Center for Composite Materials
Theories/Micromechanics
Current Workbench models and compatibility

This theory library includes wider research formulations. Check the released model directory for selectable models, required inputs, limits and exercises. The event-driven RVE branch is not enabled in hosted Workbench.

Theories / Micromechanics / Aligned discontinuous fibers

Semi-analytical aligned discontinuous-composite theory

Reference formulation — not enabled in hosted Workbench.

This Revision 8 chapter documents a separate research / compiled-solver branch. Its event-driven breaks, nonlinear shear, RVE series coupling and stochastic failure are not selectable in hosted Workbench. Cox shear-lag elastic homogenization is available, not this failure model. Released models and connections ↗

1. Theory basis and role in CDS

Henry and Pimenta model aligned short-fiber material across specimen, RVE, fiber, neighboring-fiber interaction, and interaction-segment scales. Random fiber ends create nonuniform overlaps, matrix shear transfers load, fiber strength is stochastic, and final failure occurs when a local cluster becomes unstable.

The reference implementation associates this formulation with aligned-discontinuous material type 1 / criterion 6; this is not a selectable hosted Workbench path. Its specimen response supplies longitudinal ply stiffness and tensile strength to the common orthotropic ply property definition. Laminate ABD assembly and laminate-scale progressive degradation remain separate downstream operations.

2. Paper-to-CDS traceability

Henry–Pimenta mechanismRevision 8 statusCDS implementation
Random longitudinal fiber-end locationsImplementedEach RVE draws one end location per fiber over the selected fiber length.
Square n × n aligned-fiber RVEImplementedThe user controls fibers per row and the number of independent RVEs.
Four-nearest-neighbor topologyImplementedHorizontal and vertical interactions are rebuilt from fiber ends and inserted breaks.
Generic nonlinear matrix constitutive lawImplementedAn optional piecewise-linear τ(γ) table is accepted; otherwise CDS builds an elastic-yield-friction law.
Broken and shear-lag interaction segmentsImplementedSame-fiber endpoints create broken segments; different-fiber endpoints create nonlinear shear-lag segments.
Length- and field-scaled Weibull strengthImplementedOrdered thresholds use fiber/reference length, Weibull scale and shape, and stress-field correction.
Event-driven break insertion and rebuildingImplementedThe governing break coordinate is inserted, its interaction is deactivated, and the network is rebuilt at the same strain.
Debonding and frictional pull-out toughnessImplementedResistance is integrated over realized overlaps from mode-II toughness and residual friction.
Dugdale critical-cluster instabilityImplementedSquare clusters are screened with the nonlinear energy-release expression and physical cluster radius.
Specimen curve from RVEs in seriesImplementedRVE strains are interpolated at common stress and averaged; the first RVE cutoff governs.

3. Interaction-segment mechanics

3.1 Discontinuity reconstruction

For each horizontal and vertical neighbor pair, CDS sorts both fiber ends and all inserted break coordinates. Consecutive discontinuities define the current interaction segments. If both endpoints belong to the same fiber, the segment is broken; if they belong to different fibers, load crosses the matrix through shear lag.

σBrI = (Ef/2) εBrI
Broken-segment relation

3.2 Nonlinear shear lag

With fiber half-thickness T = φf/4 and effective matrix gap tm, the fiber stress difference follows:

d²Δσ/dx² = ±λ²Δσ,   λ = [2|Gm|/(TtmEf)]1/2
Shear-lag differential equation and parameter

The active secant/tangent behavior comes from the selected piecewise-linear matrix law. The interaction stress is common to its segments, and their strain contributions are length-weighted in series. The weakest segment limits the interaction.

εRVE(σI) = (1/lf) Σs Δls εsI(σI)
Series interaction strain

4. Progressive fiber-break events

Each fiber receives ordered Weibull thresholds. Length and stress-field scaling follow:

F(σf) = 1 − exp[−ClCσ(σf/σ0)m],   Cl = lf/(4lr)
Length- and field-scaled Weibull law

Four adjacent interactions generate the fiber peak. When that peak exceeds the current threshold, CDS inserts a break at the governing neighboring discontinuity at the end of the longest segment, advances the ordered threshold, deactivates the responsible interaction, and rebuilds the network without advancing applied strain. Events repeat until stable.

5. RVE, specimen, and cluster failure

σRVE = Vf(ΣσVI + ΣσHI)/[2n(n−1)] + Vmσm
RVE stress

Independent RVEs are placed in series. At a common stress, their interpolated strains are averaged; the earliest RVE cutoff limits the specimen.

εspec(σ) = (1/NRVE) Σr εr(σ)
Series-coupled specimen strain

Cluster termination uses the nonlinear Dugdale energy release rate and the paper's cluster-radius scaling:

JNL = (32/π³)(Xg²/Eg)a ln[sec(πσ/(2Xg))],   a = naφf/√(2Vf)
Nonlinear critical-cluster energy
gdeb = (2Vf/φf)GIIcΔl,   gpo = (Vf/φf)τμΔl²
Debonding and frictional pull-out resistance

6. Connected workflow

  1. ConstituentsFiber elastic/Weibull data and matrix elastic, strength, toughness, friction, and optional τ(γ) data
  2. Stochastic geometryFiber length/diameter, volume fraction, n × n RVE, independent realizations, and seed
  3. Interaction networkEnds + breaks → broken/shear-lag segments → nonlinear segment series response
  4. Fiber eventsLocal peaks → ordered Weibull threshold → break insertion → network rebuild at the same strain
  5. RVE and specimenInteraction average → complete RVE curves → common-stress series coupling
  6. Cluster and ply property connectionDugdale cutoff → E1/Xt → 3D ply properties → laminate and structural analysis

7. What to supply and what to examine

Study quantityPhysical meaning
Fiber variability and interactionsSpecify fiber-strength statistics, representative-volume size, flaw assumptions and calibrated fracture resistance.
Matrix shear behaviorSupply measured shear strain and shear stress in Pa. Strain values must be nonnegative and strictly increasing.
Specimen responseSeries-coupled specimen curves.
RVE responseRVE curves, break counts, active-interaction counts, and cutoff state.
Fiber-break eventsEvery progressive fiber-break event and governing interaction.
Critical clustersCritical cluster location, size, JNL, and resistance.
Matrix shear lawResolved matrix shear-law points and piecewise tangent.

8. Calibration and validation boundary

  • Calibrate the matrix shear law, Weibull scale/shape/reference length, stress-field correction, interface limit, mode-II toughness, and friction stress to the intended material state.
  • RVE row count, RVE count, strain resolution, cluster limit, and flaw opportunities require convergence studies.
  • Static and analytical release checks do not replace a complete model run or coupon validation.
  • Use measured ply overrides when a qualified dataset should supersede a predicted property.

9. Primary reference

Henry, J., and Pimenta, S. (2017). “Semi-analytical simulation of aligned discontinuous composites.” Composites Science and Technology, 144, 230–244. https://doi.org/10.1016/j.compscitech.2017.01.027