Title : Analytical and computational framework for simulation of composite structures on mobile devices

The mechanical design of fiber-reinforced composite structures — spanning unidirectional (UD) laminates, 2D woven fabrics, 2.5D interlock composites and knitted architectures — requires accurate prediction of elastic stiffness properties across highly diverse microstructural configurations. Reference simulation tools (ANSYS ACP, Abaqus, WiseTex, TexGen) deliver high fidelity but demand high-performance computing infrastructure, commercial licences and expert-level training, making them inaccessible for rapid parametric design, field engineering or resource-constrained academic environments. This contribution presents a unified analytical and computational framework that addresses these limitations through five original contributions.

The first contribution is the K-PY algorithm, a systematic extension of the Chamis micromechanical model integrating a five-norm objective function (Norms 0, ∞, Cartesian, 3 and 4) grounded in Hashin-Shtrikman bounds and Lp-space theory, together with four generalised orientation and thickness equivalence strategies for heterogeneous multi-ply laminates. Validated on 15 composite systems (E-glass, T300, AS4, Kevlar 49), K-PY achieves longitudinal modulus errors below 0.13% with millisecond execution times [Engineering, MDPI, 2021].

The second contribution extends the framework to 2D woven and 2.5D interlock composites through an interactive "puzzle" interface enforcing real-time fabricability constraints — yarn continuity, pattern periodicity and symmetry — combined with a hierarchical homogenisation scheme. In-plane modulus errors remain below 2% across plain weave, twill, satin and angle-to-angle/layer-to-layer interlock architectures [Textiles, MDPI, 2022].

The third contribution resolves the long-standing challenge of continuously curved yarn paths in knitted composites by introducing a hierarchical discretisation of yarn loops into infinitesimal straight segments, each evaluated by K-PY in its local frame. This yields the first closed-form analytical prediction of the full stiffness matrix for arbitrary knitted architectures, with errors below 5.3% across four independent experimental benchmarks (Huang, Gommers, Ramakrishna) [Science and Engineering of Composite Materials, De Gruyter, 2026].

The fourth contribution transposes the complete analytical framework to smartphones and tablets via an HTML/JavaScript application requiring no installation, no licence and no server-side computation. Five integrated modules cover all architectural families plus inverse design. Benchmarked against ANSYS ACP on 15 devices, accuracy deviations remain below 2% with computation times of 1.2–8.5 seconds [Materials Sciences and Applications, SCIRP, 2025].

The fifth contribution introduces the Composite Stiffness Matrix Calculator (CSMC), a stochastic inverse design engine combining Monte Carlo sampling, pre-evaluation fabricability filtering and multi-norm minimisation. Applied to 2.5D industrial interlocks, CSMC reconstructs target stiffness tensors within 5% error, converges by the Law of Large Numbers in 10,000–50,000 draws, and executes in 10–120 seconds on smartphones — revealing the multi-modal solution structure inherent to the Hadamard ill-posed inverse problem [Journal of Composite Materials, SAGE, Accepted 2025].

Taken together, these contributions deliver a unified analytical platform achieving accuracy comparable to reference numerical methods at a computational cost compatible with mobile deployment. The framework democratises access to advanced composite simulation tools and opens new perspectives for rapid design, multi-scale optimisation and field-level structural assessment.

Keywords: Fiber-reinforced composites · Analytical homogenisation · K-PY algorithm · 2.5D interlock · Knitted composites · Mobile simulation · Stochastic inverse design · CSMC · Monte Carlo

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