Prof. Józef Ignaczak, Ph.D., Dr. Habil. |

##### Doctoral thesis

1960 | Niektóre przypadki koncentracji naprężeń cieplnych
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##### Habilitation thesis

##### Professor

1972 | Title of professor |

##### Supervision of doctoral theses

1. | 1985 | Bem Zbigniew (PŁ) | 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 (PŚ) | 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., 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, pp.1-10, 2017Abstract: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:
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2. | 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, 2015Abstract: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 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:
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3. | 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, 2015Abstract: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; here, ; t ≥ 0] represents the actuation tensor field. 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:
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4. | 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, 2012Keywords:Heat transfer, Metal films, Plane progressive heat waves, Third-order derivative-in-time heat conduction equation Affiliations:
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5. | 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, 2009Keywords:Dispersion, Dissipation, Heat transfer, Metal films, Third-order derivative-in-time heat conduction equation, Wave equation Affiliations:
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6. | 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, 2008Abstract: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:
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7. | 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, 2006Abstract: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:
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8. | 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, 2005Abstract: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:
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9. | 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 | |||||||

10. | 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 | |||||||

11. | 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 |

##### List of recent monographs

1. 491 | 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. 488 | Hetnarski R.^{♦}, 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. 490 | Ignaczak J., Ostoja-Starzewski M.^{♦}, Thermoelasticity With Finite Wave Speeds, OXFORD University Press, Oxford, pp.1-430, 2010 |

4. 80 | 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. 492 | Ignaczak J., Encyclopedia of Thermal Stresses, rozdział: , Springer, Dordrecht, Holland, edit. by R.B. Hetnarski, LXXXIII (11 vols.), 2, pp.996-1003, Domain of Influence Theorems in Generalized Thermoelasticity2014 | |

2. 493 | Ignaczak J., Hetnarski R.B.^{♦}, Encyclopedia of Thermal Stresses, rozdział: , Springer, Dordrecht, Holland, edit. by R.B. Hetnarski, LXXXIII (11 vols.), 4, pp.1974-1986, Generalized Thermoelasticity-Mathematical Formulation2014 |

##### 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, 2016Abstract: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:
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2. | Ignaczak J., Modeling Heat Transfer in Metal Films by a Third-Order Derivative-in-Time Dissipative and Dispersive Wave Equation, AI30, Acoustical Imaging 30, 2009-03-01/03-04, Monterey, California (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 |