Our research is driven by the desire to develop advanced simulation methods for engineering problems with complex solid material response. Our objective is to establish modern modeling concepts for the predictive analysis and optimization of material behavior under (non-)mechanical influences, including thermo-chemo-magneto-electro-mechanical coupling. Our approach covers mathematical formulations of theoretical and computational models with an emphasis on continuum mechanics and associated materials theory. In particular, we are interested in describing the evolution of microstructures and its link to larger length scales via homogenization and scale-briding techniques.
In this spirit, we develop nonlinear models in the field of thermo-chemo-magneto-electro-elasticity, plasticity and fracture mechanics at different length scales. A main interest is in the design of associated variational approaches that allow for the development of robust and efficient numerical solution algorithms. Furthermore, we develop homogenization methods for the analysis and optimization of the effective repsonse of smart and multifunctional composites. Our investigations also cover the analysis of the material and structural instability of microstructured solids. Examples of our research activities in theoretical and computational solid mechanics are:
Coupled and dissipative materials
- Magneto-mechanics. Magnetostrictive materials, magnetorheological elastomers
- Electro-mechanics. Ferroelectrics, electroactive polymers, liquid crystal elastomers
- Magneto-electro-mechanics. Magneto-electric composites at small and finite strains
- Thermo-mechanics. Variational formulations for standard dissipative solids
- Chemo-mechanics. Modeling of porous media (soil, lithium-ion batteries, hydrogels)
- Fracture mechanics. Phase field modeling (brittle, ductile, hydraulic, coupled fracture)
- Elasto-plasticity. (Gradient) plastiticity of crystalline and frictional materials
- Computational homogenization. Smart and multifunctional composite materials
- Phase-field modeling. Microstructure evolution, fracture, homogenization
- Variational approaches. Incremental variational formulations for solid materials
- Data-integrated methods. Data-driven mechanics, machine learning, neural networks
- Stability analysis. Material and structural stability analysis, Bloch-Floquet analysis
Microscopic fracture topology evolution
The simulation shows a phasefield based modelling of fracture processes within materials with distinct microstructure. Spherical stiff inclusions (pink) are embedded into a soft matrix. The crack surface (red) evolves around the spherical stiff inclusions and perpendicular to the horizontal macroscopic stretch direction. The simulation is carried out using a fast-Fourier-transform based solution scheme. Goal of the current research is inter alia the characterization and design of 3D-printed smart materials in lightweight applications. Felix Selim Göküzüm M.Sc.
Soft Active Materials. Computational Modeling and Stability Analysis
Examples for the soft active materials can be electro-active polymers and magneto-sensitive elastomers among others. These materials have usually light weight, controllable stress and strain response and can further undergo large deformations. Such favorable properties of these materials allow them to consider in the various industrial applications such as in robotics, automobile industries or in aerospace.
Electro-active polymer are usually considered as electrostrictive materials. This means that these materials undergo mechanical deformation under electric stimuli. But the vice verse is not the case. Electro-active polymers (EAP) are usually considered as composites which are in its simple form consists of particles distributed within a polymer matrix. If we attach deformable electrodes (for example by spraying) on the surface of an EAP composite, electric field will be generated between these electrodes. As a result, we usually observe thinning of the structure in the field direction and extension in the transverse direction. Depending on the microstructure of the EAP composites we could observe complex deformations patterns. In the video above, we observe that a periodic EAP composite, which has initially a periodicity that could be described by a representative unit-cell with only one inclusion, undergoes electrical loading in the vertical direction. However, at high values of the electric field, some of the particles attract each other and consequently the microstructure rearranges itself in an energetically more favorable configuration due to microscopic instability. This also alters the periodicity of the microstructure which can be described, as seen from the video, by only a representative volume which consists of two particles in a specific order.
A microscopic instability in an EAP composite
Similar to the electro-active polymers, the magneto-sensitive elastomers can also be considered as magnetostrictive materials. Magneto-sensitive elastomers are also composed of polymeric matrix and ironic (or in the form of its alloys) particles. These materials are usually loaded by the magnetic field with the help of electromagnets. In this video, similar to the first one, we load a representative microstructure of magneto-sensitive elastomer by magnetic field which is slightly inclined towards the horizontal direction from the vertical. In this case, we clearly see that at a certain magnetic field the periodicity of the microstructure is changed due to a microscopic instability.
A microscopic instability in an MRE composite
Hydrogels form an important class of multi-functional materials with applications ranging from drug delivery systems and contact lenses in the biomedical industry to the manufacture of soft microgears for mechanical actuation in microdevices. They are basically hydrophilic elastomers that have a profound swelling capability (upto several hundred times their original dry volume) upon imbibing a diffusing solvent. In the swollen state, they exhibit favorable mechanical properties and stiffness due to the presence of cross-links between the elastomer chains.
When the free swelling of such gels is arrested by suitable mechanical constraints, a wide variety of surface instability patterns start to appear when the compressive stresses in the gel cross a certain critical value. The amount of swelling required to activate the instability and the resulting buckled configuratrion depend significantly on the system geometry, material parameters and loading conditions. By studying these dependencies, it is possible to design hydrogel systems in such a way that they are tuned to buckle and produce specific surface patterns, making them ideal for use in microcomponent devices and as actuators. In the videos below, one can observe the onset of sinusoidal wrinkle patterns on the surfaces of flat and tubular hydrogel bilayers subjected to mechanically constrained swelling under fluid diffusion.
Wrinkling of flat hydrogel bilayers
Wrinkling of hydrogel tubes
Strain-Induced Crystallization in Rubbers
Upon stretching a natural rubber specimen, polymer chains orient themselves in the direction of the applied load and form crystalline regions. If the sample is retracted, the original amorphous state of the network is fully restored. Due to crystallization, properties of rubber change considerably. The reinforcing effect of the crystallites leads to stiffening of the rubber and an increase in the crack growth resistance.
A key characteristic observed in the stress-strain diagram of strain crystallizing rubber is the development of a hysteresis. This hysteresis is attributed to formation and melting of strain-induced crystallites. Our intention was to propose a micro-mechanically motivated material model for strain-induced crystallization in rubbers.
Lithium-ion batteries are the most attractive electro-chemical energy storage medium used in portable electronic devices. Recently, Li-ion batteries have gained more significance due to their application in hybrid and electric vehicles.
The performance of Li-ion batteries might be impaired due to unwanted electro-chemical reactions, leading to capacity loss, self-discharge and thermal runaway. Thermal effects play a crucial role in all of these issues. The intercalation and deintercalation of lithium ions in batteries is a complex interplay of electro-chemical, thermodynamical and mechanical effects. We intend to propose a thermodynamically consistent material modeling framework for diffusion of lithium ions in electrode particles of Li-ion batteries.