FeelMath - Mechanical and Thermal Properties of Microstructures

FeelMath is a fast and easy to use analysis tool for elastic micro-structures given by volume images or analytical descriptions.

Extracting Information for the Microstructure

The micro-structure of a material affects its properties like thermal conductivity, elasticity, or acoustic absorption. Image analysis provides micro-structure information needed as input for the dimensioning at the macroscale, i.e. at the level of the whole part.

SEM images, tomographies and the image analysis yield the important information for the micro structure. In addition, the representative volume element is defined small enough not to claim too much capacity but it is also large enough to stay efficiently.


Finding the Optimal Microstructure

Finally, the modeling opens the door to the so-called virtual material design and optimization of micro-structures. Simple changes of model parameters result in slightly altered geometries, in which the target property can be simulated again.

This cycle can be repeated until the optimal micro-structure is found. Thus, costly mechanical tests and production of samples can be reduced while the relation between micro-structure and reaulting properties is better understood.


is used to calculate the effective stiffness of anisotropic, elastic composites and porous materials (e.g., rocks). The big advantage is that the calculation does not require net generation, but instead takes place directly on 3D pixels (voxels).


is used to estimate the effective stiffness (directional elastic modulus) of anisotropic, elastic composites with analytical formulas (approximative formulas AF).


is used to simulate the physically and geometrically non-linear behavior (large deformations LD) of anisotropic composites and porous materials.

Project example FeelMathVOX and FeelMathLD

The automotive industry, pursuing the goal to achieve low weights, strives to use composite materials such as glass-fiber reinforced plastics (GRP), and carbon fiber reinforced plastics (CFRP). The GRP and CFRP are very well suited for lightweight construction, but the commitment to use them in mass production is still in its infancy.

One essential reason is the inability to precisely simulate crash performance. On the macroscopic level, it is very difficult to extrapolate the mechanical behavior of the material based on its microstructure. Among other things, this has consequences in the crash performance, which is due mostly to micro-cracks. Previously used methods (Finite Element Method) either are connected with high computing time or provide no sufficient accuracy (“mean field” methods).


»Micromechanical Modeling of Carbon Fiber Reinforced Plastics«

Within the MEF project (Micromechanical modeling of the crash performance of carbon-fiber reinforced plastics carried out with the Fraunhofer IWM, a numerical method was developed that allows the reliable calculation of the macroscopic mechanical behavior from the complex, heterogeneous fiber structure of the material and can replace complex experiments as a “virtual laboratory”.

The approach is based on the fast Fourier transform (FFT) to solve an integral equation and overcomes the barriers of the conventional methods using low memory and shorter processing times. The calculation on realistic three-dimensional microstructure models is accelerated to several orders of magnitude while maintaining accuracy.

Thus, overnight simulations are possible on a standard PC and the critical gap in the ability to simulate the crash performance is closed. The developed program, called FeelMathVOX, is integrated among others as a module into the Software GeoDict (www.geodict.com) developed at the Fraunhofer ITWM, and commercially distributed by the Math2Market GmbH spin-off.  

FeelMathVOX for the Investigation of Natural Porous Materials

FeelMathVOX is absolutely robust concerning the complexity of the geometry and the material properties (high material contrast, incompressible materials, and porous inclusions are easily manageable) of the micro-structure. Therefore, it can be applied to the assessment of natural porous materials like rock formations, in addition to the use for optimization of industrial materials and geometries in the aerospace and automotive industry.

© Photo ITWM

Von-Mises stresses under load in the fiber direction.

© Photo ITWM

Von-Mises stretch under load in z-direction.

© Photo ITWM

Berea sandstone.

Further Publications