Assoc. Prof. Piotr Kowalczyk, Ph.D., Dr. Habil., Eng.

Department of Information and Computational Science (ZIiNO)
Division of Computational Analysis of Advanced Structures (ZeKAZK)
position: professor IPPT
telephone: (+48) 22 826 12 81 ext.: 257
room: 421
e-mail: pkowalcz
personal site: http://bluebox.ippt.pan.pl/~pkowalcz

Doctoral thesis
1993-01-21Numeryczna analiza rozkładu naprężeń w miąższu płucnym z uwzględnieniem oddziaływań między szkieletem tkankowym a przepływającym powietrzem 
supervisor -- Prof. Michał Kleiber, Ph.D., Dr. Habil., Eng., IPPT PAN
492 
Habilitation thesis
2007-11-22Sensitivity analysis in finite element computations of elasto-plasticity931
 
Recent publications
1.Colabella L., Cisilino A.P., Häiat G., Kowalczyk P., Mimetization of the elastic properties of cancellous bone via a parameterized cellular material, Biomechanics and Modeling in Mechanobiology, ISSN: 1617-7959, DOI: 10.1007/s10237-017-0901-y, Vol.16, No.5, pp.1485-1502, 2017
Abstract:

Bone tissue mechanical properties and trabecular microarchitecture are the main factors that determine the biomechanical properties of cancellous bone. Artificial cancellous microstructures, typically described by a reduced number of geometrical parameters, can be designed to obtain a mechanical behavior mimicking that of natural bone. In this work, we assess the ability of the parameterized microstructure introduced by Kowalczyk (Comput Methods Biomech Biomed Eng 9:135–147, 2006. doi:10.1080/10255840600751473) to mimic the elastic response of cancellous bone. Artificial microstructures are compared with actual bone samples in terms of elasticity matrices and their symmetry classes. The capability of the parameterized microstructure to combine the dominant isotropic, hexagonal, tetragonal and orthorhombic symmetry classes in the proportions present in the cancellous bone is shown. Based on this finding, two optimization approaches are devised to find the geometrical parameters of the artificial microstructure that better mimics the elastic response of a target natural bone specimen: a Sequential Quadratic Programming algorithm that minimizes the norm of the difference between the elasticity matrices, and a Pattern Search algorithm that minimizes the difference between the symmetry class decompositions. The pattern search approach is found to produce the best results. The performance of the method is demonstrated via analyses for 146 bone samples.

Keywords:

Cancellous bone, Parameterized microstructure, Elastic properties, Homogenization, Symmetry classes, Optimization

Affiliations:
Colabella L.-CONICET-National University of Mar del Plata (AR)
Cisilino A.P.-CONICET-National University of Mar del Plata (AR)
Häiat G.-CNRS (FR)
Kowalczyk P.-IPPT PAN
2.Colabella L., Ibarra Pino A.A., Ballarre J., Kowalczyk P., Cisilino A.P., Calculation of cancellous bone elastic properties with the polarization-based FFT iterative scheme, International Journal for Numerical Methods in Biomedical Engineering, ISSN: 2040-7939, DOI: 10.1002/cnm.2879, Vol.33, No.11, pp.e2879-1-16, 2017
Abstract:

The Fast Fourier Transform–based method, originally introduced by Moulinec and Suquet in 1994 has gained popularity for computing homogenized properties of composites. In this work, the method is used for the computational homogenization of the elastic properties of cancellous bone. To the authors' knowledge, this is the first study where the Fast Fourier Transform scheme is applied to bone mechanics. The performance of the method is analyzed for artificial and natural bone samples of 2 species: bovine femoral heads and implanted femurs of Hokkaido rats. Model geometries are constructed using data from X‐ray tomographies, and the bone tissue elastic properties are measured using microindentation and nanoindentation tests. Computed results are in excellent agreement with those available in the literature. The study shows the suitability of the method to accurately estimate the fully anisotropic elastic response of cancellous bone. Guidelines are provided for the construction of the models and the setting of the algorithm.

Keywords:

accelerated FFT method, cancellous bone, homogenized elastic properties

Affiliations:
Colabella L.-CONICET-National University of Mar del Plata (AR)
Ibarra Pino A.A.-University of Minnesota (USA)
Ballarre J.-University of Mar del Plata (AR)
Kowalczyk P.-IPPT PAN
Cisilino A.P.-CONICET-National University of Mar del Plata (AR)
3.Kowalczyk P., Parametric constitutive model of plain-weave fabric reinforced composite ply, Advanced Composite Materials, ISSN: 0924-3046, DOI: 10.1080/09243046.2014.996959, Vol.25, No.3, pp.287-303, 2016
Abstract:

A computational model that allows to explicitly determine orthotropic elastic constants of plain-weave fabric-reinforced composite ply as functions of microstructure parameters has been developed in this study. These relationships are not given in the form of analytical formulae (as it is in the case of approximate analytical models) but in the form of an extensive database of numerically evaluated results for different microstructure instances and a numerical scheme that interpolates the results. To build the database, a standard finite-element-based homogenization technique of a periodic representative volume element is employed. As a result, a numerical algorithm is provided that may be easily employed in FE codes as a part of a regular constitutive subroutine. Sensitivity of the composite elastic constants with respect to the microstructure parameters is also directly available from the model.

Keywords:

fabric-reinforced composite, plain-weave fabric, homogenization, parametric constitutive equations, finite element analysis

Affiliations:
Kowalczyk P.-IPPT PAN
4.Kowalczyk P., Enhanced geometric model for numerical microstructure analysis of plain-weave fabric reinforced composite, Advanced Composite Materials, ISSN: 0924-3046, DOI: 10.1080/09243046.2014.898439, Vol.24, No.5, pp.411-429, 2015
Abstract:

Although there have been several numerical models used by different authors to model microstructural behaviour of a woven fabric-reinforced composite ply, they all suffer from geometric simplifications that may affect their validity or at least accuracy of results. This paper presents an enhanced model of a representative volume element RVE of this kind of composite with the plain-weave fabric pattern. Many important simplifications are overcome while the mathematical description remains simple. A dedicated FE mesh generator allows to reproduce all geometric details in the computational model. Computational examples of homogenization of orthotropic elastic constants illustrate application of the model.

Keywords:

geometric modelling, fabric-reinforced composite, plain-weave fabric, homogenization, finite element analysis

Affiliations:
Kowalczyk P.-IPPT PAN
5.Kowalczyk P., Rojek J., Stocki R., Bednarek T., Tauzowski P., Lasota R., Lumelskyy D., Wawrzyk K., NUMPRESS − integrated computer system for analysis and optimization of industrial sheet metal forming processes, HUTNIK - WIADOMOŚCI HUTNICZE, ISSN: 1230-3534, Vol.81, No.1, pp.56-63, 2014
Abstract:

The NUMPRESS System has been developed in IPPT PAN as a result of a project financially supported by European Regional Development Fund (within the Innovative Economy Programme) and is dedicated to small and middle enterprises dealing with sheet metal forming. The program consists of (i) an analytical module for analysis of forming processes with the finite element method, (ii) an optimization module controlling execution of the analytical module and performing optimization with respect to selected process parameters, in both deterministic and robust formulation, (iii) a reliability analysis module controlling execution of the analytical module to assess how random distribution of design parameters affects forming results, and (iv) a graphical user interface enabling communication between modules and easy definition of design parameters and optimization criteria. The analytical module consists of two independent programs up to the user's choice: NUMPRESS-Flow, a faster and less accurate program for implicit quasi-static analysis of rigid-viscoplastic shells (based on the flow approach) and NUMPRESS-Explicit, a program for explicit dynamical analysis of elastic-plastic and elastic-viscoplastic shells. Both programs are interfaced to a well-known commercial graphical pre- and postprocessor GiD. Fundamentals of formulations employed in the system and numerical examples are presented in the paper.

Keywords:

sheet metal forming, finite element method, deterministic and robust design optimization, reliability analysis

Affiliations:
Kowalczyk P.-IPPT PAN
Rojek J.-IPPT PAN
Stocki R.-IPPT PAN
Bednarek T.-IPPT PAN
Tauzowski P.-IPPT PAN
Lasota R.-IPPT PAN
Lumelskyy D.-IPPT PAN
Wawrzyk K.-IPPT PAN
6.Bednarek T., Kowalczyk P., Improvement of stability conditions, accuracy and uniqueness of penalty approach in contact modeling, COMPUTATIONAL MECHANICS, ISSN: 0178-7675, DOI: 10.1007/s00466-012-0775-x, Vol.51, No.6, pp.949-959, 2013
Abstract:

The main objective of this paper is to improve stability conditions, uniqueness and convergence of numerical analysis of metal forming processes with contact constraints enforced by the penalty method. A commonly known drawback of this approach is the choice of penalty factor values. When assumed too low, they result in inaccurate fulfillment of the constraints while when assumed too high, they lead to ill-conditioning of the equations system which affects stability and uniqueness of the solution. The proposed modification of the penalty algorithm consists in adaptive estimation of the penalty factor values for the particular system of finite element equations and for the assumed allowed inaccuracy in fulfillment of the contact constraints. The algorithm is tested on realistic examples of sheet metal forming. The finite element code based on flow approach formulation (for rigid-plastic and rigid-viscoplastic material model) has been used.

Keywords:

Contact modeling, Penalty approach, Metal forming, Deep drawing

Affiliations:
Bednarek T.-IPPT PAN
Kowalczyk P.-IPPT PAN
7.Bednarek T., Kowalczyk P., The sensitivity analysis of deep drawing process using flow approach, COMPUTER METHODS IN MATERIALS SCIENCE / INFORMATYKA W TECHNOLOGII MATERIAŁÓW, ISSN: 1641-8581, Vol.13, No.1, pp.22-29, 2013
Abstract:

The objective of the paper is the sensitivity analysis of deep drawing simulations using flow approach with respect to any design parameter. The sensitivity analysis is being implemented into the MFP code developed by IPPT PAN under project Numpress. First, the finite element formulation of flow approach in drawing simulations is presented. The mathematical formulation includes the consistent tangent viscosity matrix. As it is shown in the final sensitivity formulation, the tangent viscosity matrix is necessary in sensitivity calculations. Unfortunately the tangent matrix is asymmetric. The influence of the asymmetric contributions to viscosity matrix in sensitivity analysis is considered. The semi-analytical Direct Differential Method is used. This means that design derivatives of some terms are estimated by finite difference method and next substituted into analytical sensitivity formula. The mathematical formulae and the algorithm to build consistent tangent matrix and to perform sensitivity analysis are presented.

Keywords:

deep drawing, flow approach, sensitivity analysis

Affiliations:
Bednarek T.-IPPT PAN
Kowalczyk P.-IPPT PAN
8.Kowalczyk P., Parametric constitutive model of uni-directional fiber-matrix composite, FINITE ELEMENTS IN ANALYSIS AND DESIGN, ISSN: 0168-874X, DOI: 10.1016/j.finel.2011.09.015, Vol.50, pp.243-254, 2012
Abstract:

A computational model that allows to explicitly determine transversely isotropic elastic constants of uni-directional fiber–matrix composite tow as functions of microstructure parameters has been developed in this study. These relationships are not given in the form of analytical formulae (as it is in the case of approximate analytical models) but in the form of an extensive database of numerically evaluated results for different microstructure instances and a numerical scheme that interpolates the results. To build the database, a standard finite-element-based homogenization technique of a periodic RVE is employed. The technique is enhanced by introduction of averaging procedure over different shapes of the 2D fiber layout pattern in the tow cross-section. As a result, a numerical algorithm is provided that may be easily employed in FE codes as a part of a regular constitutive subroutine. Sensitivity of the composite elastic constants with respect to the microstructure parameters is also directly available from the model.

Keywords:

Uni-directional fiber–matrix composite, Parametric constitutive model, Finite element analysis, Homogenization, Representative volume element, Parameter sensitivity

Affiliations:
Kowalczyk P.-IPPT PAN
9.Wawrzyk K., Kowalczyk P., Zmodyfikowany algorytm poszukiwania kontaktu w zagadnieniach tłoczenia blach, HUTNIK - WIADOMOŚCI HUTNICZE, ISSN: 1230-3534, Vol.LXXIX, pp.28-30, 2012
Abstract:

Niniejsza praca dotyczy procedury poszukiwania kontaktu w symulacji numerycznej procesu tłoczenia blach. W pracy zaproponowano poprawkę do standardowego algorytmu poszukiwania kontaktu, pozwalającą na wyeliminowanie możliwych błędów polegających na źle wskazanym elemencie kontaktowym, bądź wskazaniu braku takiego elementu, co w konsekwencji prowadzi do błędnych wyników symulacji. Ponadto w pracy przeanalizowano koszt numeryczny przedstawionego algorytmu.

Keywords:

analiza kontaktu, tłoczenie blach

Affiliations:
Wawrzyk K.-IPPT PAN
Kowalczyk P.-IPPT PAN
10.Bednarek T., Kowalczyk P., Marczewski A., Sosnowski W., Improvement of stability conditions and uniqueness of penalty approach in contact modelling in sheet metal forming, COMPUTER METHODS IN MATERIALS SCIENCE / INFORMATYKA W TECHNOLOGII MATERIAŁÓW, ISSN: 1641-8581, Vol.11, No.2, pp.411-417, 2011
Abstract:

The main objective of this paper is to improve stability conditions, uniqueness and convergence of the flow approach algorithm with viscoplastic and plastic material models. In this paper, the problem of convergence and uniqueness of the problem of non-linear simulation of sheet metal forming processes modeled using rigid-viscoplastic material model is considered. In the numerical simulation of the deformation process MFP2D and MFP3D Finite Element programs were used. The simplicity of the algorithm is the main advantage of these codes, the Direct Differentiation method and optimization modules can be implemented in the source code. The numerical instability caused by high values of the condition number of the main system of equations is the main disadvantage of the codes. The penalty approach contact model used in the program makes the stiffness matrix condition number worse.

Keywords:

finite element method, sheet metal forming, computational stability, flow approach

Affiliations:
Bednarek T.-IPPT PAN
Kowalczyk P.-IPPT PAN
Marczewski A.-IPPT PAN
Sosnowski W.-IPPT PAN
11.Kowalczyk P., Simulation of orthotropic microstructure remodelling of cancellous bone, JOURNAL OF BIOMECHANICS, ISSN: 0021-9290, DOI: 10.1016/j.jbiomech.2009.09.045, Vol.43, pp.563-569, 2010
Abstract:

A computational model of adaptive bone remodelling is formulated as an optimization problem of instantaneous changes in microstructure that minimize a functional describing the structure quality rate. Microstructure is locally described by a set of scalar geometric parameters. Macroscopic (continuum) elastic properties are assumed orthotropic and expressed as known functions of the geometric parameters. Strain energy is considered the quality measure of bone at given load conditions.
The instantaneous rate of geometric parameters is postulated to minimize the rate of the quality functional. An optimization problem is formulated in the continuum description and then it is discretized both in space and time. Numerical simulations predict bone remodelling for femur without and with a hip endoprosthesis.

Keywords:

Adaptive bone remodelling, Orthotropy, Finite element method, Optimization

Affiliations:
Kowalczyk P.-IPPT PAN
12.Sosnowski W., Bednarek T., Kowalczyk P., Stability and uniqueness of flow approach algorithms in sheet metal forming simulations, COMPUTER METHODS IN MATERIALS SCIENCE / INFORMATYKA W TECHNOLOGII MATERIAŁÓW, ISSN: 1641-8581, Vol.10, No.1, pp.30-36, 2010
Abstract:

The objective of this paper is to improve stability conditions, uniqueness and convergence of the flow approach algorithm with rigid-viscoplastic and plastic material models. Two numerical codes, MFP2D and MFP3D, were used previously for practical industrial solutions (Sosnowski, 2001; Sosnowski, 1995; Sosnowski et al., 1992). Relative simplicity of both the codes allowed to include “exact” sensitivity calculations by direct differentiation method. This made it possible to perform very effective optimization of the whole sheet metal forming process simulation. One of significant drawbacks of rigid-viscoplastic shell approach is poor stability and convergence due to relatively high values of the condition number of the resulting system of equations. The reasons include the absence of elasticity terms in the constitutive material law and asymptotic character of the relationship between viscosity and effective plastic strain rate. Approximate character of the contact modeling (penalty approach) also affects conditioning of the system. This drawback can be overcome by some measures proposed in this paper.

Keywords:

sheet drawing, flow approach, matrix condition number

Affiliations:
Sosnowski W.-IPPT PAN
Bednarek T.-IPPT PAN
Kowalczyk P.-IPPT PAN
13.Błażkiewicz M., Kowalczyk P., Szkudelska H., Analiza ruchu kończyn dolnych podczas kroku basic step w aerobiku, ROZPRAWY NAUKOWE AWF WE WROCŁAWIU, ISSN: 0239-4375, Vol.26, pp.20-26, 2008
Abstract:

Step aerobics classes are offered at many gyms and fitness centers. It is distinguished from other forms of aerobics exercise by the use of an elevated platform (the step). The height can be tailored to individual taste by inserting risers under the step. The APAS (Ariel Performance Analysis System) was employed to obtain data needed for the analysis of movement. Six instructors’ motion was characterized at two different heights of the step (15 and 20 cm). The main objective of the paper is a description of kinematic parameters of the common moves done by the instructors. The detailed objectives concern description of the basic step technique and analysis of the position of the lower limb and of the body’s centre of gravity.

Keywords:

Key words: step aerobics, basic step, kinematographic analysis

Affiliations:
Błażkiewicz M.-other affiliation
Kowalczyk P.-IPPT PAN
Szkudelska H.-other affiliation
14.Wiśniewski K., Kowalczyk P., Turska E., Analytical DSA for explicit dynamics of elastic-plastic shells, COMPUTATIONAL MECHANICS, ISSN: 0178-7675, DOI: 10.1007/s00466-006-0068-3, Vol.39, No.6, pp.761-785, 2007
Abstract:

The paper presents an analytical constitutive design sensitivity analysis (DSA) algorithm for explicit dynamics of elastic-plastic finite rotation shells. Two explicit dynamical algorithms for finite rotation shells are presented, and the DSA is developed for the one formulated in terms of the rotation vector and its time derivatives, {ψ,ψ˙,ψ¨}. The hypo-elastic constitutive model based on the Green-McInnis-Naghdi stress rate is used to derive an incremental algorithm in terms of ‘back-rotated’ objects. The associative deviatoric Huber-Mises plasticity modified by plane stress conditions is implemented in the form suitable for finite rotation/small elastic strain increments. The analytical DSA is developed for the above-specified problem, with the design derivatives calculated w.r.t. material parameters. Design-differentiation of the dynamic algorithm and the scheme of handling the history data and the predicted values in differentiation, which is crucial in computing correct derivatives, are described. Besides, we show how to avoid Newton loops in the DSA algorithm, when such a loop is present in the constitutive algorithm. Numerical examples show that, despite a great complexity of the solution algorithm for the finite-rotation elastic-plastic shells, it is feasible to compute analytical design derivatives of very good accuracy.

Keywords:

Explicit dynamics, Finite rotation shell, Elastic-plastic material, Analytical Design Sensitivity Analysis for constitutive parameters

Affiliations:
Wiśniewski K.-IPPT PAN
Kowalczyk P.-IPPT PAN
Turska E.-Polish-Japanese Academy of Information Technology (PL)
15.Kowalczyk P., Design sensitivity analysis in large deformation elasto-plastic and elasto-viscoplastic problems, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.1592, Vol.66, pp.1234-1270, 2006
Abstract:

Implicit time integration algorithm derived by Simo for his large-deformation elasto-plastic constitutive model is generalized, for the case of isotropy and associative flow rule, towards viscoplastic material behaviour and consistently differentiated with respect to its input parameters. Combining it with the general formulation of design sensitivity analysis (DSA) for non-linear finite element transient equilibrium problem, we come at a numerically efficient, closed-form finite element formulation of DSA for large deformation elasto-plastic and elasto-viscoplastic problems, with various types of design variables (material constants, shape parameters). The paper handles several specific issues, like the use of a non-algorithmic coefficient matrix or sensitivity discontinuities at points of instantaneous structural stiffness change. Computational examples demonstrate abilities of the formulation and quality of results.

Keywords:

design sensitivity analysis, finite element method, large deformations, plasticity, viscoplasticity

Affiliations:
Kowalczyk P.-IPPT PAN
16.Kowalczyk P., Orthotropic properties of cancellous bone modelled as parameterized cellular material, COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING, ISSN: 1025-5842, DOI: 10.1080/10255840600751473, Vol.9, pp.135-147, 2006
Abstract:

Analysis of stresses and strains in bone tissues and simulation of their adaptive remodelling require exhaustive information about distribution of constitutive properties of cancellous bone and their relationships to microstructural parameters. Homogenization of “equivalent” trabecular microstructures appears to be an advantageous tool for this task. In this study, parameterized orthotropic constitutive models of cancellous bone are derived from finite element analysis of repeatable microstructure cells. The models, based on a space-filling dodecahedron, are fully three-dimensional and are parameterized with four shape parameters. Variation of the parameters allows to imitate most of typical microstructure patterns observed in real bones, along with a variety of intermediate geometries. Finite element models of cells are generated by a special-purpose structured mesh generator for any arbitrary set of shape parameter values. Static numerical tests are performed for an exhaustive number of parameter value sets (microstructure instances). Coefficients of elastic orthotropic stiffness matrix are determined as tabularized functions of elastic constants versus the shape parameters. Additionally, they are correlated to apparent density and principal fabric tensor values. Comparison of the results with micro-FE data obtained for a large set of cancellous bone specimens proves a good agreement.

Keywords:

Cancellous bone, Equivalent microstructure, Constitutive modelling, Elastic properties, Orthotropy, Fabric

Affiliations:
Kowalczyk P.-IPPT PAN
17.Kleiber M., Hien T.D., Antúnez H., Kowalczyk P. , Parameter sensitivity of elastoplastic response, Engineering Computations, ISSN: 0264-4401, DOI: 10.1108/02644409510799604, Vol.12, No.3, pp.263-280, 1995
Abstract:

The general problem of sizing, material and loading parameter sensitivity of non‐linear systems is presented. Both kinematic and path‐dependent material non‐linearities are considered; non‐linear sensitivity path is traced by an incremental solution strategy. The variational approach employed is quite general and can be employed for studying sensitivity of various path‐dependent highly non‐linear phenomena. Both the direct differentiation method (DDM) and adjoint system method (ASM) are discussed in the context of continuum and finite element mechanics. The merits of using the consistent tangent matrix and the necessity of accumulation of design derivatives of stresses and internal parameters are indicated. Aspects of sensitivity problems in metal forming are also discussed. A number of examples illustrate the paper.

Keywords:

Direct differentiation method, Adjoint system method, Metal forming

Affiliations:
Kleiber M.-IPPT PAN
Hien T.D.-IPPT PAN
Antúnez H.-IPPT PAN
Kowalczyk P. -IPPT PAN
18.Kowalczyk P., Numeryczna analiza rozkładu naprężeń w miąższu płucnym z uwzględnieniem oddziaływań między szkieletem tkankowym a przepływającym powietrzem (Praca doktorska), Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.1, pp.1-92, 1993

List of recent monographs
1.
474
Kleiber M., Kowalczyk P., Introduction to Nonlinear Thermomechanics of Solids, Springer, pp.1-345, 2016
2.
48
Kleiber M., Kowalczyk P., Wprowadzenie do nieliniowej termomechaniki ciał odkształcalnych, Instytut Podstawowych Problemów Techniki PAN, pp.1-360, 2011
3.
77
Kotulski Z.A., Kowalczyk P., Sosnowski W., Selected topics of contemporary solid mechanics. Proceedings of the 36th Solid Mechanics Conference, Gdańsk, Poland, September 9–12, 2008, IPPT PAN (Warszawa), Kotulski Z.A., Kowalczyk P., Sosnowski W. (Red.), pp.1-442, 2008
4.
78
Kowalczyk P., Sensitivity analysis in finite element computations of elasto-plasticity, Rozprawa habilitacyjna, IPPT Reports on Fundamental Technological Research, 7, pp.1-212, 2006
List of chapters in recent monographs
1.
437
Kowalczyk P., Biomechanika i Inżynieria Rehabilitacyjna, rozdział: Badania modelowe z wykorzystaniem MES w biomechanice, Akademicka Oficyna Wydawnicza EXIT, pp.363-378, 2015

Conference papers
1.Rojek J., Nosewicz S., Maździarz M., Kowalczyk P., Wawrzyk K., Lumelskyj D., Modeling of a Sintering Process at Various Scales, Procedia Engineering, ISSN: 1877-7058, DOI: 10.1016/j.proeng.2017.02.210, Vol.177, pp.263-270, 2017
Abstract:

This paper presents modeling of a sintering process at various scales. Sintering is a powder metallurgy process consisting in consolidation of powder materials at elevated temperature but below the melting point. Sintering models at the atomistic, microscopic and macroscopic scales have been presented. Sintering is a process governed by diffusion therefore the atomistic modeling using the molecular dynamics has been focused on investigation of the diffusion process. The micromechanical model has been developed within the framework of the discrete element method. It allows us to consider microstructure and its changes during sintering. The macroscopic model is based on the continuum phenomenological approach. It combines elastic, thermal and viscous creep deformation. The methodology to determine macroscopic quantities: stress, strains and constitutive viscous properties from the discrete element simulations has been presented. Possibilities of the developed models have been demonstrated by applying them to simulation of sintering of the intermetallic NiAl powder. Own experimental results have been used to calibrate and validate numerical models.

Keywords:

sintering, modeling, discrete element method, diffusion, molecular dynamics, macroscopic model

Affiliations:
Rojek J.-IPPT PAN
Nosewicz S.-IPPT PAN
Maździarz M.-IPPT PAN
Kowalczyk P.-IPPT PAN
Wawrzyk K.-IPPT PAN
Lumelskyj D.-IPPT PAN
2.Sosnowski W., Bednarek T., Kowalczyk P., Badanie stabilności i jednoznaczności algorytmów teorii plastycznego płynięcia stosowanych w symulacji tłoczenia blach, KomPlasTech 2010, XVII Konferencja Informatyka w Technologii Metali, 2010-01-10/01-13, Białka Tatrzańska (PL), pp.1-12, 2010
Abstract:

W niniejszej pracy rozważamy problem zbieżności i jednoznaczności rozwiązania nieliniowego problemu symulacji procesów tłoczenia blach modelowanych z wykorzystaniem sztywno-lepkoplastycznego modelu materiału. Do symulacji wykorzystujemy programy MFP2D i MFP3D sprawdzone w kilku zastosowaniach przemysłowych. Zaletą obydwóch kodów numerycznych jest względna prostota algorytmu, a co za tym idzie możliwość dokładnej analizy wrażliwości i optymalizacji procesu tłoczenia blach. Niestety oba programy mają poważną wadę związaną z przyjętym modelem materiału. W trakcie obliczeń obserwujemy niestabilność wywołaną stosunkowo wysokim wskaźnikiem uwarunkowania macierzy układu równań. Dodatkowo przyjęty model kontaktu zawierający funkcję kary pogarsza wskaźnik uwarunkowania macierzy sztywności. Celem badań jest między innymi poprawienie tego wskaźnika.

Keywords:

tłoczenie blach, teoria plastycznego płynięcia, wskaźnik uwarunkowania macierzy

Affiliations:
Sosnowski W.-IPPT PAN
Bednarek T.-IPPT PAN
Kowalczyk P.-IPPT PAN
3.Kowalczyk P., Computational model for anisotropic microstructure remodelling of cancellous bone, CMM 2007, 17th International Conference on Computer Methods in Mechanics, 2007-06-19/06-22, Łódź-Spała (PL), No.082020, pp.1-5, 2007
Abstract:

A computational model of adaptive bone remodelling is formulated as an optimization problem of instantaneous changes in microstructure that minimize a functional describing the structure quality rate. Microstructure is locally described by a set of scalar geometric parameters. Macroscopic (continuum) elastic properties are assumed anisotropic and expressed as known functions of the geometric parameters. Strain energy is considered as the quality measure of bone at given load conditions. Rate of geometric parameters is postulated to minimize the rate of the quality functional. An optimization problem is formulated in the continuum description and then iit is discretized both in space and time, taking finally a form of a system of nonlinear algebraic equations on unknown microstructure parameter increments, repeatedly solved in subsequent time instants.

Keywords:

adaptive remodelling, anisotropy, finite element method, optimization

Affiliations:
Kowalczyk P.-IPPT PAN
4.Kowalczyk P., Parameterized orthotropic cellular microstructures as mechanical models of cancellous bone, ECCM 2006, 3rd European Conference on Computational Mechanics, 2006-06-05/06-08, Lisbon (PT), No.1151, pp.1-13, 2006
Abstract:

Constitutive properties of cancellous bone depend on microstructural geometry. Evaluation of the interrelationship is a crucial issue in analysis of stresses and strains in bone tissues and simulation of their remodelling. Known limitations of experimental methods as well as of the micro-FE techniques make the analysis and homogenization of ‘equivalent’ trabecular microstructures an advantageous tool for this task. In this study, parameterized orthotropic constitutive models of cancellous bone are derived from finite element analysis of repeatable microstructure cells. The models are fully three-dimensional, have realistic curvilinear shapes and are parameterized with four shape parameters. Variation of the parameters allows to imitate most of the typical microstructure patterns observed in real bones, along with variety of intermediate geometries. The models are a geometrically enhanced version of those presented in the author’s previous work. Static numerical tests are performed with the finite element method for an exhaustive number of parameter value sets (microstructure instances). Repeatability of the microstructure allows to test only a sigle cell with appropriate boundary conditions. Values of computed stresses and strains allow to determine all coefficients of elastic orthotropic stiffness matrix. Results have a form of tabularized functions of elastic constants versus the shape parameters. Comparison of the results with micro-FE data obtained for a large set of cancellous bone specimens proves a good agreement.

Keywords:

Cancellous Bone, Equivalent Microstructure, Constitutive Modelling, Elastic Properties, Orthotropy, Fabric

Affiliations:
Kowalczyk P.-IPPT PAN

Conference abstracts
1.Wawrzyk K., Nosewicz S., Rojek J., Kowalczyk P., A constitutive model and numerical simulation of sintering processes at macroscopic level, CMM-2017, 22nd International Conference on Computer Methods in Mechanics, 2017-09-13/09-16, Lublin (PL), pp.MS02-13-MS02-14, 2017
Abstract:

This document presents modelling of single-phase powder sintering processes at the macroscopic level. In particular, its constitutive formulation, numerical implementation and numerical test are described. Numerical tests were carried out for a cylindrical specimen under hydrostatic and uniaxial pressure. Results of macroscopic analysis are compared against the microscopic model results.

Keywords:

sintering porcesses, numerical analysis, multiscale modelling

Affiliations:
Wawrzyk K.-IPPT PAN
Nosewicz S.-IPPT PAN
Rojek J.-IPPT PAN
Kowalczyk P.-IPPT PAN
2.Rojek J., Nosewicz S., Maździarz M., Kowalczyk P., Wawrzyk K., Multiscale modelling of powder sintering processes, COMPLAS 2017, XIV International Conference on Computational Plasticity. Fundamentals and Applications, 2017-09-05/09-07, Barcelona (ES), pp.1-1, 2017
3.Nosewicz S., Rojek J., Maździarz M., Kowalczyk P., Wawrzyk K., Chmielewski M., Pietrzak K., Multiscale modeling of pressure-assisted sintering process, EUROMAT 2017, European Congress and Exhibition on Advanced Materials and Processes, 2017-09-17/09-22, Thessaloniki (GR), pp.1, 2017
4.Kowalczyk P., Parametric Constitutive Modelling of Cancellous Bone, IAMMC 2017, Interaction of Applied Mathematics and Mechanics Conference, 2017-05-09/05-11, Paris (FR), pp.11-12, 2017
5.Rojek J., Nosewicz S., Maździarz M., Kowalczyk P., Wawrzyk K., Modelling of sintering at atomistic, microscopic and macroscopic scales, Komplastech 2017, XXIV International Conference on Computer Methods in Materials Technology, 2017-01-15/01-18, Zakopane (PL), pp.126-128, 2017
6.Rojek J., Kowalczyk P., Nosewicz S., Jurczak K., Wawrzyk K., Micro-macro relationships from discrete element simulations of sintering, ECCOMAS 2016, European Congress on Computational Methods in Applied Sciences and Engineering, 2016-06-05/06-10, Hersonissos (GR), pp.1, 2016
Keywords:

sintering, discrete element method, multi-scale modeling

Affiliations:
Rojek J.-IPPT PAN
Kowalczyk P.-IPPT PAN
Nosewicz S.-IPPT PAN
Jurczak K.-IPPT PAN
Wawrzyk K.-IPPT PAN
7.Wawrzyk K., Kowalczyk P., Macroscopic constitutive model of sintering processes and its numerical implementation, SolMech 2016, 40th Solid Mechanics Conference, 2016-08-29/09-02, Warszawa (PL), No.P210, pp.1-2, 2016
Keywords:

sintering, constitutive model

Affiliations:
Wawrzyk K.-IPPT PAN
Kowalczyk P.-IPPT PAN
8.Rojek J., Nosewicz S., Maździarz M., Kowalczyk P., Wawrzyk K., Modelling of powder sintering at various scales, SolMech 2016, 40th Solid Mechanics Conference, 2016-08-29/09-02, Warszawa (PL), No.P193, pp.1-2, 2016
Keywords:

sintering, multiscale modelling

Affiliations:
Rojek J.-IPPT PAN
Nosewicz S.-IPPT PAN
Maździarz M.-IPPT PAN
Kowalczyk P.-IPPT PAN
Wawrzyk K.-IPPT PAN
9.Kowalczyk P., Rojek J., Stocki R., Bednarek T., Tauzowski P., Lasota R., Lumelskyy D., Wawrzyk K., NUMPRESS – integrated computer system for analysis and optimization of industrial sheet metal forming processes: examples of use, AutoMetForm/SFU 2014, New Materials for Vehicle Components, 2014-11-03/11-05, Freiburg (DE), pp.284-286, 2014
Abstract:

This paper presents NUMPRESS System that has been developed in IPPT PAN as a result of a project financially supported by European Regional Development Fund (within the Innovative Economy Programme) and is dedicated to small and middle enterprises dealing with sheet metal forming. It seems undoubted that efficient design of an industrial sheet forming process requires reliable computer simulations and a tool for numerical optimization of the process parameters. It has to be also admitted that. among small and medium enterprises (SME) in this industrial branch, there are many who do not use any such numerical tools in their practice.
Computer simulation of sheet metal forming processes is a very specific branch of computational mechanics. Finite element systems dedicated strictly to this kind of processes are needed and actually present on the market. Commercial systems (like Autoform, PAM-Stamp, Stampack, etc.) are, due to their prices, usually beyond financial ability of SME.

Design of the drawing process and tools, i.e. choice of proper values of several design parameters, require efficient optimization strategy. In this process, random character of at least some of the parameters has to be taken into account. In view of this fact, the traditional, deterministic approach to optimization is insufficient and elements of robust design optimization techniques and reliability analysis have to be included in the formulation of the optimization problem. It has to be admitted that, even if some of the mentioned commercial simulation systems offer numerical optimization modules, not all of them reach beyond the deterministic concept of the optimization process.

Keywords:

sheet metal forming, finite element method, deterministic and robust design optimization, reliability analysis

Affiliations:
Kowalczyk P.-IPPT PAN
Rojek J.-IPPT PAN
Stocki R.-IPPT PAN
Bednarek T.-IPPT PAN
Tauzowski P.-IPPT PAN
Lasota R.-IPPT PAN
Lumelskyy D.-IPPT PAN
Wawrzyk K.-IPPT PAN
10.Kowalczyk P., Rojek J., Stocki R., Bednarek T., Tauzowski P., Lasota R., Lumelskyy D., Wawrzyk K., NUMPRESS – integrated computer system for analysis and optimization of industrial sheet metal forming processes: numerical investigation of square cup drawing, SolMech 2014, 39th Solid Mechanics Conference, 2014-09-01/09-05, Zakopane (PL), pp.237-238, 2014
Abstract:

This paper presents basic features of the NUMPRESS system and some examples ofuse. The system has been developed at IPPT PAN as a result of a project financially supported by European Regional Development Fund and is dedicated to small and middle enterprises (SME) dealing with sheet metal forming. The program consists of (i) an analytical finite element method module (ii) an optimization module, (iii) a reliability analysis module, and (iv) a graphical user interface enabling communication between modules. The analytical module consists of two independent programs up to the user’s choice: NUMPRESS-Flow, a faster and less accurate program for implicit quasi-static analysis of rigid-viscoplastic shells (based on the flow approach) and NUMPRESS-Explicit, a program for explicit dynamical analysis of elastic-plastic shells. Both programs are interfaced to a well-known commercial graphical pre-and postprocessor GiD.

Keywords:

sheet metal forming, finite element method, deterministic and robust design optimization, reliability analysis

Affiliations:
Kowalczyk P.-IPPT PAN
Rojek J.-IPPT PAN
Stocki R.-IPPT PAN
Bednarek T.-IPPT PAN
Tauzowski P.-IPPT PAN
Lasota R.-IPPT PAN
Lumelskyy D.-IPPT PAN
Wawrzyk K.-IPPT PAN
11.Bednarek T., Kowalczyk P., Sensitivity analysis of deep drawing process with rigid-viscoplastic material model, CMM 2013, 20th International Conference on Computer Methods in Mechanics, 2013-08-27/08-31, Poznań (PL), No.TS02, pp.13-14, 2013
Abstract:

The objective of the paper is formulation of sensitivity analysis for flow approach simulations of deep drawing problems with respect to arbitrary design parameters. First, finite element formulation of the primary problem is presented. Its important feature is the full algorithmic tangent viscosity matrix which, as it will be shown, is a necessary tool in sensitivity calculations. The algorithmic (consistent) tangent matrix is unfortunately asymmetric, which is addressed in our considerations. The semi-analytical formulation of sensitivity is used, which means that some complex design derivatives in the sensitivity equations are estimated by finite difference method. The finite difference method will be used as a reference method for verification of the sensitivity results.

Keywords:

finite element method, flow approach, sensitivity analysis

Affiliations:
Bednarek T.-IPPT PAN
Kowalczyk P.-IPPT PAN
12.Bednarek T., Kowalczyk P., Adaptive estimation of penalty factors in contact modelling, SolMech 2012, 38th Solid Mechanics Conference, 2012-08-27/08-31, Warszawa (PL), pp.42-43, 2012
Keywords:

finite element method, contact analysis, sheet metal forming

Affiliations:
Bednarek T.-IPPT PAN
Kowalczyk P.-IPPT PAN
13.Wawrzyk K., Kowalczyk P., Modified contact search algorithm for sheet metal forming, SolMech 2012, 38th Solid Mechanics Conference, 2012-08-27/08-31, Warszawa (PL), pp.68-69, 2012
Keywords:

finite element method, contact analysis, sheet metal forming

Affiliations:
Wawrzyk K.-IPPT PAN
Kowalczyk P.-IPPT PAN
14.Bednarek T., Kowalczyk P., Improvement of penalty approach in contact modeling, CMM 2011, 19th International Conference on Computer Methods in Mechanics, 2011-05-09/05-12, Warszawa (PL), pp.127-128, 2011
Abstract:

An improved approach to penalty modeling in contact mechanics is proposed. The presented algorithm enables evaluation of the optimum values of the penalty factor for each constrained degree of freedom in the finite element model. The values are chosen so as to ensure desired accuracy in fulfillment of the geometric constraints while keeping the condition number of the modified stiffness matrix at a moderate level. Thus, the main weakness for which the penalty approach is often criticised — excessive worsening of the system conditioning—is fairly limited. Numerical examples confirm advantages of the method.

Keywords:

contact modeling, penalty approach, matrix condition number

Affiliations:
Bednarek T.-IPPT PAN
Kowalczyk P.-IPPT PAN
15.Kowalczyk P., Orthotropic remodelling of cancellous bone based on a parametric constitutive model - discussion of local microstructure constraints, Biomechanics 2010, International Conference of the Polish Society of Biomechanics, 2010-08-25/08-28, Warszawa (PL), pp.113-114, 2010
Abstract:

In this study, a numerical model that allows to simulate the process of anisotropic remodelling of cancellous bone is presented. The bone is treated as continuum with linear elastic anisootropic mechanical properties that result from predefined microstructure topology and parameterized geometric proportions of trabeculae. Elastic constants and relative density are explicitly known functions of the geometric parameters. The microstructure parameters (including orientation directions) are non-uniformly distributed in the bone volume and subject to changes in time according to a remodelling rule that takes the form of minimization of the elastic strain energy rate. Special attention is focused on constraints in the optimization procedure that allow to eliminate unrealistic microstructure instances.

Keywords:

cancellous bone, constitutive model, orthotropy, bone remodelling

Affiliations:
Kowalczyk P.-IPPT PAN
16.Kowalczyk P., Parametric model of uni-directional fiber-matrix composite, SolMech 2010, 37th Solid Mechanics Conference, 2010-09-06/09-10, Warszawa (PL), pp.364-365, 2010
Keywords:

Uni-directional fiber–matrix composite, Parametric constitutive model, Finite element analysis, Homogenization, Representative volume element, Parameter sensitivity

Affiliations:
Kowalczyk P.-IPPT PAN
17.Kowalczyk P., Orthotropic model of cancellous bone. Application to simulation of adaptive remodelling, SolMech 2008, 36th Solid Mechanics Conference, 2008-09-09/09-12, Gdańsk (PL), pp.30-31, 2008
Abstract:

A numerical model that allows to simulate the process of anisotropic remodelling of cancellous bone is presented. The bone is treated as continuum with linear elastic orthotropic mechanical properties. Elastic constants and relative density are explicitly known functions of geometric parameters of microstructure. The parameters are nonuniformly distributed in the bone volume. The remodelling rule is an optimization problem in which the “cost” functional is a time rate of a certain global measure of bone quality at a given load state. Instantaneous rates of the parameters are supposed to minimize the functional. The numerically predicted evolution of the parameters is obtained from the time integration of the results of the instantaneous optimization problem.

Keywords:

cancellous bone, constitutive model, orthotropy, bone remodelling

Affiliations:
Kowalczyk P.-IPPT PAN
18.Wiśniewski K., Kowalczyk P., Turska E., DSA for Elastic-plastic Shells and Explicit Dynamics, 8th U.S. National Congress on Computational Mechanics, 2005-07-24/07-28, Austin, Texas (US), No.1681, pp.1, 2005
Keywords:

design sensitivity analysis, finite element method, shell structures, elasto-plasticity

Affiliations:
Wiśniewski K.-IPPT PAN
Kowalczyk P.-IPPT PAN
Turska E.-Polish-Japanese Academy of Information Technology (PL)
19.Wiśniewski K., Kowalczyk P., Turska E., DSA for elastic-plastic finite rotation shells under dynamic loads, ICTAM XXI, 21st International Congress of Theoretical and Applied Mechanics, 2004-08-15/08-21, Warszawa (PL), No.12679, pp.361, 2004
Keywords:

Design sensitivity analysis, finite element method, finite rotations, shell elements

Affiliations:
Wiśniewski K.-IPPT PAN
Kowalczyk P.-IPPT PAN
Turska E.-Polish-Japanese Academy of Information Technology (PL)
20.Wiśniewski K., Kowalczyk P., Turska E., DSA for elastic-plastic finite rotation shells under dynamic loads, ICTAM04, 21st International Congress of Theoretical and Applied Mechanics, 2004-08-15/08-21, Warszawa (PL), No.12679, pp.1-2, 2004
Abstract:

The paper describes a constitutive algorithm for elastic-plastic finite rotation shells and explicit dynamics with design derivatives calculated w.r.t. We show that despite a great complexity of the solution algorithm for the finite-rotation elastic-plastic shells, it is feasible to compute analytical design derivative of this algorithm, and the yielded sensitivities are of very good accuracy.

Keywords:

design sensitivity analysis, finite elment method, shell structures, dynamics, finite rotations

Affiliations:
Wiśniewski K.-IPPT PAN
Kowalczyk P.-IPPT PAN
Turska E.-Polish-Japanese Academy of Information Technology (PL)