inequalities, and reverse cover inequalities. PI is 𝒩𝒫–hard; in this paper we focus on a special case, called PIC. We describe a polynomial algorithm for PIC, and we use this algorithm to derive an extended formulation of polynomial size for PIC. Projecting from this extended formulation onto the original space of variables, we show that (l, S) inequalities, cover inequalities, and reverse cover inequalities suffice to solve the special case PIC by linear programming. We also describe fast combinatorial separation algorithms for cover and reverse cover inequalities for PIC. Finally, we discuss the relationship between our results for PIC and a model studied previously by Goemans. Received: December 13, 2000 / Accepted: December 13, 2001 Published online: October 9, 2002 RID="★" ID="★" Some of the results in this paper have appeared in condensed form in Miller et al. (2001). Key words. mixed integer programming – polyhedral combinatorics – production planning – capacitated lot–sizing – fixed charge network flow – setup times This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister's Office, Science Policy Programming. The scientific responsibility is assumed by the authors. This research was also supported by NSF Grant No. DMI-9700285 and by Philips Electronics North America.     

Pseudoelasticity of Shape Memory Alloys - a 1D Material Model and Finite Element Implementation

This contribution is concerned with the formulation of a 1D-constitutive model accounting for the pseudoelastic behavior of shape memory alloys. The stress-strain-relationship is idealized by a hysteresis both in the compression as in the tension loading range. It is characterized by an upper loading path, which is to be ascribed to the transformation of the lattice to a martensitic structure. Unloading the material, a lower path is described, because of the reverse transformation into austenitic lattice. The constitutive model is based on a switching criterion which serves as a potential function for the evolution of the internal state variables. The model distinguishes between local and global variables to describe the hysteresis effects for the compression and tension range. A strain driven algorithm which captures the complete nonlinear material behavior is presented. The boundary value problem is solved for a truss element applying the finite element method. A consistent linearization of the nonlinear equations is derived. Simple examples will demonstrate the applicability of the proposed model. For future developments the usage of shape memory alloys within civil engineering structures is aimed. The advantage of the material is the very good damping behavior and the potential to overcome great strains. Both properties are distinguished to be of engineering interest. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the coupling property and the Liouville theorem for Ornstein–Uhlenbeck processes

Using a coupling for the weighted sum of independent random variables and the explicit expression of the transition semigroup of Ornstein–Uhlenbeck processes driven by compound Poisson processes, we establish the existence of a successful coupling and the Liouville theorem for general Ornstein–Uhlenbeck processes. Then we present the explicit coupling property of Ornstein–Uhlenbeck processes directly from the behaviour of the corresponding symbol or characteristic exponent. This approach allows us to derive gradient estimates for Ornstein–Uhlenbeck processes via the symbol.     

Asymmetric effects of polymers in finite thermoviscoplasticity

Glassy polymers such as polycarbonate exhibit different behaviours in different loading scenarios, such as tension and compression. For the simulation of these asymmetric effects we present a framework for thermoviscoplastic modelling of polymers at large strains. To this end a flow rule is postulated within a thermodynamic consistent framework in a mixed variant formulation which is decomposed into a sum of weighted stress mode related quantities. The different stress modes are chosen such that they are accessible to individual examination in the laboratory, where tension and compression are typical examples. The characterisation of the stress modes is obtained in the octahedral plane of the deviatoric stress space in terms of the Lode angle, such that stress mode dependent scalar weighting functions can be constructed. Furthermore the numerical implementation of the resulting set of constitutive equations is used in the finite element program ABAQUS to simulate the laser transmission welding process. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A continuous model for investigation of physically nonlinear deformation of orthotropic sandwich plates

A phenomenological yield condition for quasi-brittle and plastic orthotropic materials with initial stresses is suggested. All components of the yield tensor are determined from experiments on uniaxial loading. The reliability estimates of the criterion suggested is discussed. For a plastic material without initial stresses, the given condition transforms into the Marin—Hu criterion. The defining equations of the deformation theory of plasticity with isotropic and “anisotropic” hardening, associated with the yield condition suggested, are obtained. These equations are used as the basis for a highly accurate nonclassical continuous model for nonlinear deformation of thick sandwich plates. The approximations with respect to the transverse coordinate take into account the flexural and nonflexural deformations in transverse shear and compression. The high-order approximations allow us to model the occurrence of layer delamination cracks by introducing thin nonrigid interlayers without violating the continuity concept of the theory. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. pp. 329–340, May–June, 2000.