From elastic response to a design study

1. Property and model connections

Constituent records feed the selected micromechanics model. Its effective lamina properties—or a directly selected material—feed each laminate ply. Ply angle and thickness transform and integrate those properties into the laminate stiffness. The structural case supplies loads and geometry. Thermal and moisture analyses use the linked process and boundary histories; their recovered states can supply environmental free strains when that contribution is enabled.

Saved results retain the state used by their run. Editing an upstream record changes the current model, not an earlier saved result. WB live CLT recovers current elastic response, while stored process residuals require a new solver run after relevant edits. Optimization snapshots freeze the search inputs and results for later review.

Operating guide: live sync, records and result freshness

2. Laminate stiffness and recovery

For a perfectly bonded, small-strain plane-stress laminate, each ply contributes its transformed reduced stiffness Q̄. Using the laminate mid-plane as z = 0:

A = Σ Q̄k (zk − zk−1)
B = ½ Σ Q̄k (zk² − zk−1²)
D = ⅓ Σ Q̄k (zk³ − zk−1³)
[N; M] = [A B; B D] [ε⁰; κ] − [N*; M*]
σk(z) = Q̄k [ε⁰ + z κ − ε*k(z)]

N is membrane force per width, M is moment per width, ε⁰ is mid-plane engineering strain, κ is curvature and ε* is the enabled free strain. With Q̄ in MPa and z in mm, A is N/mm, B is N and D is N·mm. Keep this consistent with the input load units. Local stresses require the ply-axis transformation, including the engineering shear convention.

The six-by-six inverse ABD gives compliance. Effective Ex = 1/(a11 h), Ey = 1/(a22 h), Gxy = 1/(a66 h) and νxy = −a12/a11 for the corresponding force-controlled compliance definition. An unsymmetric laminate can couple extension and curvature; these values are not the same as artificially imposing zero curvature.

Full CLT and environmental coupling reference

3. Implemented WB first-ply criteria

WB implements Maximum stress, Maximum strain, Tsai–Hill, Tsai–Wu and plane-stress Hashin screening. Puck is not implemented. LaRC04 linear-shear initiation is available as a separate reference-state study; it is not an envelope or progressive-degradation option. Positive tensile/compressive strengths, shear allowable and elastic moduli are required.

• Maximum stress compares the absolute local normal stresses with sign-appropriate strengths and shear with S12.
• Maximum strain compares local strains with explicit strain limits when available; otherwise limits are derived from strength/modulus. That derivation is an assumption, not measured strain-to-failure data.
• Tsai–Hill uses sign-dependent X and Y and the implemented interaction σ1²/X² − σ1σ2/X² + σ2²/Y² + τ12²/S12².
• Tsai–Wu combines linear tension/compression terms with quadratic interaction. The normalized interaction F12* defaults to −0.5; it must be strictly between −1 and 1. Calibrate it when evidence is available.
• Hashin separates tensile/compressive fiber and matrix interactions. WB’s r17-derived shear-dominant attribution maps the governing interaction to shear damage; it is not a separate experimental failure-mode identification.

For proportional elastic loading with no fixed residual offset, each active criterion can be written qR² + lR = 1. The positive root gives a reserve factor; a linear criterion gives R = 1/l. The minimum across sampled ply locations and modes controls first failure. A general failure index is not always the reciprocal of reserve factor.

Failure criterion definitions and assumptions

4. Envelopes and progressive damage are different analyses

An envelope samples directions in a two-component load plane and searches for the first-failure point along each ray under the specified background state. The joined points are a numerical approximation. If a residual load/free-strain state is present, the response is affine rather than purely proportional: evaluate the fixed state plus the ramped increment. Do not blindly scale the complete combined response.

Progressive failure updates the selected mode stiffness after activation, recomputes equilibrium and continues to the selected terminal condition or search limit. First activation, terminal load, retained stiffness and last-ply metrics are not interchangeable. Increment size, same-load iterations, degradation factors, criterion and stopping rule affect the outcome.

Through-thickness sampling can reveal variation in a recovered field but cannot validate missing transverse, cohesive, fatigue or nonlinear physics. The WB interactive plane-stress workflow is narrower than the complete compiled solver theory library.

Progressive update reference · Envelope operating procedure

5. Carpet plots: fixed-stack elastic sweeps

Two distinct absolute-angle families are selected from the current visible stack. Their magnitudes are swept independently over 0–90°, using 2–21 samples each. Existing negative signs, other angle families, material properties, ply thicknesses and ordering are retained. Each grid point is a fresh elastic laminate-property calculation.

The α lines are solid and the β lines dashed. Their color gradients identify the swept angles. The current stack is a reference point; the live laminate preview displays the hovered candidate. Balance is checked from matched positive/negative angle contributions with compatible elastic properties and thickness. A family originally at 0° has no implicit negative partner, so sweeping it can create an unbalanced candidate.

These curves describe elastic design sensitivity—not failure probability, a feasible strength region, or manufacturing approval. Select a candidate and evaluate all relevant load, stability and process constraints separately.

6. Discrete laminate optimization

The current WB search uses one material, uniform ply thickness, elastic CLT and a mechanical resultant vector. It rejects reused process free strains after redesign. For each candidate it calculates the selected first-failure reserve factor λ, areal mass mA = Σρk tk and the selected absolute mid-plane strain at first failure.

Mass objective: minimize mA, subject to λ ≥ λrequired
Strength objective: maximize λ at fixed ply count
Strain objective: maximize |ε⁰component(λ)| at fixed ply count

The strain objective uses εx, εy or γxy in microstrain at first failure—not displacement, service-load strain or a guaranteed ductility measure. Under pure bending, a mid-plane component can be zero. Load factors from different cases are relative to different reference vectors and must not be compared without their context.

Allowed angles are discrete. Symmetry mirrors the half-stack; balanced-pair construction uses adjacent ±θ pairs, with repeated 0°/90° blocks. Both options together constrain counts to multiples of four. This is a restricted construction space, not every possible balanced laminate.

Small spaces are enumerated completely. Larger spaces use a seeded multi-start elitist mutation search with random exploration and a bounded candidate budget. Report “best found,” the budget, seed, feasible count and objective. A flat curve or exhausted budget does not establish a global optimum.

Constraints on contiguity, disorientation, buckling, fatigue, joints, defects, delamination and coupled environmental response are not implicitly enforced. Apply the candidate or create a separate laminate, then rerun the complete engineering assessment.

7. Evidence and reproducibility

An optimization snapshot stores the study, source ply properties, load vector, configuration, baseline, candidates and convergence. It is immutable evidence of that search—not an automatic update to a simulation or a solver certification. Keep its downloaded CDS_DB together with the complete simulation dependency package.

Document which execution path produced each result: WB live elastic preview, interactive WB failure/optimization, saved coupled solver run, or compiled solver/Runtime release. Preserve model identity, units, calibration sources and unavailable-contribution warnings. Existing compiled acceptance evidence applies only to its tested release and cases.

Step-by-step failure and optimization guide · Laminate assumptions and limitations