Applications — reading path
The Applications assemble the pieces of the Manual into complete micromechanical models of real materials. Each one follows a published model, cited at the top of its page, and sets the values the paper reports against those the library computes. Where a tutorial isolates one feature of the API, an application chains several — a microstructure over two or three scales, a chemistry that supplies the volume fractions, a time-dependent behavior, a strength criterion — and says where the model, rather than the library, sets the limit.
If the package is new to you, Getting started and Schemes and RVEs come first; every page below then opens with the theory and manual pages it relies on.
The chapter starts with general concepts, which hold whatever the material, then turns to the materials, one section each. Within a section a page comes after the pages it builds on.
General concepts
| Page | What it models |
|---|---|
| Hill tensors by transformation: closed forms derived step by step | the Hill tensor of an ellipsoid as that of a sphere in a transformed medium, and the closed form it gives for a spheroid in a coaxial transversely isotropic matrix, derived symbolically and held to the numerical back-ends |
| The cluster model on cubic arrays | inclusions that see where their neighbors are: the pairwise interactions within a cluster, on periodic arrays |
| The equivalent inclusion method, against a published table | the Galerkin form of the Lippmann–Schwinger equation on a planar assembly of disks, against a published table |
| A recycled-concrete aggregate, by axisymmetric Fourier elements | an old aggregate wrapped in a shell of adhered mortar, off center, solved by finite elements and checked against the concentric layered sphere |
| Concave pores: superspheres and superspheroids | pores with no Eshelby solution, computed by finite elements and set against the only published data for this shape family |
Cementitious materials
| Page | What it models |
|---|---|
| Multiscale elasticity of a hydrating cement paste | the Young modulus of a Portland cement paste along its hydration, over two scales |
| A hydrating blended cement paste, coupled to its chemistry | the volume fractions computed by the chemistry of hydration instead of a Powers-type correlation, then the elasticity of a blended paste |
| Hydration through the pore solution | the same paste, its hydration driven through the ionic species of the pore solution rather than stated solid reactions |
| Cement paste: chloride diffusivity and elasticity | one multiscale model that predicts both the chloride diffusivity and the elastic moduli |
| Aging creep of solidifying cementitious materials | a phase that solidifies progressively, as C-S-H does, and the aging relaxation kernel that results |
| Quasi-brittle strength of cement paste and mortar | the uniaxial compressive strength upscaled from the hydrate foam to the paste and the mortar |
| The interfacial transition zone in concrete | the more porous shell of paste around each aggregate, and the stiffness it costs the concrete |
| The elastic limit of concrete: ITZ failure and ITZ–aggregate separation | where microcracks start around the aggregates: the stress in the ITZ from the Hadamard jump conditions, and the elastic limit surface |
Geomaterials
| Page | What it models |
|---|---|
| A lamellar porous material: swelling clays and C-S-H | stacks of parallel platelets with water in between, over two scales chained on symbols |
| Friction of a granular medium from its contacts | rigid grains bonded by springs, the macroscopic friction coefficient they give, and how it falls as the medium loosens |
| The strength of a sandstone: crushing grains and sliding contacts | grains that yield and cemented contacts that slide, combined by the modified secant method |
Bituminous materials
| Page | What it models |
|---|---|
| Viscoelastic complex modulus of a bituminous mixture | the complex modulus |
The finite elements met in the first section are a solver called inside homogenization, for one inclusion; the opposite use, homogenization called inside a structural solver as the constitutive law at each Gauss point, is the subject of Finite-element coupling.