ACE&S Ltd has a few significant results in computational mechanics

The founders of ACE&CS Ltd have been doing research into materials and their computer simulation for nearly two decades. During this period of time they have developed quite a few material models and improved many existing mathematical formulations in computational mechanics to model deformable body behavior using the finite element method (FEM) and the discrete element method (MDP).

ACE&CS Ltd has been playing a pioneering role in the development of universal material models with internal/material damping to simulate thermodynamics of large deformations at wide range of strain rates.  

The company has also been involved in the development of various mathematical models for numerical simulation of various manufacturing processes and technological procedures, such as arc welding, friction-stir welding, various metal forming processes, etc. While developing new material models, ACE&CS Ltd has utilized all the scientific results of the founders of the company. A selection of the most significant results and their brief descriptions are presented below:

  1. Thermal-structural analyses with one-way coupling do not model a real thermodynamic problem.

    Mechanical deformations always generate heat and vice-versa, though a change in the temperature may not always be significant. Thermal-structural analyses with a one-way coupling model an idealized problem of a deforming body in which deformations take place at zero velocity. The one-way coupling in the above analyses has resulted from incomplete weak forms of the conservation laws used in the analyses, which did not capture the strong coupling between the temperature field and the displacement field on the boundary of the body. The founders of ACE&CS Ltd in 2005 as the first presented an improved weak form of a heat equation, which took into account the strong coupling via the boundary conditions. Without the coupling the heat equation had to contain a mechanical coupling term in order that the strong coupling was ensured. For more information on the weak form please refer to the following publications:

    ÉCSI, Ladislav. Numerical behaviour of a solid body under various mechanical loads using finite element method with new energy balance equation for fully coupled thermal-structural analysis. In Proceedings of the sixth internationale congress on THERMAL STRESSES : Volume 2 : Vienna /Austria/, May, 2005. Wien : Technische Universität Wien, 2005, s.543-546. ISBN 3-901167-12.

    ÉCSI, Ladislav - ÉLESZTÖS, Pavel. Moving toward a more realistic material model of a ductile material with failure mode transition. In Materialwissenschaft und Werkstofftechnik. Vol. 43, No. 5 (2012), s.379-387. ISSN 0933-5137.

    ÉCSI, Ladislav - ÉLESZTÖS, Pavel - BALÁZSOVÁ, Kinga. An improved finite element model for numerical simulation of phase changes of iron under extreme conditions. In Numerical modeling of materials under extreme conditions. 1st. ed. Berlin : Springer-Verlag Berlin Heidelberg, 2014, s. 173-197. ISBN 978-3-642-54257-2.

  2. Development of a universal material model with internal/material damping to model the behaviour of a deformable body which undergoes large deformations at wide range of strain rates.

    In current finite element analyses (FEA) the Rayleigh damping is used frequently to model internal/material damping. The Rayleigh damping however is not suitable to model internal /material damping, as it does not differentiate between rigid body motion and deformation. As a result, the model applies the damping irrespective of whether rigid body motion or deformation takes place. The founders of ACE&CS Ltd in 2012 as the first presented a proper internal damping model which eliminated the above shortcoming. By adjusting the Kelvin-Voigt material model, they have developed a material model capable of considering material damping when large elastic or plastic deformations take place at wide range of strain rates. For more information on the model please refer to the following paper:

    ÉCSI, Ladislav - ÉLESZTÖS, Pavel. Moving toward a more realistic material model of a ductile material with failure mode transition. In Materialwissenschaft und Werkstofftechnik. Vol. 43, No. 5 (2012), s.379-387. ISSN 0933-5137.

  3. The stress tensor calculation must be independent of an objective rate when proper rate forms of the constitutive equation of a material, based on various objective rates, are used for stress calculation.

    Until now it has been assumed to be acceptable that various rate forms of the constitutive equation of a material based on various objective rates resulted in various calculated stresses. Many such models in addition have had other disadvantages, such as creation of residual stresses which moreover accumulated in repeated cycles when a body was loaded along an elastic closed strain path using tension, shear, compression and shear in the opposite direction until its fibers have returned back to their original position, or stress oscillation when a Jaumann rate based rate form of the constitutive equation of a material was used in an analysis when the body underwent large shearing deformations. The founders of ACE&CS Ltd at the Advanced Computing Engineering and Experimenting Conference (ACE-X 2014) in 2014 as the first presented their contribution titled a "Two-Dimensional Analytical Study on Objective Stress Rates", in which they proved that all the aforementioned disadvantages are actually caused by incorrect constitutive sides of the rate forms and that there are two rate forms of the constitutive equation only, based on the Oldroyd rate of the Kirchhoff stress and the Thruesdell rate of the Cauchy stress, where the constitutive equation sides can formally be expressed as an inner product of a fourth order elastic material tensor and a spatial strain rate tensor. For more information on the rate form based constitutive modelling please refer to the following paper:

    ÉCSI, Ladislav - ÉLESZTÖS, Pavel – JANČO, Roland. On the stress solution of hypoelastic material based models using objective stress rates. In Proceedings of the 15. Conference on Applied Mathematics, APLIMAT 2016, 2. - 4. 2. (2016), Bratislava.

  4. Contemporary mathematical models of a deformable body using large strain formulations might not be quite correct.

    The founders of ACE&CS Ltd at the Advanced Computing Engineering and Experimenting Conference (ACE-X 2015) in 2015 as the first presented a contribution titled "An Improved Fully Coupled Thermal-Structural Finite Element Model for Strain Path Dependent Materials Undergoing Large Deformations at Wide Range of Strain Rates", in which they proved that there might be serious flaws in current rate forms of constitutive equations of  a material using large strain formulation, which can be summarised as follows:

    In current rate forms of constitutive equations of materials using additive decomposition of a spatial strain rate tensor into an elastic part, a plastic part and a thermal part, a large strain form is used for the spatial strain rate tensor, but small strain forms are used for its elastic, plastic and thermal parts respectively. As a result, the evaluation of the elastic part of the spatial strain rate tensor, as a difference of the spatial strain rate tensor and the sum of its thermal and plastic parts, cannot be correct either. The authors also have shown that the product of a plastic multiplier and a yield surface normal can have different physical interpretation than a plastic part of the spatial strain rate tensor, which also allowed them to argue about the correctness of contemporary material models based on multiplicative decomposition of the deformation gradient into an elastic part, a plastic part and a thermal part.