By Milan Micunovic

ISBN-10: 0387894896

ISBN-13: 9780387894898

ISBN-10: 038789490X

ISBN-13: 9780387894904

This booklet includes geometrical and thermodynamical concerns fundamental for improvement of a rational conception of thermoviscoplasticity. Geometrical photograph of coupled thermomagnetomechanical histories of broken solids is outfitted either through Kroener's incompatibility method to boot through Eshelbian implanting eigenstrains. Duality of Euclidean anholonomic and non-Euclidean usual country area can be defined during this book.

Damaged inelastic fabrics of differential style, discrete and infinitesimal reminiscence are received from precept of thermo-inelastic reminiscence. factor of plastic spin is taken into account. Postulate of minimum plastic paintings and corresponding non-associativity 4-tensor are then used to teach no matter if associativity of move rule holds. Postulates of Drucker, Iliushin and Hill are mentioned. Thermodynamics of inelasticity is greatly mentioned in classical, rational, prolonged and endochronic model with account to statistical thermodynamics. A non-steady getting older is utilized in endochronic thermodynamics to hide creep-pasticity coupled inelastic histories. Multiaxial dynamic experiments with cylindrical, ``bichierino'' and cruciform specimen from austenitic stainless steels are analyzed. Quasi-rate independence and Rabotnov's plastic hold up is mixed with tensor illustration. Inelastic ferromagnetics are handled by way of prolonged to boot endochronic thermodynamics. For low cycle fatigue the experimentally saw displacement of magnetic induction heritage with admire to emphasize historical past is analyzed.

Self constant procedure utilized to inelastic polycrystals is predicated on limited micro-rotations and loose meso-rotations. a different consciousness is dedicated to moderate ailment of polycrystal grains. the speculation is faced with classical J2-theory. assorted inelastic multiaxial pressure histories are analyzed and corresponding energetic slip platforms made up our minds. For numerical effects micro quasi cost independence and cozy Taylor's version are used. the speculation of inelastic micromorphic polycrystals with couple stresses wishes a truly small variety of precious fabric constants. Nonproportionality of pressure heritage in addition to intergranular continuity are regarding antisymmetry of rigidity tensor.

Key topics:

* features a unique description of the geometry of thermo-deformation with neighborhood evolving common country configuration

* offers a comparative assessment of assorted versions of thermodynamics (classical, rational, endochronic, statistical) with new angle to inelastic excessive velocity histories

* Introduces quasi-rate independence and its program to plastic waves, ratcheting, and diffuse localization

* Explores the sensor illustration method of thermo-inelastic coupled fields attached to a generalized associativity of circulation rule in addition to a comparability with the J2-approach

* Examines micromechanics in keeping with micro grain technique resulting in lowered variety of fabric constants

* offers biaxial cruciform specimen Hopkinson bar results

* Reexamines the Hill’s yield functionality for nonproportional stress-thermo-strain histories

This booklet is meant for fabric technological know-how specialists and execs drawn to impression experiments, continuum mechanics researchers, engineers in learn institutes and graduate and Phd scholars aiming to use FEM to calculate power of constructions at time various thermo-mechanical excitations.

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**Extra resources for Thermomechanics of Viscoplasticity: Fundamentals and Applications**

**Sample text**

8)): 2 2 ω (dsω ν ) − (dsν ) = 2 drν EP drν , ωT 2 Eω Πω − 1ν . 70) K dX . 71) P ≡ ∇ν ⊗ EP . This tensor will be used in the following subsection for general deﬁnition of geometric objects in (νtω )-space. 2 Torsion, curvature and nonmetricity in natural state For anholonomic coordinates in a non-Euclidean 3-space coeﬃcients of connection have the following form (cf. γ = Hαβ + Tαβ. 3 Characteristics of the intrinsic structure. γ + hγδ (Sδαβ + Sδβα ) Tαβ. γ − hγδ (Ωδαβ + Ωδβα ). 74) The skew symmetric anholonomic object is responsible for lack of global transformation either from material to structural coordinates or from structural to spatial coordinates.

21) reduces to ∞ S(t) ≈ S0 (γ # ) + h(τ )K(γ # , τ ) : Πt (τ ) dτ. 22) 0 The above formula is said to describe a linear viscoplastic material of integral type. Obviously, a similar procedure could lead to higher order materials of integral type. 11. (Discrete memory) An alternative approach is to take the discrete memory inﬂuence extending γ # to include δpm := max εP (τ ) ≡ max VP (τ ) − 1 τ τ which is especially suitable for cyclic inelastic processes (cf. [MSD73, Mic87b]). In this case h(t) is given by corresponding Dirac delta-functions at temporal points where such maxima appear.

Let us restrict our attention to disclination-free distribution of defects. For the sake of illustration we give the following two examples. 26 1 Physical and Geometrical Background Anholonomic coordinates in E3 Suppose that there exists only quasi-plastic strain due to inhomogeneous temperature ﬁeld in (χt ). Then, it is enough for an adequate description to consider damaged natural space elements as a mosaic in Euclidean 3-space with anholonomic coordinates. γ Γαβ = Hαβ + Tαβ. γ (Q, Ω). 80) {EPω (θ)} = ⎝ 0 0 α3 (θ − θ0 ) such that the corresponding thermal nonmetricity tensor is Q(θ)λαβ = αλ δαβ (∇ν )λ θ.

### Thermomechanics of Viscoplasticity: Fundamentals and Applications by Milan Micunovic

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