Nature is full with intricate shapes and forms. Engineering design has long been dominated by orthogonal Cartesian principles. Nature inspired equation based mathematical surfaces are under renewed interest due to their innovative design potential and practical viability by digital engineering. This research explores the role of nature-inspired structural surfaces in engineering and architectural design. These geometries, rooted in mathematical elegance and observed in natural systems, present unique opportunities for efficiency, aesthetics, and performance. Surfaces are categorized as,  Ruled Surfaces, Surfaces of Revolution, Spiral Surfaces, and Exotic Surfaces. Each is analysed through its definition, parametric equation, natural manifestation, CAD representation, current engineering use, & potential future applications. By incorporating these geometries into architecture, engineering systems, and materials science, engineers and designers can create products and structures that are both functional and aesthetically pleasing, while also optimizing resource usage and enhancing performance, leading to more sustainable and efficient technologies. The future of engineering innovation will continue to benefit from the study and application of these natural and mathematical forms.

This establishes the feasibility and technical basis for Selective Infrared Reflectivefilms. for solar control. This selectively reflects near-infrared (NIR) radiation while maintaining high visible-light transmittance, thereby reducing solar heat gain without compromising transparency. The proposed approach targets NIR wavelengths near 850, 1050, and 1250 nm using multilayer thin-film structures comprising alternating PC & PMMA layers. Based on quarter-wave-stack or Bragg-reflector principles, these multilayers form photonic bandgap structures that reflect selected IR wavelengths while transmitting visible light. Digital Simulations demonstrate IR reflectance above 98%, depending on layer count, with visible transmittance up to 80%. Multiband spectral selectivity can be achieved through multilayer configurations on both sides of the substrate. Multi-manifold co-extrusion provides a scalable manufacturing route for continuous production.. The technology offers a pathway to high-LSGR, low-SHGC materials with engineered spectral selectivity for next-gen  passive solar control.

Metamaterial cloaking offers a revolutionary approach to manipulating wave propagation, electromagnetic, acoustic, optical, and elastic, to render objects undetectable, stealth. Despite significant theoretical and experimental advancements, large-scale application remains hindered by fabrication constraints at micro and nanoscales. This report explores a practical alternative: macro-optical cloaking,  applied to a critical automotive safety problem, the A-pillar blind spot. This study focuses on a case of ray optics-based cloaking using conventional lenses and Fresnel elements to mitigate the visual obstruction caused by the A-pillar. Utilizing Multiphysics simulation and fabricating physical prototypes, the study demonstrates the feasibility of constructing cloaking systems with standard optical components and materials. The results validate macro cloaking as a scalable and cost-effective solution to improve driver visibility without compromising structural integrity, opening new avenues in automotive design and safety engineering. A FRP based structural optical solution is also proposed.

Multimaterial design as a core element within the broader M5-enabled Engineering Innovation framework.  MultiMaterial design expands the engineering solution space by integrating materials with complementary properties to overcome conflicting requirements of strength, weight, cost, and performance. This outlines the evolution of multimaterial design through the 4-Blocker, highlights natural inspirations and manufacturing enablers, and emphasizes the role of computational CAE tools in integrating complex material systems. A case study on Floor Reaction Orthosis (FRO) demonstrates the comparative advantages of nylon, steel, CFRP, and a multimaterial hybrid design. Results revealed that multimaterial systems offers favourable balance of stiffness, weight, and cost, validating their potential as a transformative approach to engineering innovation 

Water scarcity is an escalating global concern, particularly in arid and semi-arid regions. Dew harvesting, an ancient yet underutilized method of atmospheric water collection, offers a sustainable, passive solution for potable water generation. This study explores how nature-inspired architectural forms can significantly enhance dew collection efficiency. Drawing biomimetic inspiration from the desert beetle’s condensation mechanisms, we investigate helicoidal and Dini’s spiral surfaces based flat, funnel, helicoidal, and spiral collectors. Dini’s spiral design demonstrated a remarkable 443% improvement in collection efficiency. This shows transformative potential of bio-inspired CAD in addressing water scarcity. The study highlights how natute inspired forms can enable dew harvesting systems that are efficient, low-cost, and scalable for water-stressed regions. 

The natural world spans vast length and time scales, while engineering design typically focuses on a narrow spectrum dominated by a single scale. Multiscale modelling bridges this gap by linking atomic, microstructural, and continuum levels, enabling advanced design and innovation. Within the M5 framework, comprising Multimaterial, Multifunctional, Multiscale, Multiphysics, and Multimodal domains—multiscale modelling plays a pivotal role in integrating insights across scales to optimize performance. This report shows the fundamentals of multiscale modelling and demonstrates its application through a case study of wind turbine blades, where atomic-scale carbon structures are connected to macro-scale structural performance, highlighting the transformative potential of this approach for next-generation engineering design.

Material unity has historically advanced science by unifying diverse phenomena, from Newton’s gravity to Einstein’s spacetime. A similar unifying approach built on M5 promises transformative innovation. Among these, multifunctionality—embedding several uses into a single material, product, or system—emerges as a powerful driver of resource efficiency and sustainability. Nature offers exemplary models of multifunctionality, such as proteins, butterfly wings, and spider silk, where structures inherently perform multiple roles. Modern products like smartphones illustrate how multifunctionality reshapes industries by integrating diverse features within compact designs. Supported by multifunctional materials, additive manufacturing, and hybrid principles, multifunctional design paves the way for efficient, sustainable, and high-performance engineering innovations. A case study on Multiwall Roof Sheets demonstrates the potential of multifunctional design validated by Digital computational engineering, showcasing structural, thermal, acoustic, and optical performance enhancements.

Self-reporting mechanochromic materials provide a passive, distributed approach to structural health monitoring (SHM) by converting mechanical deformation into a visible colour change. Unlike conventional sensor networks, they can operate without power, wiring, or signal-conditioning infrastructure, enabling the structure itself to function as a sensing surface. This case study investigates nature-inspired structural-colour mechanisms using COMSOL Multiphysics wave-optics modelling of diffraction gratings and butterfly-inspired photonic structures under strain. Reflection spectra were converted into RGB/HEX colours using CIE 1931 colour matching functions, D65 illumination, and a 2° standard observer. The butterfly-inspired structure exhibited a peak reflection shift from 384 to 448 nm over 0–18% volumetric strain, corresponding to a 64 nm red shift and approximately 3.64 nm/% strain sensitivity. The concept offers an Open Innovation platform for developing photonic coatings, films, structural skins, and AI-enabled visual inspection systems for distributed infrastructure SHM.

Materials with an order variable in thermal conductivity as a function of temperature is desirable for thermoelectric heat energy recovery, building thermal insulation and solar thermal applications. Thermal Conductivity is an inherent material property. Engineering the fundamental Thermal conductivity needs manipulation at thermal photon level for conventional materials. Engineering thermal photonic band gaps are under research and development. This paper mainly focuses on the commercially available material and leverages composite material principle to design the materials for the variable thermal conductivity as a function of temperature. This approach is expected to enable faster, commercially viable and robust products. The variable thermal conductivity material concept highlights the engineered thermal composite material concept which takes temperature as input to change the internal morphology of composite and constituents to change the thermal conductivity significantly. These are critical in, heat exchangers, cooling systems, and electronic devices to improve thermal performance.