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)     

A constitutive model for shape memory alloy fibres and its applicability to prestressed composites

This contribution is concerned with a constitutive model for shape memory fibres. The 1D-constitutive model accounts for the pseudoplastic and shape memory effect (SME). The macroscopic answer of the material is determined by the evolution from a twinned martensitic lattice into a deformed and detwinned one. On the macroscopic scale these effects are responsible for the upper boundary of the hysteresis which is situated around the origin of the stress-strain-diagram. During the phase transition process inelastic strains arise. When the lattice is fully detwinned, a linear elastic branch at the end of the hysteresis is observed. The initial state of the material is recovered by unloading and heating the material subsequently. The constitutive model is derived from the Helmholtz' free energy and fulfils the 2nd law of thermodynamics. For the present model five internal state variables are employed. Two of them are used to describe the inelastic strain and a backstress. The others represent the martensitic volume fraction and are necessary to describe the SME. The latter variables are depending on the deformation state as well as on temperature. A change on temperature goes along with a reduction of the inelastic strain. The model is incorporated in a fibre matrix discretization to prestress the surrounding structure. The boundary value problem is solved for a truss element applying the finite element method. Examples will demonstrate the applicability in engineering structures. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mixed Tetrahedral Elements for the Analysis of Structures with Material and Geometric Nonlinearities

A new mixed tetrahedral element, particularly suited for the analysis of structures exhibiting nonlinear material and geometric behavior, is here presented. Its derivation is based on a Hu–Washizu type formulation, including also rotation and skew-symmetric stress fields as independent variables, instrumental to equip the element with nodal rotational degrees of freedom. A Gauss-point-discontinuous interpolation is selected for the total strain field, in order to account for its possibly highly nonlinear spatial distribution due to inelastic strains. Accordingly, the resulting tetrahedron can properly describe inelastic effects occurring over a space scale smaller than the element size. An original and efficient iterative procedure is proposed to perform the element state determination. Geometric nonlinearities are treated by means of the corotational approach. A numerical simulation is presented to analyze the element performances. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Eulerian Rate Model for Pseudoelastic NiTi Shape Memory Alloys

A phenomenological material model for the pseudoelastic material behavior of polycrystalline NiTi is presented. It is consistently derived within the Eulerian framework using the Kirchhoff stress (weighted Cauchy stress) and the stretching tensor. Deformation–like variables such as elastic or inelastic strains are omitted. The model is based on a non–convex Helmholtz free energy function for the phases austenite and martensite, which is formulated in terms of the Kirchhoff stress, temperature, mass fraction of martensite, and a tensorial internal variable accounting for the average orientation of the martensite variants. Evolution equations for the mass fraction of martensite as well as for the average orientation of the martensite variants are derived, taking into account the restrictions imposed by thermodynamics. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of elastoplastic effects of cables under large spatial deformation

Cables are complex components consisting of a multi-layer structure and various materials. The structural setup includes for example conducting wires, isolating shields and protecting sheaths. This leads to several inelastic effects under large deformations like pull-out of wires, delamination of layers or friction between the constituents. The materials used in cables belong to different material classes and consequently show different behavior under load. Elastoplastic behavior has to be expected for metallic wires, whereas polymer layers behave viscoelastically. The combination of these inelastic effects caused by the structure and constituents of cables motivates the inclusion of inelasticity in the material model on a phenomenological level. Since cables are flexible, slender structures, they can be described physically correctly by the theory of Cosserat rods. In this context, the constitutive equations are formulated in terms of the sectional quantities. The related model parameters have to be determined in suitable experiments. As cables undergo large multiaxial deformations in applications, uniaxial experiments are not sufficient for their characterization. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A novel model to describe the intervertebral disc mechanical response

The main objective of the present work is the development of a simplified, efficient and easy-to-implement single-phase material model, which is able to describe the essential effects characterising the behaviour of multi-phase saturated materials, such as of intervertebral discs (IVDs). The presented new model mainly focuses on extending a viscoelastic material model in order to not only take the mechanical behaviour of the solid part into account, but also the fluid-flow-dependent behaviour of the material. By applying this model, the complexity and constitutive parameters are reduced, the implementation is more convenient and the experimental investigations can be better supported in comparison to multi-phase material models of IVDs. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A finite elasto-plasticity model for thick adhesive layers based on generalized stress-strain measure

The collective term adhesives includes a wide field of materials with a diversity of different material properties. Regarding high-strength adhesives, the assumption of small strains often holds according to their brittle behavior. The experience with plasticity models based on the additive decomposition into elastic and inelastic strains indicates an appropriate approach to characterize such materials. In some cases, due to a more ductile material response, the assumption of infinitesimal strains is not valid anymore. In particular this is the case for high-strength adhesives with additives like rubber. But ductile behavior is also observed for specific stress states in one adhesive, e.g. when the behavior for tensile is quite brittle while large shear-strains could appear. The objective of this work is to overcome the theoretical restriction of small strains and to archive the practical experiences. For the failure criterion two stress invariants are used, which involves the hydrostatic pressure as well as the deviator stress state. The flowrule is introduced for the evolution of the inelastic variables. Herein the flow rule has to be of non-associated type to ensure the thermodynamical consistency of the model. The plasticity model also includes hardening as well as softening. The presented finite strain model makes use of the fact that the eigenvalues for Green-Lagrange strains and generalized strains are the same. Thus the limit of applicability is extended to finite strains. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Configurational-Force-Driven Crack Propagation and Adaptive Mesh Refinement in Finite Inelasticity

We introduce a consistent variational framework for inelasticity at finite strains, yielding dual balances in physical and material space as the Euler equations. The formulation is employed for the simultaneous usage of configurational forces as both driving forces for crack propagation as well as h-adaptive mesh refinement. The theoretical basis builds upon a global balance of internal and external power, where the mechanical response is exclusively governed by two scalar functions, the free energy function and a dissipation potential. The resulting variational structure is exploited in the context of fracture mechanics and yields evolution equations for internal variables. In the discrete setting, we present a geometry model fully separated from the finite element mesh structure that represents structural changes of the material configuration due to crack propagation. Advanced meshing algorithms provide an optimal discretization at the crack tip. Local and global criteria are obtained via error estimators based on configurational forces being interpreted as indicators of an energetic misfit due to an insufficient discretization. The numerical handling is decomposed into a staggered algorithm scheme for the dual set of equilibrium equations in material and physical space and efficient mesh generation tools. Exemplary numerical examples are considered to illustrate the method and to underline the effects of inelastic material behaviour in the presented context. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical investigation of the deformation characteristics and heat generation in pneumatic aircraft tires : Part I. Mechanical modeling

A numerical methodology to study the temperature rise in aircraft tires under free rolling conditions is presented in this article. In the first part, we study the deformation characteristics of the tire to determine the heat generation due to the inelastic deformation (viscoelasticity), which is assumed to be the main source of heat generation under free rolling conditions. The heat generation is then used as an input to solve the heat transfer problem which is addressed in the second part of this article. A methodology which considers a 2-D formulation with the contribution of out-of-plane forces is presented. This methodology allows for a significant reduction of the computational requirements of 3-D analysis while capturing the main 3-D effects. The deformation pattern as well as the stress and strain fields are presented for a cross-section of the tire at several locations.     

Exploitation of Configurational Forces in Extended Nonlocal Continua with Microstructure

We investigate aspects of the application of configurational forces in extended nonlocal continua with microstructure. Focussing on multifield approaches to gradient–type inelastic solids, the coupled problem is governed by the macroscopic deformation field, while nonlocal inelastic effects on the microstructure are described by a family of order parameter fields. The dual macro– and micro–field equations are derived within an incremental variational framework. Using an incremental principle, due to the variation with respect to the material position, an additional balance in the material space appears with the dual macro–micro–balances in the physical space. In view of the numerical implementation of this coupled problem by a finite element method, the incremental variational framework is recast into a discrete format in terms of discrete macro– and micro–physical nodal forces and configurational nodal forces. Applying a staggered solution scheme, the configurational branch is used as a postprocessing procedure with all the ingredients known from the solution of the coupled macro–micro–problem. The procedure is implemented for a nonlocal, viscous damage model. The consequences with regard to the configurational nodal forces are assessed by means of a numerical example. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Biphasic Approach for the Simulation of Growth Processes in Soft Biological Tissues Incorporating Damage-Induced Stress Softening

In this contribution a coupled material framework is presented, which considers the effects of damage and growth in soft biological tissues. The tissue is described as a porous medium by taking into account a solid and a fluid phase. The fluid phase is assumed to carry nutrients supplying growth of the solid phase. The latter one is described as a fiber-reinforced material, where a damage variable is introduced for the fiber part of the associated free energy function. The performance of the proposed model is demonstrated in a finite element analysis of a simplified human heart model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

一类指定应力问题的变分原理与应用

针对有限元分析中对应力或内力有指定条件的问题,引入非弹性应变作为实现指定应力条件的附加未知量,在小变形条件下描述了指定应力条件应当满足的弹性力学控制方程;以位移和未知非弹性应变作为独立变量,建立了具有指定应力条件问题的势能变分原理和虚功方程;以位移、弹性应变、未知非弹性应变和应力为独立变量,建立了一个含四类变量的广义变...     

Modeling and Simulation of Damage Processes based on a Gradient-Enhanced Free Energy Function

Taking into account softening effects in connection with conventional inelastic material models can cause ill-posed boundary value problems. These problems can be established by obtaining no unique solution for the resulting algebraic system or by having a strong mesh dependence of the numerical results. This is the consequence of losing ellipticity of the governing field equations. A possible approach to solve these problems is to introduce a non-local field function in the model which includes an internal material length scale. For this purpose a gradient-enhanced free energy function is used for the current continuum damage model from which two variational equations are resulting. Calculations with less effort can be achieved due to the enhancement of the free energy function in comparison to other approaches. The mentioned model is applied to a material with locally varying damage properties (yield limits). Furthermore, the model is able to describe crack propagation in cases of completely damaged material. Therewith, a matrix material including precipitates, such as carbides, is modeled. This allows to investigate ship screws, which usually exhibit the mentioned composition, with regard to the influence of cavitation. Cavitation describes the implosion of risen vapor bubbles, whereby the impact on screws causes heavy damages which can lead to a complete destruction. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fracture Mechanical Investigation of Elastomeric Material

The increasing use of elastomeric components in advanced engineering applications requires a thorough understanding of the complex material properties and a reliable assessment of the quality and durability of the products. This contribution concentrates on the computational determination of fracture mechanical parameters for rubber material using the material force method. For dissipative, inelastic material, a distinction between two fracture mechanical parameters is presented. The time-dependent behaviour of these fracture mechanical parameters is illustrated by an application to the dwell-effect. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multi-scale modeling of double network hydrogels

A double network hydrogel (DN gel) is a class of elastomeric gels formed by polyelectrolyte and neutral polymer networks. The DN gel is the toughest material among the conventional hydrogels. It shows inelastic features such as necking instability [1] and the stress softening [2], similar to that one known in elastomers. In this contribution, we purpose a micro-mechanically motivated model to characterize relation between internal damage and inelastic deformations in the DN gel. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical modeling of flows through inelastic porous solids

We propose a framework, based on classical mixture theory, to describe the isothermal flow of an incompressible fluid through a deformable inelastic porous solid. The modeling of the behavior of the inelastic solid takes into account changes in the elastic response due to evolution in the microstructure of the material. We apply the model to a compression layer problem. The mathematical problem generated by the model is a free boundary problem.     

Thermo-visco-elasticity for Norton–Hoff-type models

Our research is directed to a quasi-static evolution of the thermo-visco-elastic model. We assume that the material is subject to two kinds of mechanical deformations: elastic and inelastic. Moreover, our analysis captures the influence of the temperature on the visco-elastic properties of the body. The novelty of the paper is the consideration of the thermodynamically consistent model to describe this kind of phenomena related with a hardening rule of Norton–Hoff type. We provide the proof of existence of solutions to thermo-visco-elastic model in a simplified setting, namely the thermal expansion effects are neglected. Consequently, the coupling between the temperature and the displacement occurs only in the constitutive function for the evolution of the visco-elastic strain.