Section 6: Material modelling in solid mechanics - GAMM 2012

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22 Section 6: Material modelling in solid mechanics [3] Marckmann G, Verron E (2006), Comparison of hyperelastic models for rubber-like materials. Rubber Chemistry and Technology, 79 (2006) 835-858 Accelerating constitutive modeling by automatic tangent generation Steffen Rothe, Stefan Hartmann (TU Clausthal) Nowadays models become more and more complex. Within the framework of finite elements a material, i.e. consistent, tangent is required for the overall Newton-like method. Obtaining these derivatives is time consuming and error-prone which contradicts to the goal of changing the model during the developing process. On the one hand the calculation by hand can be very expensive and on the other hand also the implementation has to be done with high diligence. Therefore, a fast and safe way of consistent tangent generation will be presented with the help of automatic differentiation (AD) techniques. Analytical tangents have the advantage that they are exact. However during the constitutive modeling process a change of the model is natural. Thus, the effort is very high to calculate the derivative after every modification. Numerical tangents computed by finite differences are easy to compute, but can lead to a significant slowdown or even to a failure of the simulation due to numerical errors. Tangents generated by OpenAD have no round-off errors and are easily computed by the help of automatic differentiation. These three methods (analytical, numerical and automatic differentiation) for tangent generation will be analyzed concerning the simulation time and applicability for a number of different constitutive models. S6.9: Microheterogeneous Materials Thu, 13:30–15:30 Chair: Johannes Schnepp, Eleni Agiasofitou S1|01–A03 The boundary value problems of the full coupled theory of poroelasticity for materials with double porosity Merab Svanadze (Ilia State University, Tbilisi) Porous materials play an important role in many branches of engineering, e.g., the petroleum industry, chemical engineering, geomechanics, and, in recent years, biomechanics. The construction and the intensive investigation of the theories of continua with microstructures arise by the wide use of porous materials into engineering and technology. The general 3D theory of poroelasticity for materials with single porosity was formulated by Biot (1941). The double porosity model was first proposed by Barenblatt and coauthors (1960). The quasi-static theory of poroelasticity for materials with double porosity in the framework of mixture theory was presented by Aifantis and his co-workers (1982). In this paper the full coupled theory of poroelasticity for materials with double porosity is presented. This theory unifies the earlier proposed quasi-static model of Aifantis of consolidation with double porosity. The boundary value problems (BVPs) of the steady vibrations are investigated. The fundamental solution of system of equations of steady vibrations is constructed. The basic properties of plane waves and the radiation conditions for regular vector are established. The uniqueness theorems of the internal and external BVPs of steady vibrations are proved. The basic properties of elastopotentials are established. The representation of general solution of equations of steady vibrations is obtained. The existence of regular solution of the BVPs by means of the boundary integral method and the theory of singular integral equations are proved.
Section 6: Material modelling in solid mechanics 23 Application of an anisotropic growth and remodelling formulation to computational topology optimisation Tobias Waffenschmidt (TU Dortmund), Andreas Menzel (TU Dortmund / Lund University) A classical topology optimisation problem consists of a problem-specific objective function which has to be minimised in consideration of particular constraints with respect to design and state variables. In this contribution we present a conceptually different approach for the optimisation or rather improvement of the topology of a structure which is not based on a classical optimisation technique. Instead, we establish a constitutive micro-sphere-framework in combination with an energy-driven anisotropic microstructural growth formulation, which was originally proposed for the simulation of adaptation and remodelling phenomena in hard biological tissues such as bones. The key aspect of this contribution is to investigate this anisotropic growth formulation with a special emphasis on its topology-optimising characteristics or rather topology-improving properties. To this end, several illustrative three-dimensional benchmark-type boundary value problems are discussed and compared qualitatively with the results obtained by classic topologyoptimisation strategies. The simulation results capture the densification effects and clearly identify the main load bearing regions. It turns out, that even though making use of this conceptually different growth formulation as compared to the procedures used in the more classic topologyoptimisation context, we identify qualitatively very similar topologies. Moreover, in contrast to common topology optimisation strategies, which mostly aim to optimise merely the structure, i.e. size, shape or topology, our formulation also contains the optimisation or improvement of the material itself, whichapart from the structural improvementresults in the generation of problemspecific local material anisotropy and textured evolution. Amplification damping properties of multiphase composites with spherical and fibers inclusions Sergey Lurie (Institute of Applied Mechanics, RAS), Natalia Tuchkova (Dorodnicyn Computing Centre, RAS), Juri Soliaev (Institute of Applied Mechanics, RAS) We consider composite materials reinforced with spherical and fibrous inclusions coated with a layer of lossy viscoelastic material. For the coating layers, typical viscoelastic properties of a polymer at and well above the glass transition region are assumed. It is shown that the remarkable loss amplification mechanism is also operative in such particulate-morphology materials. The aim of our study is to determine the effective loss modulus composites, which formally defines the rate of energy dissipation per unit volume. We use a combination of modeling and numerical tools to study composite materials consisting of a matrix filled with spherical and fibrous inclusions coated with a layer of lossy viscoelastic material. The method of the four phases is used to describe the damping properties of composites filled with multiphase spherical inclusions and monolayer with multiphase fibrous inclusions. The constituent phases are supposed to be isotropic. Using the Eshelby method the effective moduli are determined self-consistently, by requiring that the average strain in the composite inclusion is the same as the macroscopic strain imposed at infinity. The analytical solution of this problem were received. The effective dynamic modulus and loss modulus were found using a viscoelastic analogy. It is shown[1] that the analytical give very similar, practically indistinguishable predictions from the numerical solutions which were received using finite element method. Hence, when studying such systems one can rely on the predictions of the four-phase sphere model, which are much easier to achieve than the finite element ones. a polymer at and well above the glass transition region are assumed. It is shown that by optimizing the thickness of the layers, one can achieve multiphase materials with effective loss characteristics significantly exceeding those of the
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