A Review on Computational Modeling of Time-Evolving Functionality in 4d Manufacturing: From Smart Materials to Surface-Driven Systems

Abstract

4D manufacturing has emerged as a significant area in advanced engineering, enabling systems that evolve over time in response to external stimuli. Despite growing interest, most studies focus on shape morphing in smart materials, limiting a broader computational understanding. This paper reframes 4D manufacturing as a computer-augmented design paradigm in which geometry, material properties, and structural behavior are intentionally programmed to evolve in a controlled, time-dependent manner. The review focuses on computational modeling frameworks based on internal state variables, constitutive evolution laws, and multiphysics finite element formulations. Bulk-driven systems, including shape memory alloys and polymers, are discussed to establish the constitutive and computational foundations of time-dependent functional behavior. The particular emphasis is focused on surface-driven 4D manufacturing, where residual stresses, gradient microstructures, and surface integrity act as programmable drivers of long-term performance. In contrast to bulk-responsive systems dominated by reversible actuation, surface-driven mechanisms are localized, depth-dependent, and often irreversible, with significant implications for fatigue, wear, and structural reliability. However, such effects remain underrepresented in current computational analyses. To address this gap, the review examines modeling approaches for surface processing techniques, including ball burnishing, ultrasonic surface peening, and laser-based treatments, evaluating their role in enabling programmable surface states. Finally, finite element methods, time-dependent constitutive models, reduced-order approaches, and data-driven techniques are critically assessed in terms of predictive capability and computational efficiency. The major challenges, including surface-bulk coupling, gradient-aware modeling, and long-term predictability, are identified, along with future directions for advancing predictive, design-driven 4D manufacturing frameworks.