Evaluation of hyperelastic models for unidirectional short fibre reinforced materials using a representative volume element with refined boundary conditions

The simulation of a short fibre reinforced structure by means of the FEM requires the knowledge of the material behaviour at every Gauss point. In order to obtain such information, a representative volume element (RVE) containing unidirectional short fibres is analysed in the presented work. In order to cover the complete anisotropic effect of the fibres, deformations with different angles to the fibre direction have to be conducted. In contrast to other works, this task is tackled using the application of periodic boundary conditions to the RVE in tensorial form, which enables a simple access to consider varying fibre angles with one and the same RVE. As the RVE’s average response represents the homogenised behaviour at a macroscopic material point, the material models’ parameters can be identified by fitting them to stress-strain curves obtained from simulations with the RVE. The findings of these analyses are used to assess the applicability of several hyperelastic models describing transversal isotropic materials under consideration of large deformations. For example it is shown, that the formulation of mixed invariants with the isochoric right Cauchy-Green tensor is insufficient to reproduce the RVE’s behaviour at purely volumetric deformations. Both the modelling and the calculations are carried out with the commercial FEMsoftware ABAQUS. Insight is given to the implementation of the boundary conditions as well as the underlying constitutive equations

Combined Shape and Parameter Identification Applied to a Porous Media Simulation

For material parameter estimation as well as shape identification a variety of research and commercial software exists. These tools are often integrated directly into an FEM program or use the FEM solver as a subroutine. However, the two problems are always considered as separate tasks which are solved by separate software packages. When simulating structured specimens, the considered domain often consists of different material types. These are modeled using different material domains. Frequently, the material parameters and the shape of the material domains are unknown. As both components considerably influence the simulation results, separate identification yields poor results. The inhouse identification and optimization software SPC-Opt developed at the department of Solid Mechanics at Chemnitz University of Technology is capable of solving shape and parameter identification simultaneously. Here, the key concept is an abstract formulation of parameters as variables that influence FEM computations. In this paper, the general design and algorithms are presented. Moreover, the application is demonstrated on an academic example using a simple porous media constitutive model

Automatic Verification of Parametric Specifications with Complex Topologies

The focus of this paper is on reducing the complexity in verification by exploiting modularity at various levels: in specification, in verification, and structurally. \begin{itemize} \item For specifications, we use the modular language CSP-OZ-DC, which allows us to decouple verification tasks concerning data from those concerning durations. \item At the verification level, we exploit modularity in theorem proving for rich data structures and use this for invariant checking. \item At the structural level, we analyze possibilities for modular verification of systems consisting of various components which interact. \end{itemize} We illustrate these ideas by automatically verifying safety properties of a case study from the European Train Control System standard, which extends previous examples by comprising a complex track topology with lists of track segments and trains with different routes

On Deciding Local Theory Extensions via E-matching

Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software. This makes them important tools for automating verification problems. A limitation frequently encountered is that verification problems are often not fully expressible in the theories supported natively by the solvers. Many solvers allow the specification of application-specific theories as quantified axioms, but their handling is incomplete outside of narrow special cases. In this work, we show how SMT solvers can be used to obtain complete decision procedures for local theory extensions, an important class of theories that are decidable using finite instantiation of axioms. We present an algorithm that uses E-matching to generate instances incrementally during the search, significantly reducing the number of generated instances compared to eager instantiation strategies. We have used two SMT solvers to implement this algorithm and conducted an extensive experimental evaluation on benchmarks derived from verification conditions for heap-manipulating programs. We believe that our results are of interest to both the users of SMT solvers as well as their developers