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continuum mechanics

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Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005431
EISBN: 978-1-62708-196-2
... methods. This article introduces the methods of so-called meshed solutions, with an emphasis on the FEM. It presents some basic differential equations that are used to model the responses of structures, components, processes, or systems with emphasis on continuum mechanics. The article provides an outline...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006767
EISBN: 978-1-62708-295-2
... analysis (BEA). While FEA discretizes the entire volume into small elements (normally tetrahedra or hexahedra), BEA only discretizes the boundary. Both methods, however, employ continuum material models and produce only approximations. In general, accuracy improves as the number of elements increases...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005424
EISBN: 978-1-62708-196-2
... symmetries are anisotropies of the mechanical properties, both elastic and plastic, of the individual crystals. Anisotropy is evident even at the continuum scale in aggregates of crystals having preferred orientations of the crystal lattices, known as crystallographic texture. The behaviors observed during...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005418
EISBN: 978-1-62708-196-2
... Abstract Self-consistent models are a particular class of models in continuum micromechanics, that is, the field concerned with making predictions of the properties and evolution of aggregates whose single-crystal deformation behavior is known. This article provides information on the...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005237
EISBN: 978-1-62708-187-0
... Abstract In order to model macrosegregation, one must consider convection and the partitioning of the segregating elements at the dendritic length scale. This article describes microsegregation with diffusion in the solid. It presents a continuum model of macrosegregation and illustrates the...
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 November 1995
DOI: 10.31399/asm.hb.emde.a0003025
EISBN: 978-1-62708-200-6
... Abstract Mechanical properties are often the most important properties in the design and selection of engineering plastics. Temperature, molecular structure, crystallinity, viscoelasticity, and effects of environment, fillers and reinforcements are considered as the basic factors affecting the...
Book Chapter

By Sammy Tin
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005404
EISBN: 978-1-62708-196-2
... to a physical representation of the microstructure, such as changes in dislocation density, grain size, precipitate size, morphology, and volume fraction. To effectively model the creep behavior of engineering alloys using these kinematic creep equations, one can use the continuum damage mechanics...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006774
EISBN: 978-1-62708-295-2
... Abstract Engineering component and structure failures manifest through many mechanisms but are most often associated with fracture in one or more forms. This article introduces the subject of fractography and aspects of how it is used in failure analysis. The basic types of fracture processes...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006775
EISBN: 978-1-62708-295-2
... behavior, they become tools to use for quantitative evaluation of fracture in failure analysis. Multiple approaches have been used; some are based on continuum mechanics to predict behavior of the bulk assembly (without assumptions of the microscopic-scale details and operative mechanisms of crack...
Series: ASM Handbook
Volume: 4E
Publisher: ASM International
Published: 01 June 2016
DOI: 10.31399/asm.hb.v04e.a0006271
EISBN: 978-1-62708-169-6
... focuses on simulation of the quenching step, because this step is mainly responsible for component residual stresses and distortion. Heat treatment simulation is presented on a macroscopic, continuum mechanical scale, using the finite-element method. Figure 1 shows the schematic course...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005433
EISBN: 978-1-62708-196-2
... scientists have worked on phenomenological and physics-based equations. On the other hand, engineering mechanics researchers have come up with continuum-based constitutive equations. For more details on constitutive equations, see the article “Constitutive Equations” in Metalworking: Bulk Forming , Volume...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006778
EISBN: 978-1-62708-295-2
... along the shear plane in the basic principles of continuum mechanics). Thus, even though the overall applied stress is still a tensile load, deformation makes a transition to the shear plane in the outer regions of the specimen. In the mode II region, voids grow in sheets at an oblique angle (~45° to...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005455
EISBN: 978-1-62708-196-2
... Abstract A computational tool would require the contribution of the strengthening mechanisms of metallic material to be predicted and then summed in an appropriate way to derive an estimate of the tensile properties. This article focuses on the modeling of deformation mechanisms pertinent to...
Book Chapter

By S. Lampman
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006645
EISBN: 978-1-62708-213-6
... characteristic peaks of x-rays associated with fluorescence (from electrons that move from outer atomic orbits to inner orbits of the sample). There is some background x-ray radiation with a continuum of energies from many different interactions, but the characteristic energies of electrons moving within atoms...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005421
EISBN: 978-1-62708-196-2
..., the function F( σ M / σ ¯ ) has been determined using continuum mechanics approaches ( Ref 30 , Ref 31 , Ref 32 ) as well as semiempirical methods ( Ref 34 ). In many cases, cavities do not grow as simple spheres whose radii increase with strain; rather, they grow as...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005405
EISBN: 978-1-62708-196-2
... distributions of slip and various fatigue indicator parameters (FIPs). These FIPs enable assessment of the relative potency of fatigue crack formation based on continuum-level quantities associated with each relevant mechanism. For example, the Fatemi-Socie ( Ref 43 , 44 ) shear-dominated parameter can be...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005419
EISBN: 978-1-62708-196-2
... stress fields and driving forces by g a linear elastic fracture mechanics or energy-based continuum approach. Because of this, they can offer some insight into the forces that drive the crack, but they are still dependent upon the experimental crack-growth data that incorporates the stress-ratio effects...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009003
EISBN: 978-1-62708-185-6
... encountered in multiaxial stress states. The construction of a processing map based on deformation mechanisms is also discussed. ductile fracture multiaxial stress stress-strain curve workability WORKABILITY refers to the relative ease with which a metal can be shaped through plastic deformation...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005450
EISBN: 978-1-62708-196-2
... travelled between each molecular collision of 6.35 × 10 −6 cm. Therefore, the overall motion of the fluid is of interest, not the motion of individual molecules, and the fluid can be treated as a continuous medium, also called a continuum. Pressure is defined at a point in a continuum as: (Eq 1) p...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005403
EISBN: 978-1-62708-196-2
... properties of which will be obtained by averaging that of all the grains in the aggregate. Such an approach is close to the self-consistent models commonly used in the continuum mechanics of heterogeneous materials. It precludes topological effects, such as necklacing, which are expected, however, to be...