Institute of Fundamental Technological Research
Polish Academy of Sciences

Staff

Prof. Józef Ignaczak, PhD, DSc

Department of Theory of Continuous Media and Nanostructures (ZTOCiN)
Analytical Mechanics and Field Theory (PMAiTP)
retiree
e-mail:

Doctoral thesis
1960 Niektóre przypadki koncentracji naprężeń cieplnych 
supervisor -- Prof. Witold Nowacki, PhD, DSc, IPPT PAN
 
Habilitation thesis
1963 Zagadnienie zupełności dla naprężeniowych równań ruchu w liniowej teorii sprężystości  
Professor
1972 Title of professor
Supervision of doctoral theses
1.  1985 Bem Zbigniew  
()
Ciągła zależność rozwiązania od danych w termosprężystości z czasami relaksacji 
2.  1984 Klecha Tadeusz   Fale powierzchniowe w niejednorodnej izotropowej półprzestrzeni sprężystej 
3.  1983 Jakubowska Matylda   Wzór Kirchhoffa dla ciała termosprężystego 
4.  1983 Biały Jerzy  
()
Obszar wpływu w termosprężystości ze skończonymi falowymi prędkościami 
5.  1982 Gładysz Jacek  
(PWr)
Splotowe zasady wariacyjne w termosprezystosci ze skonczonymi predkosciami falowymi 
6.  1978 Iwaniec Grażyna   Zupełne rozwiązania naprężeniowych równań w liniowej elastodynamice 
7.  1969 Rożnowski Tadeusz   Dwuwymiarowe zagadnienia brzegowe termosprężystości z ruchomym polem temperatury 
8.  1969 Rao C.R.A.  
(Monash University)
Separation of the stress equations of motion in nonhomogeneous isotropic elastic media 

Recent publications
1.  Ignaczak J., Stress characterization of elastodynamics for a rotating cylinder, Mathematics and Mechanics of Complex Systems, ISSN: 2325-3444, DOI: 10.2140/memocs.2021.9.143, Vol.9, No.2, pp.143-151, 2021

Abstract:
In the present paper, the stress characterization of elastodynamics for a rotating inhomogeneous transversely isotropic cylinder under plane strain conditions is proposed. It is assumed that the geometrical axis of the cylinder coincides with the axis of rotational symmetry of the cylinder. The cylinder rotates together with the Cartesian coordinate system xi (i=1,2,3), in which the geometrical axis of the cylinder coincides with the x3-axis, with a uniform angular velocity Ω in such a way that the acceleration of the cylinder is a sum of three components: (i) classical acceleration, (ii) centripetal acceleration, and (iii) Coriolis acceleration. It is shown that the propagation of an elastic wave in the 3D rotating cylinder can be described by a solution to the associated 2D pure stress initial-boundary value problem. Such a reduction of the 3D problem to the 2D one is based on the theorem on an alternative representation of the displacement vector field u in terms of the stress field S. An example of a complete pure stress formulation of the traction initial-boundary value problem is presented.

Keywords:
stress language of elastodynamics, rotating cylinder, classical acceleration, centripetal acceleration, Coriolis acceleration, transversely isotropic inhomogeneous elastic materials, completeness of stress formulation, natural stress traction initial-boundary value problem

Affiliations:
Ignaczak J. - IPPT PAN
2.  Ignaczak J., Stress-heat flux characterization of linear dynamic coupled thermoelasticity for an inhomogeneous isotropic infinite cylinder under plane strain conditions and zero heat flux normal to the plane, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495739.2018.1492358, Vol.41, pp.1201-1211, 2018

Abstract:
Stress-heat flux characterization of linear dynamic coupled thermoelasticityfor an inhomogeneous isotropic infinite cylinder under plane strain conditions and zero heat-flux normal to the plane is presented. It is shown that for a bounded cross-section of the cylinder, a 3D stress-heat flux process is generated by a 2D one, and a uniqueness theorem for the associated 2D initial-boundary value problem is established. In addition, an asymptotic approach to the 2D stress-heat flux initial-boundary value problem, in the form of a power series with respect to a small thermoelastic coupling field, is proposed. Also, Green' s formulas for time-periodic complex-valued solutions to 2D stress-heat flux field equations are obtained; and the existence of a globally constrained real-valued periodic and attenuated on the timeaxis stress-heat flux mode satisfying homogeneous natural boundary conditions is proved. The stress-heat flux characterization covers a large class of FGM's with physical properties smoothly distributed over the cross-section of the infinite cylinder. The results obtained are complementary to those of linear dynamic coupled thermoelasticity published up to date and should prove useful for a number of researchers in the field.

Keywords:
existence of a stress-heat flux mode, Green's formulas, isotropic inhomogeneous media, linear dynamic coupled thermoelasticity, stressheat flux characterization, stress-heat flux field equations of linear thermo-elastodynamics, uniqueness theorem

Affiliations:
Ignaczak J. - IPPT PAN
3.  Ignaczak J., Domański W., An asymptotic approach to one-dimensional model of nonlinear thermoelasticity at low temperatures and small strains, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495739.2016.1276872, Vol.40, No.8, pp.1030-1039, 2017

Abstract:
A one-dimensional nonlinear homogeneous isotropic thermoelastic model with an elastic heat flow at low temperatures and small strains is analyzed using the method of weakly nonlinear asymptotics. For such a model, both the free energy and the heat flux vector depend not only on the absolute temperature and strain tensor but also on an elastic heat flow that satisfies an evolution equation. The governing equations are reduced to a matrix partial differential equations, and the associated Cauchy problem with a weakly perturbed initial condition is solved. The solution is given in the form of a power series with respect to a small parameter, the coefficients of which are functions of a slow variable that satisfy a system of nonlinear second-order ordinary differential transport equations. A family of closed-form solutions to the transport equations is obtained. For a particular Cauchy problem in which the initial data are generated by a closed-form solution to the transport equations, the asymptotic solution in the form of a sum of four traveling thermoelastic waves admitting blow-up amplitudes is presented.

Keywords:
low temperatures, nonlinear thermoelasticity, small strains, weakly nonlinear asymptotics

Affiliations:
Ignaczak J. - IPPT PAN
Domański W. - Military University of Technology (PL)
4.  Ignaczak J., Stress characterization of elastodynamics for an inhomogeneous transversely isotropic infinite cylinder under plane strain conditions, Mechanics Research Communications, ISSN: 0093-6413, DOI: 10.1016/j.mechrescom.2015.02.004, Vol.68, pp.40-45, 2015

Abstract:
Stress characterization of isothermal elastodynamics for an inhomogeneous transversely isotropic infinite cylinder under plane strain conditions is presented. The cylinder, referred to the Cartesian coordinates xi (i = 1,2,3) and denoted here by View the MathML sourceBi(3), is identified with an infinite solid cylinder of which the rotational symmetry axis coincides with the x3-axis, and the geometrical axis coincides with the xi-axis (i = 1,2,3); and the plane strain conditions exist in the plane xi = 0, (i = 1,2,3). A cross-section of the cylinder View the MathML sourceBi(3) with the plane xi = 0 is denoted by View the MathML sourceCi(3). It is shown that a 3D stress wave Sij (i,j = 1,2,3) propagating in the cylinder View the MathML sourceBi(3) is generated by a solution to a 2D pure stress initial-boundary value problem for View the MathML sourceCi(3), and a uniqueness theorem for the 2D problem is established. In particular, a pure stress initial boundary value problem for View the MathML sourceC3(3) involving only two (out of five) elastic moduli: c11 and c12 is formulated, and it is shown that the problem accommodates two types of the surface stress wave problems for a transversely isotropic semi-space with a traction free boundary and with an inhomogeneity depending on its depth. The first type is obtained when View the MathML sourceC3(3) is the semi-space: |x1|<∞, 0
The results obtained should prove useful for both the analytical and numerical studies of the surface stress waves in an inhomogeneous transversely isotropic elastic semi-space under plane strain conditions.

Keywords:
Stress characterization, Isothermal elastodynamics, Transversely isotropic inhomogeneous media, Functionally graded materials (FGM), Plane strain stress equations of motion, Stress-rate energy of linear elastodynamics

Affiliations:
Ignaczak J. - IPPT PAN
5.  Ignaczak J., Stress Characterization of Nonisothermal Elastodynamics for Nonhomogeneous Anisotropic Body under Plane Strain Conditions, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495739.2014.985554, Vol.38, No.2, pp.156-164, 2015

Abstract:
Stress characterization of non-isothermal elastodynamics for an anisotropic nonhomogeneous infinite cylinder under plane strain conditions is presented. The cylinder is referred to the Cartesian coordinates x i  (i = 1, 2, 3) in which the axis of the cylinder is parallel to the x 3-axis and a cross-section of the cylinder at x 3 = 0, denoted by C, is a domain of the time-dependent stresses S ij = S ij (x α, t), [i, j = 1, 2, 3; α = 1, 2; x α ∈ C; t ≥ 0]. The density of the cylinder ρ, the compliance tensor K ijkl [i, j, k, l = 1, 2, 3], and the stress-temperature tensor M ij depend on x 2 only, while a thermomechanical load that complies with the plane strain conditions, depends on (x 1, x 2) ∈ C and time t ≥ 0 only. It is shown that S ij = S ij (x α, t) is generated by a unique solution S αβ = S αβ(x γ, t), [α, β, γ = 1, 2; t ≥ 0] to a pure stress initial-boundary value problem of nonisothermal elastodynamics on C × [0, ∞), and the in-plane stress components generate the out-of plane stress components provided the inner product of a compliance dependent tensor field and the tensor does not vanish. Also, a body-force analogy for S αβ = S αβ(x γ, t) is formulated from which it follows that S αβ = S αβ(x γ, t) can be identified with a solution to a pure stress initial-boundary value problem of isothermal elastodynamics. The stress characterization presented here should prove useful in a study of stress waves in an infinite cylinder made of an anisotropic functionally graded material within both the isothermal and non-isothermal elastodynamics.

Keywords:
Anisotropic and nonhomogeneous bodies, Body force analogy for transient thermal stresses, Functionally graded materials (FGM), Non-isothermal elastodynamics, Plane strain stress equations of motion, Stress characterization, Time-dependent actuation tensor field

Affiliations:
Ignaczak J. - IPPT PAN
6.  Ignaczak J., Plane Progressive Heat Waves in Metal Films, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495739.2012.637459, Vol.35, No.1-3, pp.48-60, 2012

Keywords:
Heat transfer, Metal films, Plane progressive heat waves, Third-order derivative-in-time heat conduction equation

Affiliations:
Ignaczak J. - IPPT PAN
7.  Ignaczak J., Modeling Heat Transfer in Metal Films by a Third-Order Derivative-In-Time Dissipative and Dispersive Wave Equation, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495730802637548, Vol.32, No.8, pp.847-861, 2009

Keywords:
Dispersion, Dissipation, Heat transfer, Metal films, Third-order derivative-in-time heat conduction equation, Wave equation

Affiliations:
Ignaczak J. - IPPT PAN
8.  Ignaczak J., Domański W., Nonlinear Hyperbolic Rigid Heat Conductor of the Coleman Type, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495730701876833, Vol.31, No.5, pp.416-437, 2008

Abstract:
A one-dimensional nonlinear hyperbolic homogeneous isotropic rigid heat conductor proposed by Coleman is analyzed using the method of weakly nonlinear geometric optics. For such a model the law of conservation of energy, the dissipation inequality, the Cattaneo's equation, and a generalized energy-entropy relation with a parabolic variation of the energy and entropy along the heat-flux axis, are postulated. First, it is shown that the model can be described by a non-homogeneous quasi-linear hyperbolic matrix partial differential equation of the first order for an unknown vector u = (θ, Q) T, where θ and Q are the dimensionless absolute temperature and heat-flux fields, respectively. Next, the Cauchy problem for the matrix equation with a weakly perturbed initial condition is formulated, and an asymptotic solution to the problem in terms of the amplitudes σα (α = 1, 2) that satisfy a pair of nonlinear first order partial differential equations, is obtained. The Cauchy problem is then solved in a closed form when the initial data are suitably restricted. Numerical examples are included.

Keywords:
Asymptotic methods, Blow-up heat waves, Coleman heat conductor, Hyperbolic, Nonlinear geometrical optics, Rigid heat conductor

Affiliations:
Ignaczak J. - IPPT PAN
Domański W. - Military University of Technology (PL)
9.  Ignaczak J., Nonlinear Hyperbolic Heat Conduction Problem: Closed-Form Solutions, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495730600710232, Vol.29, pp.999-1018, 2006

Abstract:
A nonlinear rigid heat conductor obeying the first and second laws of thermodynamics, Cattaneo's law, and a generalized energy-entropy relation in which both the energy and entropy are parabolic functions of the heat flux, is revisited. For a one-dimensional Cauchy problem in which both the temperature and heat flux are time-dependent only, a solution in terms of elementary functions is obtained. Also, for a one-dimensional traveling wave problem, a solution in terms of elementary functions is presented. Graphs illustrating the solutions are included.

Keywords:
Closed-form solutions, Heat conductor, Hyperbolic, Nonlinear, Rigid

Affiliations:
Ignaczak J. - IPPT PAN
10.  Ignaczak J., The Second Law of Thermodynamics for a Two-Temperature Model of Heat Transport in Metal Films, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495730590964918, Vol.28, No.9, pp.929-942, 2005

Abstract:
The second law of thermodynamics asserts that heat will always flow “downhill”, i.e., from an object having a higher temperature to one having a lower temperature. For a parabolic rigid heat conductor with a single temperature T and a single heat-flux q this amounts to the statement that the inner product of q and ∇T must be non-positive for every point x of the conductor and for every non-negative time t. For a homogeneous and isotropic body in which classical Fourier law with a heat conductivity coefficient k is postulated, the second law is satisfied if k is a positive parameter. For ultra-fast pulse-laser heating on metal films, a parabolic two-temperature model coupling an electron temperature Te with a metal lattice temperature Tl has been proposed by several authors. For such a model, at a given point of space x and a given time t there are two different temperatures Te and Tl as well as two different heat-fluxes q e and q l related to the gradients of Te and Tl, respectively, through classical Fourier law. As a result, for a homogeneous and isotropic model the positive definiteness of the heat conductivity coefficients ke and kl corresponding to Te and Tl, respectively, implies that the second law of thermodynamics is satisfied for each of the pairs (Te, q e) and (Tl, q l), separately. Also, the positive definiteness of ke and kl, and of the corresponding heat capacities ce and cl as well as of a coupling factor G imply that a temperature initial-boundary value problem for the two-temperature model has unique solution. In the present paper, an alternative form of the second law of thermodynamics for the two-temperature model with kl = 0 and q l = 0 is obtained from which it follows that in a one-dimensional case the electron heat-flux qe(x, t) has direction that is opposite not only to that of ∂Te(x, t)/∂x but also to that of ∂Tl(x, t + τT)/∂x, where τT is an intrinsic small time of the model. Also, for a general two-temperature rigid heat conductor in which ke, kl, ce, cl, and G are positive, an inequality of the second law of thermodynamics type involving a pair (Te − Tl, q e − q l) is postulated to prove that a two-heat-flux initial-boundary value problem of the two-temperature model has a unique solution. For a one-dimensional case, the semi-infinite sectors of the plane ( q l, q e) over which uniqueness does not hold true are also revealed.

Keywords:
Heat conduction, Ultra-fast heating, Metal films, Parabolic two-temperature model, Second law of thermodynamics

Affiliations:
Ignaczak J. - IPPT PAN
11.  Ignaczak J., Plane harmonic waves in a microperiodic layered thermoelastic solid revisited, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495730390425080, Vol.27, No.9, pp.779-793, 2004

Keywords:
harmonic thermoelastic waves, microperiodic composites

Affiliations:
Ignaczak J. - IPPT PAN
12.  Ignaczak J., Plane harmonic waves in a microperiodic layered infinite thermoelastic solid, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/714050871, Vol.26, No.11, pp.1033-1054, 2003
13.  Ignaczak J., Saint-venant's principle for a microperiodic composite thermoelastic semispace: the dynamical refined average theory, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495730290074649, Vol.25, No.11, pp.1065-1079, 2002
14.  Ignaczak J., A spatial decay estimate for transient thermoelastic process in a composite semispace, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/014957300280533, Vol.23, No.1, pp.1-14, 2000

Abstract:
A Saint-Venant's principle associated with a one-dimensional dynamic coupled ther moelastic effective modulus theory for a microperiodic layered semispace is presented. In such a theory, the displacement u=u(x,t) and the temperature theta=theta(x,t) (x>=0,t>=0) are approximated by u(x,t)=U(x,t)+h(x)V(x,t) and theta(x,t)=THETA(x,t)+ h(x)PHI(x,t), where U(x,t) and PHI(x,t) represent a macrodisplacement and a macrotemperature, respectively; V(x,t) and PHI(x,t)denote a displacement corrector and a temperature corrector, respectively; h=h(x) is a prescribed periodic microshape function; and the pairs (U,THETA) and (V,PHI) are found by solving an initial boundary value problem described by a system of linear partial differential equations with effective thermoelastic moduli subject to suitable initial and boundary conditions. It is shown that the thermoelastic energy associated with a solution to the problem and stored in the semi-space lying beyond a distance x from the loaded boundary x=0 over the time interval [0,t] decays exponentially as x to infinity and its decay length L depends on the time t, an effective velocity of thermoelastic wave (c*l), an effective time (T*), and an effective thermoelastic coupling parameter (epsilon*). In particular, it is shown that for small (large) times the function L reveals behavior of the decay length for a pure thermal (elastic) energy of a semispace.

Affiliations:
Ignaczak J. - IPPT PAN
15.  Ignaczak J., Saint-venant type decay estimates for transient heat conduction in a composite rigid semispace, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495739808956144, Vol.21, No.3, pp.185-204, 1998
16.  Ignaczak J., Baczyński Z.F., On a refined heat conduction theory for microperiodic layered solids, JOURNAL OF THERMAL STRESSES, ISSN: 0149-5739, DOI: 10.1080/01495739708956127, Vol.20, pp.749-771, 1997

Abstract:
A refined averaged theory of a rigid heat conductor with a microperiodic structure is used to solve a one-dimensional initial boundary value problem ofheat conduction in a periodically layeredplate with a largenumber of homogeneous isotropic layers. A uniqueness theorem for the averaged problem is proved, and two closed-form solutions for a periodically layered semispace are obtained. One of the two solutions represents the temperature field in the layered semispace due to a sudden heating of the boundary plane, while the other stands for the temperaturefield in the layeredsemispace produced by laser surface heating. Numerical examples are included.

Affiliations:
Ignaczak J. - IPPT PAN
Baczyński Z.F. - IPPT PAN
17.  Ignaczak J., Hetnarski R.B., On solition-like thermoelastic waves, Applicable Analysis, ISSN: 0003-6811, DOI: 10.1080/00036819708840557, Vol.65, No.1, pp.183-204, 1997
18.  Ignaczak J., Rayleigh waves in a non-homogeneous isotropic elastic semi-space (part 1), ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.15, No.3, pp.341-346, 1963
19.  Ignaczak J., A completeness problem for stress equations of motion in the linear elasticity theory, ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.15, No.2, pp.225-234, 1963
20.  Ignaczak J., On the stress equations of motion in the linear thermoelasticity, ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.15, No.5, pp.691-695, 1963

List of recent monographs
1. 
Eslami Reza M., Hetnarski R.B., Ignaczak J., Noda N., Sumi N., Tanigawa Y., Theory of Elasticity and Thermal Stresses; Explanations, Problems and Solutions, Springer, Springer Dordrecht Heidelberg New York London, pp.1-789, 2013
2. 
Hetnarski R.B., Ignaczak J., The Mathematical Theory of Elasticity, CRC Press Taylor and Francis Group, Boca Raton London New York, second edition (Taylor and Francis 2004, New York, NY 10001, first edition 2004), pp.1-837, 2011
3. 
Ignaczak J., Ostoja-Starzewski M., Thermoelasticity With Finite Wave Speeds, OXFORD University Press, Oxford, pp.1-430, 2010
4. 
Hetnarski R.B., Ignaczak J., Solutions manual (to accompany Mathematical theory of elasticity), Taylor & Francis Group, pp.1-160, 2005

List of chapters in recent monographs
1. 
Ignaczak J., Encyclopedia of Thermal Stresses, rozdział: Domain of Influence Theorems in Generalized Thermoelasticity, Springer, Dordrecht, Holland, edit. by R.B. Hetnarski, LXXXIII (11 vols.), 2, pp.996-1003, 2014
2. 
Ignaczak J., Hetnarski R.B., Encyclopedia of Thermal Stresses, rozdział: Generalized Thermoelasticity-Mathematical Formulation, Springer, Dordrecht, Holland, edit. by R.B. Hetnarski, LXXXIII (11 vols.), 4, pp.1974-1986, 2014

Conference papers
1.  Ignaczak J., Domański W., One-dimensional model of nonlinear thermo-elasticity at low temperatures and small strains, 11th International Congress on Thermal Stresses, 2016-06-05/06-09, Salerno (IT), pp.123-126, 2016

Abstract:
A one -dimensional nonlinear homogeneous isotropic thermo-elastic model with an elastic heat flow at low temperatures and small strains is analyzed using the method of weakly nonlinear asymptotics. For such a model both the free energy and the heat flux vector depend not only on the absolute temperature and strain tensor but also on an elastic heat flow that satisfies an evolution equation. The governing equations are reduce d to a matrix PDE, and the associated Cauchy problem with a weakly perturbed initial condition is solved. The solution is given in the form of a power series with respect to a small parameter the coefficients of which are functions of a slow variable that satisfy a system of nonlinear second-order ordinary differential transport equations. For a particular Cauchy problem in which the initial data are generated by a closed-form solution to the transport equations, the principal part of the asymptotic solution is a sum of four travelling thermo-elastic waves admitting blow-up amplitudes.

Keywords:
nonlinear thermo-elasticity, low temperatures, small strains, weakly nonlinear asymptotics

Affiliations:
Ignaczak J. - IPPT PAN
Domański W. - Military University of Technology (PL)
2.  Ignaczak J., Modeling Heat Transfer in Metal Films by a Third-Order Derivative-in-Time Dissipative and Dispersive Wave Equation, Proceedings of the 8th International Congress on THERMAL STRESSES 2009, 2009-06-01/06-04, Urbana-Champaign, Illinois (US), pp.597-600, 2009
3.  Ignaczak J., The Second Law of Thermodynamics for a Two-Temperature Model of Heat Transport in Metal Films, 6th International Congress on Thermal Stresses, 2005-05-26/05-29, Wiedeń (AT), pp.493-496, 2005

Category A Plus

IPPT PAN

logo ippt            Pawińskiego 5B, 02-106 Warsaw
  +48 22 826 12 81 (central)
  +48 22 826 98 15
 

Find Us

mapka
© Institute of Fundamental Technological Research Polish Academy of Sciences 2021