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)     

Construction of the Equivalent Plastic Strain Increment

Strain hardening plastic deformation of a material possessing a yield locus (f(σ_ij)) which may be written as a homogeneous function of the stress components (σ_ij), and which obeys the classical associated flow rule for metals (e.g. Bishop and Hill, 1951) is considered. The material may be anisotropic and may display plastic dilatation. A method is given for constructing the equivalent plastic strain increment in such a way that the increment of plastic work is always equal to the product of the equivalent plastic strain increment and the equivalent yield stress. Construction of the equivalent plastic strain at a corner in the yield locus is given. The method given here is implied in classical treatments of hardening (e.g. Hill, 1950) but seems not to have been given explicitly heretofore.     

应变空间中的岩土屈服准则与本构关系

本文从Илъюшин公设出发评述了在应变空间中研究岩土弹塑性问题的必要性和特点.建立了应力不变量与弹性应变不变量之间的关系式,实现了应力屈服面到应变屈服面的转换,导出和讨论了十二个以应力表达的屈服准则的应变表达式.应用正交法则导出了十二个与上述应变屈服准则相联系的理想塑性材料的本构关系.本文工作的结果可供实际应用,并有助于应变空间塑性理论的进一步研究.     

On Plane Dilatational Plasticity

The plane plastic deformation of a generally anisotropic rigid-plastic material which possesses a yield condition dependent upon mean triaxial stress and which, through the classical associated flow rule, exhibits plastic dilatation, is considered. This model is used to represent the behavior of micro-porous ductile metals in which the micro-cavities may be strongly aligned due to large prior plastic strains, as for example the material surrounding the tip of an extending notch in a ductile metal. It is shown that the stress and velocity fields are hyperbolic where a line of vanishing extension rate may be found in the plane of deformation, and that the characteristics of both the stress and velocity fields coincide with the lines of vanishing extension rate. Coincidence of the characteristics of stress and velocity fields in general anisotropic plastic bodies seems not to have been expected in earlier writings, but is a natural consequence of the associated flow rule. Simple means of determining whether a given stress state at yield lies in a hyperbolic or elliptic field are discussed. The role of characteristics in providing ductile fracture nuclei is discussed.     

Anisotropic multiplicative elastoplasticity for the prediction of earings in sheet forming

In this work, the simulation of earings in cup drawing by means of a recently developed anisotropic combined hardening material model is discussed. The model represents a multiplicative formulation of anisotropic elastoplasticity in the finite strain regime with nonlinear kinematic and isotropic hardening. Plastic anisotropy is described by the use of second-order structure tensors as additional arguments in the representation of the yield function and the plastic flow rule. The evolution equations are integrated by a form of the exponential map that preserves the plastic volume and the symmetry of the internal variables. Finite element simulations of cylindrical cup drawing processes are performed by means of ABAQUS/Standard where the discussed material model has been implemented into a user-defined reduced integration solid-shell element. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

极限应变法在圆形隧洞稳定分析中的应用

材料的屈服和破坏是不同的,屈服准则已有大量研究,但缺少严格的破坏准则.理想弹塑性模型用应力表述难以区别屈服与破坏,为此该文提出极限应变破坏判据,可用于判断材料的局部和整体破坏.给出了不同材料极限应变的确定方法,并作为破坏判据用于岩土类材料的稳定分析,称为极限应变法.将极限应变法应用于圆形隧洞,研究隧洞的破坏过程、围岩破坏深度及其安全系数,并与滑移线理论和实际模型试验的结果进行对比.研究表明:极限应变法能够判断圆形隧洞的破坏过程与极限状态,求得准确的安全系数,与滑移线场法和模型试验的结果一致,验证了极限应变法在隧洞中应用的可行性.极限应变判据具有明确的力学意义,能反映材料破坏的全过程,为岩土类材料极限分析提供了一种新的方法.     

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)     

Rate‐type Model for electro‐rheological Material Behaviour consistent with Extended Thermodynamics: Application to a steady viscometric flow

Based on extended thermodynamics, a class of rate‐type constitutive equations for electrorheological materials is presented. It is shown unlike many recent works using standard methods of continuum mechanics, that this approach, which consists in postulating expressions which relate the time derivative of the Cauchy stress to the motion, takes well account of the viscoelastic‐plastic effects as well as the coupling between the motion and the electric field. By considering special cases it turns out that the derived nonlinear algebraic model embeds a variety of existing differential models in the literature. The accuracy of the model is illustrated by considering a steady shear flow in which the electric field is applied perpendicularly to the flow direction. Analytical solutions with various parameter variations are obtained and discussed. The model predicts well the behaviour associated with material instabilities observed in viscometric flows for which the existence of the yield stress is required as confirmed by many experiments.     

基于L-D流动法则模糊弹粘塑性的有限变形分析

为了进行岩土材料有限变形的动力分析,采用Green应变和第二类Kirchoff应力描述材料的几何非线性。将隶属度函数引入到屈服函数中,并采用L-D屈服准则,得到了基于L-D流动法则的模糊弹粘塑性本构模型。应用非线性有限元原理,得到了土样动三轴实验有限变形的数值结果,并与小变形的数值结果和土样的动三轴实验结果进行了对比。通过对比发现有限变形的结果更加接近动三轴的实验结果,且模糊弹粘塑性模型能很好地反映循环荷载作用下岩土的动力性质,是岩土动力分析的一种有效方法.     

On the parameter identification of visco-hyperelastic material models for adhesive tapes

In this work we investigate the performance of a visco-hyperelastic material model to predict the time-dependent deformation behaviour of highly elastic adhesives. The model is based on the hyperelastic Arruda-Boyce model with a Prony series approach. The parameter identification is conducted for fixed relaxations times which are predicted via evaluating an integral ansatz for the shear modulus. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal die design for work-hardening metals

This paper discusses a die design problem for rigid-plastic metals under plane strain conditions. The strain distribution in the end product is required to be uniform, a condition which is satisfied when the principal stress directions coincide with streamlines of the flow. All possible deformations corresponding to a linear work hardening rule will be described.     

Efficient time integration in multiplicative inelasticity

In Shutov et al. (Comput Methods Appl Mech Eng 265:213–225, 2013), the numerical time integration of a famous large strain model of Maxwell fluid type has been considered. The underlying model is based on the multiplicative decomposition of the deformation gradient and includes a Neo-Hookean hyperelasticity relation as well as an incompressible viscous flow rule. Shutov et al. presented a time stepping algorithm for implicit time integration of the inelastic flow rule, which is based on Euler backward time discretisation, prevents error accumulation and is iteration free. In this contribution, the basic idea of the this approach is applied to more general models of multiplicative viscoelasticity. Here, extended hyperelastic relations including general functions of the first principal invariant of deformation tensors are regarded. An efficient time stepping algorithm is derived, where only one scalar equation for one scalar unknown has to be solved within every time step. The approach is applied to a specific viscoelastic model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Functional Fatigue in polycrystalline Shape Memory Alloys

Shape memory alloys show the well known effect of pseudo-elasticity associated with the formation of two stress plateaus in the stress/strain diagram for tension tests. Due to cyclic loading, the stress plateaus decrease with every load cycle, particularly the upper one. This important effect of functional fatigue results from plastic deformations that are produced during solid-solid phase transformations between the austenitic and martensitic state. Outgoing from a polycrystalline approach for shape memory alloys we develop a micromechanical material model that is based on the Principle of the Minimum of the Dissipation Potential and predicts the evolution of plastic strains. Therefore, only a small number of material parameters is necessary and additionally, only a few assumptions are sufficient to model the effect of functional fatigue. We present yield functions as well as evolution equations for the volume fractions of austenite and martensite, and the plastic strains. Furthermore, we show an exemplary calculation for Nickel Titanium and compare it with experimental measurements to demonstrate the ability of our model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A generalized polyconvex hyperelastic model for anisotropic solids

A generalized polyconvex hyperelastic model for anisotropic solids is presented. The strain energy function is formulated in terms of convex functions of generalized invariants and is given by a series with an arbitrary number of terms. The model addresses solids with orthotropic or transversely isotropic material symmetry as well as fiber-reinforced materials. Special cases of the strain energy function suitable for anisotropic elastomers and soft biological tissues are proposed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Constitutive modelling of thermo-viscoelastic-plastic behaviour of adhesively bonded joints

For ductile structural adhesives under thermal and mechanical loading, a thermo-viscoelastic-plastic interfacial constitutive model is introduced using a generalised MAXWELL solid in series with a thermal strain element and a ST.-VENANT body with isotropic hardening for plasticity. The temperature dependency of the viscosity is taken into account on assuming thermorheologically simple material behaviour, while the yield threshold and the hardening parameters depend on empirical functions of temperature. Numerical examples for the model verification and validation are discussed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of Uncertain Inelastic Material Behaviour using the Stochastic Finite Element Method

In this work, an approach for computing three-dimensional structures with random material properties, such as the yield stress, Young's modulus and hardening parameters is proposed. The random material properties are represented as random fields which are realized with the Spectral Representation Method (SPRM). The proposed approach is coupled with Monte Carlo Simulation (MCS) to determine the response statistics of a simple mechanical structure. The numerical results are compared with those obtained from classical Latin Hypercube Sampling (LHS). (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermoviscoplasticity of Glassy Polymers in the Logarithmic Strain Space Based on the Free Volume Theory

In this contribution a new constitutive model of finite thermo-visco-plastic behavior of amorphous glassy polymers and details of its numerical implementation are outlined. In contrast to existing kinematical approaches to finite plasticity of glassy polymers, the formulation applies a plastic metric theory based on an additive split of Lagrangian Hencky-type strains into elastic and plastic parts [1, 3]. The characteristic strain hardening of the model is derived from a polymer network model, the thermo-visco-plastic flow rule in the logarithmic strain space uses structures of the free volume flow theory [4]. The integration of this micromechanically motivated approach in a three-dimensional computational model is the key novel aspect of this work. An important aspect of this work is the model validation based on experimental findings, whereas the excellent performance of the proposed formulation is demonstrated by means of numerical examples. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)