The next generation ofcomputational engineering.

Seemlessly integrating classical and fractional CAE for the simulation of complex engineering systems.

Advanced CAE for multiscale and multiphysics engineering.

M3SIM develops computer-aided engineering (CAE) and scientific-computing tools that integrate classical and fractional models when physics demands it. We turn measured behavior into calibrated numerical models and scalable computation for engineering decisions.

M3SIM current focus

Computational solid mechanics.

Fractional CAE and finite element analysis

Modeling of mechanical and transport processes under memory-dependent, hereditary, and non-stationary conditions.

Multiphysics and multiscale coupling

Coupled multiphysics behavior across length scales and operating conditions.

AI-enabled modeling

ML-assisted material discovery and data-informed calibration for effortless analysis setup.

Production-ready for industry. Exploration-ready for academia and national labs.

Industry

For decision-critical CAE and FEA models requiring reliability across changing operating conditions.

Academia

For researchers advancing the application of fractional order models in computational physics.

National labs

For mission-driven simulation programs requiring traceable assumptions, and rigorous yet cutting-edge models for open-ended computational challenges.

Why Fractional Order Models in CAE

When a CAE model is accurate in one regime, but does not generalize across operating conditions.

Classical finite element analysis remains the foundation of engineering simulations. In multiscale and multiphysics systems, however, a calibration that is accurate for one regime may lose predictive fidelity under different load histories, geometric scales, or coupled-field interactions. M3SIM develops and evaluates fractional and classical formulations to diagnose these gaps and improve model robustness for engineering decisions.

A familiar framework, broadened where needed

Where classical assumptions and fractional formulations diverge.

Not every CAE problem requires a fractional formulation. Some examples where fractional formulations can better represent the physical response.

Memory
Instantaneous response depends on prior loading path
Classical finite element view
The constitutive response is modeled as state-based with limited history
Fractional modeling view
The constitutive response includes distributed memory of prior loading
Hereditary behavior
Post-load relaxation and creep persist across longer time scales
Classical finite element view
Relaxation is often represented with a small number of characteristic times
Fractional modeling view
Long-tail relaxation and creep can be represented with power-law memory
Nonlocality
Effects extend beyond nearby regions
Classical finite element view
Influence is primarily local (short-range)
Fractional modeling view
Distant regions can also contribute (long-range)
Multiscale bridging
Scale interactions drive system-level response
Classical finite element view
Scales are typically separated, with fine-scale effects embedded through effective properties
Fractional modeling view
Cross-scale coupling can be represented directly without fully resolving every scale
Anomalous transport
Field transport differs from the expected rate
Classical finite element view
Standard diffusion or propagation behavior
Fractional modeling view
Anomalous transport can be captured
Phractals | Platform in Development

Phractals: A fractional finite element platform for advanced CAE workflows.

Phractals is being developed for regimes where integer-order models can lose predictive fidelity across load history, scale interaction, and coupled physics.

Phractals logo
Phractals

Phractals is being built as a commercial, ready-to-deploy platform for solving fractional-order models in engineering practice. It is designed for industry, academia, and national-lab teams that need reproducible workflows to model phenomena that are often underrepresented by integer-order CAE formulations.

Work with M3SIM before Phractals launches.

M3SIM partners with teams on challenging CAE, finite element analysis, scientific computing, and engineering-design problems.