Abstract Facial skin dynamics are inherently challenging to simulate due to a combination of geometric, material, and anatomical complexities. Human skin is a nonlinear layered material with spatially heterogeneous attachments to the underlying tissues. During contact events, localized compression and shear induce mechanical instabilities, leading to fine‐scale wrinkling patterns governed by a delicate interplay of geometry, boundary conditions, and through‐the‐thickness stresses. We present a finite element framework to simulate contact‐induced wrinkling of facial skin. We model skin as a viscoelastic material with time‐dependent relaxation that governs the rate, persistence, and damping of wrinkle formation. We employ high‐order prismatic solid‐shell elements to resolve through‐thickness stresses and high‐frequency deformation modes. Central to our approach, we introduce a continuum‐based formulation of skin ligaments to model heterogeneous skin attachments and provide anatomically inspired mobility constraints. These skin ligaments control the formation and appearance of facial wrinkles by modulating their amplitude, wavelength, and spatial distribution. We evaluate our method on a set of synthetic examples and compare simulations with real‐world footage. These results demonstrate that our skin model produces temporally coherent and visually realistic wrinkle patterns during transient contact.

Abstract Structured sheet materials such as 3D‐printed rod networks, multi‐material thin shells, and multi‐layer laminates exhibit diverse mechanical behaviors. To avoid the computational burden of native‐scale simulations, data‐driven homogenization offers a promising alternative. This process involves probing a representative patch of material—a unit cell—with a set of stretching and bending tests subject to periodic boundary conditions. Because macro‐scale bending moments are not directly available from native‐scale simulations, existing methods exclusively rely on elastic energy data. Unfortunately, using only elastic energy from uniaxial tests is not sufficient for capturing the full moment‐curvature relationship, and imposing biaxial curvature states would necessarily break periodicity. We present a moment‐based homogenization method that infers curvature coupling using only uniaxial bending tests. Our method computes macro‐scale bending moments from native‐scale simulations for a wide range of mechanical models. To this end, we translate internal deformations into elastic stresses and then integrate these stresses through the thickness and across the unit‐cell patch. We use the resulting homogenized bending moments along with energy data to fit neural bending energy density functions. We demonstrate our method on a diverse set of materials, including multi‐material shells, rod networks, and multi‐layer sheets. Our results show improved accuracy compared to existing approaches and realistic double‐curvature behavior when applied to larger samples.

We present a computational framework for numerical homogenization of origami materials—thin sheets structured with periodic crease patterns that, once folded, exhibit diverse and often unusual mechanical properties. Whereas the in-plane stiffness of conventional sheet materials is typically orders of magnitude larger than their resistance to bending, origami-based folding introduces geometric structure that can drastically reshape both bending and stretching behavior. However, predicting how a particular crease pattern gives rise to effective macroscopic properties remains challenging due to the complex coupling of crease geometry, folding kinematics, and surface deformations. In this work, we introduce a computational framework that integrates simulation-based folding and numerical homogenization to explore the relationship between crease pattern and effective material behavior. To describe the macromechanical response of origami materials, we employ a quadratic energy model based on Classical Laminate Theory, together with a simplified treatment of crease plasticity. Our unified representation accommodates both straight- and curved-crease designs, revealing a rich space of origami materials with diverse behavior. In particular, we examine how pattern symmetry governs material symmetries, demonstrating examples that span the full spectrum from perfectly isotropic to highly anisotropic membrane and bending responses. Our framework further enables controlled exploration of parameter variations, illustrating how geometric features such as crease curvature shape macroscopic mechanical behavior. We showcase the potential of this approach through a broad set of examples, ranging from canonical straight-crease patterns such as Miura-ori to complex curved-crease tessellations. While a quantitative analysis is left for future work, we validate our homogenized descriptions against native-scale simulations and qualitatively compare deformation behaviors with real-world prototypes.

We introduce ViSkin, a biomechanically principled approach to simulate skin mechanics on personalized avatars. Our model captures the salient characteristics of human skin, i.e., nonlinear stretching properties, anisotropic stiffness, direction-dependent pre-stretch, and heterogeneous sliding behavior. In particular, we introduce a novel representation of Langer lines, which describe the distribution of principal material directions across the human body. We further propose an optimization-based approach for inferring spatially-varying pre-stretch from motion capture data. We implement our new model using a computationally efficient intrinsic representation that simulates skin as a two-dimensional Lagrangian mesh embedded in the three-dimensional body surface. We demonstrate our method on a diverse set of body models, shapes, and poses and compare to experimentally-obtained skin motion data. Our results indicate that our method produces smoother and more plausible skin deformations than a baseline method and shows good accuracy compared to real-world data.

We present a computational approach for modeling the mechanical behavior of flexible scaled sheet materials---3D-printed hard scales embedded in a soft substrate. Balancing strength and flexibility, these structured materials find applications in protective gear, soft robotics, and 3D-printed fashion. To unlock their full potential, however, we must unravel the complex relation between scale pattern and mechanical properties. To address this problem, we propose a contact-aware homogenization approach that distills native-level simulation data into a novel macromechanical model. This macro-model combines piecewise-quadratic uniaxial fits with polar interpolation using circular harmonics, allowing for efficient simulation of large-scale patterns. We apply our approach to explore the space of isohedral scale patterns, revealing a diverse range of anisotropic and nonlinear material behaviors. Through an extensive set of experiments, we show that our models reproduce various scale-level effects while offering good qualitative agreement with physical prototypes on the macro-level.

Stripe patterns are ubiquitous in nature and everyday life. While the synthesis of these patterns has been thoroughly studied in the literature, their potential to control the mechanics of structured materials remains largely unexplored. In this work, we introduce Differentiable Stripe Patterns---a computational approach for automated design of physical surfaces structured with stripe-shaped bi-material distributions. Our method builds on the work by Knöppel and colleagues [2015] for generating globally-continuous and equally-spaced stripe patterns. To unlock the full potential of this design space, we propose a gradient-based optimization tool to automatically compute stripe patterns that best approximate macromechanical performance goals. Specifically, we propose a computational model that combines solid shell finite elements with XFEM for accurate and fully-differentiable modeling of elastic bi-material surfaces. To resolve non-uniqueness problems in the original method, we furthermore propose a robust formulation that yields unique and differentiable stripe patterns. We combine these components with equilibrium state derivatives into an end-to-end differentiable pipeline that enables inverse design of mechanical stripe patterns. We demonstrate our method on a diverse set of examples that illustrate the potential of stripe patterns as a design space for structured materials. Our simulation results are experimentally validated on physical prototypes.

Soft robotics offers unique advantages in manipulating fragile or deformable objects, human-robot interaction, and exploring inaccessible terrain. However, designing soft robots that produce large, targeted deformations is challenging. In this paper, we propose a new methodology for designing soft robots that combines optimization-based design with a simple and cost-efficient manufacturing process. Our approach is centered around the concept of robotic skins---thin fabrics with 3D-printed reinforcement patterns that augment and control plain silicone actuators. By decoupling shape control and actuation, our approach enables a simpler and cost-efficient manufacturing process. Unlike previous methods that rely on empirical design heuristics for generating desired deformations, our approach automatically discovers complex reinforcement patterns without any need for domain knowledge or human intervention. This is achieved by casting reinforcement design as a nonlinear constrained optimization problem and using a novel, three-field topology optimization approach tailored to fabrics with 3D-printed reinforcements. We demonstrate the potential of our approach by designing soft robotic actuators capable of various motions such as bending, contraction, twist, and combinations thereof. We also demonstrate applications of our robotic skins to robotic grasping with a soft three-finger gripper and locomotion tasks for a soft quadrupedal robot.

We propose an optimization-driven approach for automated, physics-based pattern design for tight-fitting clothing. Designing such clothing poses particular challenges since large nonlinear deformations, tight contact between cloth and body, and body deformations have to be accounted for. To address these challenges, we develop a computational model based on an embedding of the two-dimensional cloth mesh in the surface of the three-dimensional body mesh. Our Lagrangian-on-Lagrangian approach eliminates contact handling while coupling cloth and body. Building on this model, we develop a physics-driven optimization method based on sensitivity analysis that automatically computes optimal patterns according to design objectives encoding body shape, pressure distribution, seam traction, and other criteria. We demonstrate our approach by generating personalized patterns for various body shapes and a diverse set of garments with complex pattern layouts.