Search

The main objective of this work is to follow the evolution of the stiffness tetrad during large plastic strains. For this purpose, the framework of a general theory of finite plasticity is developed. Some special cases are investigated and the case of a material plasticity theory is considered in more detail. Its main feature is that the elasticity law changes during plastic deformations, for which we develop an approach. We use three types of fiber‐reinforced composites as example materials. Finite element simulations of representative volume elements for uni‐, bi‐ and tri‐directionally reinforced materials with periodic boundary conditions are used for numerical experiments and verification of the model's predictions. From these, we extract the stiffness tetrads before and after large deformations of the material. We quantify the change in stiffness tetrads due to fiber reorientation. Finally, we propose an analytical evolution with three parameters that reproduces reasonably well the evolution of the stiffness tetrads. [ABSTRACT FROM AUTHOR]

A current topic in the photovoltaic industry is the analysis and evaluation of possible structural and material properties. This requires the effective material characteristics of polycrystalline silicon, which is an important component for the functional performance of the photovoltaic modules in use. Since this assessment is associated with high costs, it is to be carried out already in the product development process. Due to very thin silicon layers, the effect of the layer thickness on the effective material characteristics has to be investigated (see). In this work, a procedure to determine these characteristic values is listed to investigate the size effect on different film thicknesses of this material (see). With the knowledge of the properties of the silicon single crystal with its cubic symmetry on the micro level, a homogenization of the properties to the macro level can be done. The polycrystal structure with a cubic sample geometry forms the macro level. This structure is now cut into thinning layers for investigation. The open‐source software Neper is used to create the crystal structure and the inter‐connectivity for this purpose. With the help of Matlab, this information is passed on to the finite element program Abaqus, where the results are evaluated after an elastic calculation using Python. The focus is on the expected change in material properties as a function of the layer thickness. [ABSTRACT FROM AUTHOR]

Strain-gradient elasticity is a special case of high-gradient theories in which the potential energy density depends on the first and second gradient of the displacement field. The presence of a coupling term in the material law leads to a non-diagonal quadratic form of the stored energy, which makes it difficult for the derivation of fundamental theorems. In this article, two variational principles of the minimum of potential and complementary energies are argued in the context of the coupled strain-gradient elasticity theory. The basis of the proofs of both variational principles is the equivalent transformation of the stain and strain-gradient energy density that allows to avoid the complication related to the presence of the fifth-rank coupling tensor C 5 in the equation for the potential energy density and leads to diagonalization of the quadratic form of the stored energy. This transformation enables to inverse Hook's law, to determine compliance tensors, and to obtain closed-form relation for the complementary energy. After that the proofs of both principles of a minimum of potential and complementary energies are provided in the usual manner adopted in the classical theory of elasticity. [ABSTRACT FROM AUTHOR]

The inverse Hooke's law and complementary strain energy density has been examined in the context of the theory of coupled gradient elasticity for second gradient materials. To this end, it was assumed that the potential energy density is a quadratic form of the strain and of the second gradient of displacement. Existence of the coupling term significantly complicates the problem. To avoid this complication the equation for the potential energy density was transformed in order to present it as an uncoupled quadratic form of a modified strain and the second gradient of displacement or of the strain and a modified second gradient of displacement. These transformations, which is in essence a block matrix diagonalization, lead to a decoupling of strains and strain gradient in the potential energy density and makes it possible to determine tensorial relations for the compliance tensors of fourth‐, fifth‐ , and sixth‐rank. Both modifications result in the same compliance tensors and are valid for an arbitrary material symmetry class. In the case of hemitropic materials, the compliance tensors have the same symmetry and the same form as the stiffness tensors and are characterized by eight independent constants, namely the two classical isotropic constants, five constants in the strain gradient part and one constant in the coupling term. Explicit expressions for these eight parameters are obtained from the tensorial relations for the compliance tensors and are compared with the direct solution of a linear system for the compliance's. All three solutions are identical, what we consider as a verification of the presented results. The inverse Hooke's law and complementary strain energy density has been examined in the context of the theory of coupled gradient elasticity for second gradient materials. To this end, it was assumed that the potential energy density is a quadratic form of the strain and of the second gradient of displacement. Existence of the coupling term significantly complicates the problem. To avoid this complication the equation for the potential energy density was transformed in order to present it as an uncoupled quadratic form of a modified strain and the second gradient of displacement or of the strain and a modified second gradient of displacement.... [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a framework for modelling the deformation behaviour of friction welded hybrid structures. The constitutive model is developed for large deformations and nonlinear material behaviour. Moreover, to demonstrate the model's applicabilities, it was implemented into a finite element system (ABAQUS). Subsequently, the simulation results were critically evaluated using experimental data. [ABSTRACT FROM AUTHOR]

Convexity of a function or set is an often needed and important mathematical property. In the case of yield functions ϕ ( T ) (or elastic ranges) in terms of stresses, almost all empirical and mechanism-based yield functions have this property. However, requiring positive plastic dissipation does not necessarily exclude non-convex yield functions, which is confirmed by the fact that non-convex yield functions are observed experimentally, although this rarely happens. We therefore ask whether this nice mathematical property reflects a physical material property. This is investigated in an elastic–plastic, small strain, 2D setting. It appears that, at least in this setting, no specific material property can be attributed to the convexity of the yield function. [ABSTRACT FROM AUTHOR]

Highlights: [•] The proof of the Hill–Mandel-condition is given more detailed in the Appendix. [•] Cubical RVE are considered also. [•] Many minor changes have been incorporated. [ABSTRACT FROM AUTHOR]

A sparse matrix bandwidth reduction method is analyzed. It consists of equation splitting, substitution and introducing new variables, similar to the substructure decomposition in the finite element method (FEM). It is especially useful when the bandwidth cannot be reduced by strategically interchanging columns and rows. In such cases, equation splitting and successive reordering can further reduce the bandwidth, at cost of introducing new variables. While the substructure decomposition is carried out before the system matrix is built, the given approach is applied afterwards, independently on the origin of the linear system. It is successfully applied to a sparse matrix, the bandwidth of which cannot be reduced by reordering. For the exemplary FEM simulation, an increase of performance of the direct solver is obtaine. [ABSTRACT FROM AUTHOR]

Present‐day research in the field of product development are increasingly focused on the efficient use of energy and raw material resources. In the light of this context, the design principle of consistent lightweight construction is gaining more and more importance. One possible approach is the targeted combination of different materials with favourable technological properties in hybrid structures. Against this background, the rotary friction welding (RFW), is particularly advantageous allowing the joining of dissimilar materials, like aluminium and steel in order to create such lightweight structures. The purpose of the paper at hand, is to present a framework for modelling the elastoplastic behaviour of those manufactured structures under the assumption of large deformation and non‐linear material behaviour. Moreover, the presented model was implemented into a finite element analysis program (ABAQUS), in order to simulate a tensile test of a friction welded lightweight structure. Subsequently, the simulation results were critically evaluated using experimental data. [ABSTRACT FROM AUTHOR]

Abstract: We present a phenomenological finite elasto‐plasticity theory that includes the evolution of the elastic anisotropy. The theory is called Material Plasticity after [1] and [2], assuming that the axes of anisotropy deform as material line elements. It is applicable to fiber‐reinforced materials. The main feature is the different evolutions of the stiffness tetrad and of the stress‐free placement. For this purpose we extend the well known isomorphy concept (see [3]). To identify and compare the stiffness tetrads before and after large plastic deformations a representative volume element (RVE) [4] with a fiberous microstructure is used. Uni‐, bi‐ and and tridirectionally reinforced samples are considered. On the microscale a standard elastic‐plastic material model is used. After calculating the effective stiffnesses of the different material samples we investigate their evolution during different deformations. It turns out that it is possible to denote the change of the stiffness with sufficient accuracy using one additional second order tensor. After investigating the change in the stiffness tetrads we finally propose an analytical evolution equation for this tensor. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In this contribution, we make use of the fact homogenization of elastic properties of laminates [1] can be extended relatively easy to the plastic case [2] to derive exact expressions for the effective yield limit and the ultimate loading in monotonic tension test. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]