arXiv subjects

Franz Dammaß

Publications and source records attributed to Franz Dammaß.

7 recordsLinked to original sources

arXiv2026

Reliable training of neural hyperelastic models via full-field data

We present a systematic investigation of the robustness and limitations of equilibrium gap-based calibrations for hyperelastic physics-augmented neural networks (PANNs), where we consider the special case of isotropic and polyconvex PANNs. In full-field parameterizations, it is commonly assumed that the displacement field is captured with sufficient spatial resolution for an accurate evaluation of the deformation field, and that the specimen is thin enough for plane stress to hold to a good approximation. Since these assumptions are never ideally satisfied in real experiments, we investigate, using synthetically generated data, how severely an under-resolved surface measurement and a non-negligible specimen thickness can affect the model parameterization. Furthermore, we perform calibration on real experimental data for a set of inhomogeneous specimen geometries. We show that the coverage of the admissible deformation states during calibration governs the ability of a model to generalize to unseen geometries and load cases; this ability can be improved further by appropriate combinations of specimens. Accurately depicting the material behavior underlying this rich data, however, requires a sufficiently flexible constitutive model, for which PANNs are well suited. Yet a rich coverage of deformation states alone is not sufficient: unless the calibration data comprise biaxial-tension-like states, models that include the second deformation invariant extrapolate unphysically towards equi-biaxial tension, whereas restricting the PANN to the first invariant remains reliable.

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arXiv2026

Construction of minimal integrity basis for anisotropic hyperelasticity via structural tensors

We present minimal integrity bases for all common anisotropies in hyperelasticity via the structural tensor concept, which can be used to formulate any algebraic invariant function in the elements of the respective bases. Hence, the provided minimal integrity bases are of great interest for formulating a concise but general anisotropic material model. Our work covers results for the 11 types of anisotropy that arise from the classical 7 crystal systems, as well as findings for 4 additional non-crystal anisotropies derived from the cylindrical, spherical, and icosahedral symmetry systems. By using well-known results from literature about structural tensors, isotropic invariants, and isotropic extension, functional bases are directly determined. A simple analytical-numerical approach is employed to identify polynomial relations between the invariants of these functional bases, thereby enabling the construction of functional bases of reduced cardinality. After that, we show that the determined reduced functional bases are also minimal integrity bases by identifying polynomial relations to known integrity bases from literature. Furthermore, fundamental concepts from invariant theory, including the Hironaka decomposition of invariant rings and the closely related Hilbert series, are employed to further validate the results. Alongside the presented findings, this article also aims to provide an introductory overview of the complex field of modeling anisotropic materials, especially for researchers with an engineering background.

cond-mat.mtrl-sci↗

arXiv2026

Precise, efficient and flexible modeling of crystallizing elastomers based on physics-augmented neural networks

We propose a precise and efficient physics-augmented neural network (PANN) to model strain-induced crystallization in rubbery polymers. We demonstrate that the model can be flexibly employed for both unfilled and filled natural rubber (NR). The approach is based on a two potential framework, similar to the concept of generalized standard materials (GSMs). To describe the material behavior, neural network-based free energy and dissipation potentials are employed. The evolution of crystallinity is derived from the two potentials. To ensure boundedness of the crystallinity, a novel constrained GSM-type evolution problem is proposed. To this end, two additional Lagrange multipliers together with the corresponding Karush-Kuhn-Tucker conditions are introduced. As a result, it is guaranteed that crystallinity can be interpreted as a variable of concentration type. The neural network-based potentials ensure all physically desirable properties by construction. Most importantly, objectivity, material symmetry and thermodynamic consistency are automatically fulfilled. In addition, an alternative derivation of the governing model equations in time-discrete form is presented based on an incremental variational framework, which also serves as the basis for a finite element implementation. We demonstrate the predictive capability of the PANN using three different experimental data sets from literature, considering both stress and crystallinity evolution at material point level as well as the corresponding field distributions in a notched specimen. Moreover, we show that model parameterization is also possible when experimental crystallinity data is not available, still enabling suitable stress predictions.

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arXiv2025

When invariants matter: The role of I1 and I2 in neural network models of incompressible hyperelasticity

For the formulation of machine learning-based material models, the usage of invariants of deformation tensors is attractive, since this can a priori guarantee objectivity and material symmetry. In this work, we consider incompressible, isotropic hyperelasticity, where two invariants I1 and I2 are required for depicting a deformation state. First, we aim at enhancing the understanding of the invariants. We provide an explicit representation of the set of invariants that are admissible, i.e. for which (I1, I2) a deformation state does indeed exist. Furthermore, we prove that uniaxial and equi-biaxial deformation correspond to the boundary of the set of admissible invariants. Second, we study how the experimentally-observed behaviour of different materials can be captured by means of neural network models of incompressible hyperelasticity, depending on whether both I1 and I2 or solely one of the invariants, i.e. either only I1 or only I2, are taken into account. To this end, we investigate three different experimental data sets from the literature. In particular, we demonstrate that considering only one invariant, either I1 or I2, can allow for good agreement with experiments in case of small deformations. In contrast, it is necessary to consider both invariants for precise models at large strains, for instance when rubbery polymers are deformed. Moreover, we show that multiaxial experiments are strictly required for the parameterisation of models considering I2. Otherwise, if only data from uniaxial deformation is available, significantly overly stiff responses could be predicted for general deformation states. On the contrary, I1-only models can make qualitatively correct predictions for multiaxial loadings even if parameterised only from uniaxial data, whereas I2-only models are completely incapable in even qualitatively capturing experimental stress data at large deformations.

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arXiv2023

Rate- and temperature-dependent ductile-to-brittle fracture transition: Experimental investigation and phase-field analysis for toffee

The mechanical behaviour of many materials, including polymers or natural materials, significantly depends on the rate of deformation. As a consequence, a rate-dependent ductile-to-brittle fracture transition may be observed. For toffee-like caramel, this effect is particularly pronounced. At room temperature, this confectionery may be extensively deformed at low strain rates, while it can behave highly brittle when the rate of deformation is raised. Likewise, the material behaviour does significantly depend on temperature, and even a slight cooling may cause a significant embrittlement. In this work, a thorough experimental investigation of the rate-dependent deformation and fracture behaviour is presented. In addition, the influence of temperature on the material response is studied. The experimental results form the basis for a phase-field modelling of fracture. In order to derive the governing equations of the model, an incremental variational principle is introduced. By means of the validated model, an analysis of the experimentally observed ductile-to-brittle fracture transition is performed. In particular, the coupling between the highly dissipative deformation behaviour of the bulk material and the rate-dependent fracture resistance is discussed.

cond-mat.mtrl-sci↗

arXiv2022

Phase-field modelling and analysis of rate-dependent fracture phenomena at finite deformation

Fracture of materials with rate-dependent mechanical behaviour, e.g. polymers, is a highly complex process. For an adequate modelling, the coupling between rate-dependent stiffness, dissipative mechanisms present in the bulk material and crack driving force has to be accounted for in an appropriate manner. In addition, the fracture toughness, i.e. the resistance against crack propagation, can depend on rate of deformation. In this contribution, an energetic phase-field model of rate-dependent fracture at finite deformation is presented. For the deformation of the bulk material, a formulation of finite viscoelasticity is adopted with strain energy densities of Ogden type assumed. The unified formulation allows to study different expressions for the fracture driving force. Furthermore, a possibly rate-dependent toughness is incorporated. The model is calibrated using experimental results from the literature for an elastomer and predictions are qualitatively and quantitatively validated against experimental data. Predictive capabilities of the model are studied for monotonic loads as well as creep fracture. Symmetrical and asymmetrical crack patterns are discussed and the influence of a dissipative fracture driving force contribution is analysed. It is shown that, different from ductile fracture of metals, such a driving force is not required for an adequate simulation of experimentally observable crack paths and is not favourable for the description of failure in viscoelastic rubbery polymers. Furthermore, the influence of a rate-dependent toughness is discussed by means of a numerical study. From a phenomenological point of view, it is demonstrated that rate-dependency of resistance against crack propagation can be an essential ingredient for the model when specific effects such as rate-dependent brittle-to-ductile transitions shall be described.

cond-mat.mtrl-sci↗

arXiv2020

Phase-Field Modeling of Crack Branching and Deflection in Heterogeneous Media

This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the crack evolution in a regularized manner. The interface modeling implements two combined approaches. Firstly, a method from the literature is extended where the interface is incorporated by a local reduction of the fracture toughness. Secondly, variations of the elastic properties across the interface are enabled by approximating the abrupt change between two adjacent subdomains using a hyperbolic tangent function, which alters the elastic material parameters accordingly. The approach is validated qualitatively by means of crack patterns and quantitatively with respect to critical energy release rates with fundamental analytical results from Linear Elastic Fracture Mechanics, where a crack impinges an arbitrarily oriented interface and either branches, gets deflected or experiences no interfacial influence. The model is particularly relevant for phase-field analyses in heterogeneous, possibly complex-shaped solids, where cohesive failure in the constituent materials as well as adhesive failure at interfaces and its quantification play a role.

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