Wyniki wyszukiwania - BazTech

1

Objectivity and frame indifference of acceleration-sensitive materials

Muschik W.

Journal of Theoretical and Applied Mechanics

|

2012

|

Vol. 50 nr 3

807-817

EN

Constitutive equations have to be compatible with material axioms. Here, the axioms of material frame indifference and material motion dependence, that are the transformation properties of the constitutive equations by changing observer and by changing the motion of the material, are discussed. Starting out with the observer-independent material mapping, its domain – the state space – is extended by a second entry describing the motion of the material with regard to a fixed standard frame of reference. This results in observerindependent tensorial constitutive equations. Different component representations of these equations belong to different observers. Finally, two examples –anisotropic heat conduction and Maxwell’s equations – are considered.

PL

Równania konstytutywne muszą być zgodne z aksjomatami obiektu. W pracy przedyskutowano aksjomat niezmienniczości względem układu współrzędnych oraz zależność od ruchu, które stanowią podstawę transformacji równań konstytutywnych przy zmianie położenia obserwatora oraz przy uwzględnieniu ruchu obiektu. Rozważania rozpoczęto od odwzorowania niezależnego od obserwatora, którego dziedzina – przestrzeń stanu – została rozszerzona o drugi element opisujący ruch obiektu względem ustalonego, standardowego układu odniesienia. To doprowadziło do sformułowania niezależnych równań konstytutywnych w postaci tensorowej. Różne składowe reprezentacji tych równań należą do różnych obserwatorów. Na zakończenie przedstawiono dwa przykłady – problem anizotropowego przewodzenia ciepła i równania Maxwell’a.

2

Mesoscopic theory of microcracks

Papenfuss C., Van P., Muschik W.

Archives of Mechanics

|

2003

|

Vol. 55, nr 5-6

481-499

EN

The mesoscopic concept is a way to deal with complex materials with an internal structure within continuum mechanics. It consists of extending the domain of the balance equations by mesoscopic variables and of introducing a local distribution function of these variables as a statistical element. In our case microcracks are modelled as penny-shaped and are completely characterized by their diameter and the unit normal to the crack surface. Two examples of crack dynamics are given as well as a possible definition of a damage parameter. Orientational order parameters (fabric-alignment tensors) are defined and balance-like dynamic equations for them are derived.

3

Eight formulations of the second law

Muschik W.

Zeszyty Naukowe Politechniki Świętokrzyskiej. Mechanika

|

1998

|

Z. 66

181-191

4

Kink conditions for isobars in binary v-x-phase diagrams induced by the second low

Bauer W., Muschik W.

Archives of Thermodynamics

|

1998

|

Vol. 19, no 3/4

59-83

EN

Conditions describing the behaviour of the kink of the isobars at the dew line in v-x-phase diagrams of binary mixtures are proved using the second low. These conditions are tested using a generalized Bender equation of state with mixture rules of Tsai and Shuy. The complete set of formulas of such a type of equation is worked out for being useful in programming or modification of other equations of state or mixture rules.

5

Objectivity and frame indifference, revisited

Muschik W.

Archives of Mechanics

|

1998

|

Vol. 50, nr 3

541-547

EN

Because one has to distinguish between changing the observer and changing the state of motion of materials, objectivity and material frame indifference are redefined: Objectivity denotes a special tensor property in case of changing the observer, wheras material frame indifference is characterized by quantities being independent of different states of motion of the material. To describe these different states of motion of the material, an arbitrary standard frame of reference and a Constitutive Family is introduced. We prove that the constitutive map is isotropic in the state variables, if these and the material prperties are objective.