An official website of the United States government
Abstract This study computationally investigates the elastic interaction of two pressurized cylindrical cavities in a 2D hyperelastic medium. Unlike linear elasticity, where interactions are exclusively attractive, nonlinear material models (neo-Hookean, Mooney–Rivlin, Arruda–Boyce) exhibit both attraction and repulsion between the cavities. A critical pressure-shear modulus ratio governs the transition, offering a pathway to manipulate cavity configurations through material and loading parameters. At low ratios, the interactions are always attractive, while at high ratios, both attractive and repulsive regimes exist depending on the separation between the cavities. The effect of the strain-stiffening on these interactions is also analyzed. These insights bridge theoretical and applied mechanics, with implications for soft material design and subsurface engineering.
more »
« less
A comparative study of two constitutive models within an inverse approach to determine the spatial stiffness distribution in soft materials
A comparative study is presented to solve the inverse problem in elasticity for the shear modulus (stiffness) distribution utilizing two constitutive equations: (1) linear elasticity assuming small strain theory, and (2) finite elasticity with a hyperelastic neo-Hookean material model. Assuming that a material undergoes large deformations and material nonlinearity is assumed negligible, the inverse solution using (2) is anticipated to yield better results than (1). Given the fact that solving a linear elastic model is significantly faster than a nonlinear model and more robust numerically, we posed the following question: How accurately could we map the shear modulus distribution with a linear elastic model using small strain theory for a specimen undergoing large deformations? To this end, experimental displacement data of a silicone composite sample containing two stiff inclusions of different sizes under uniaxial displacement controlled extension were acquired using a digital image correlation system. The silicone based composite was modeled both as a linear elastic solid under infinitesimal strains and as a neo-Hookean hyperelastic solid that takes into account geometrically nonlinear finite deformations. We observed that the mapped shear modulus contrast, determined by solving an inverse problem, between inclusion and background was higher for the linear elastic model as compared to that of the hyperelastic one. A similar trend was observed for simulated experiments, where synthetically computed displacement data were produced and the inverse problem solved using both, the linear elastic model and the neo-Hookean material model. In addition, it was observed that the inverse problem solution was inclusion size-sensitive. Consequently, an 1-D model was introduced to broaden our understanding of this issue. This 1-D analysis revealed that by using a linear elastic approach, the overestimation of the shear modulus contrast between inclusion and background increases with the increase of external loads and target shear modulus contrast. Finally, this investigation provides valuable information on the validity of the assumption for utilizing linear elasticity in solving inverse problems for the spatial distribution of shear modulus associated with soft solids undergoing large deformations. Thus, this work could be of importance to characterize mechanical property variations of polymer based materials such as rubbers or in elasticity imaging of tissues for pathology.
more »
« less
- Award ID(s):
- 1663435
- PAR ID:
- 10057051
- Date Published:
- Journal Name:
- International journal of mechanical sciences
- Volume:
- 140
- ISSN:
- 0020-7403
- Page Range / eLocation ID:
- 446-454
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying full‐field heterogeneous elastic properties of soft materials using traditional engineering approaches is fundamentally challenging due to difficulties in estimating local stress fields. Recently, there has been a growing interest in data‐driven models for learning full‐field mechanical responses, such as displacement and strain, from experimental or synthetic data. However, research studies on inferring full‐field elastic properties of materials, a more challenging problem, are scarce, particularly for large deformation, hyperelastic materials. Here, a physics‐informed machine learning approach is proposed to identify the elasticity map in nonlinear, large deformation hyperelastic materials. This study reports the prediction accuracies and computational efficiency of physics‐informed neural networks (PINNs) in inferring the heterogeneous elasticity maps across materials with structural complexity that closely resemble real tissue microstructure, such as brain, tricuspid valve, and breast cancer tissues. Further, the improved architecture is applied to three hyperelastic constitutive models: Neo‐Hookean, Mooney Rivlin, and Gent. The improved network architecture consistently produces accurate estimations of heterogeneous elasticity maps, even when there is up to 10% noise present in the training data.more » « less
-
The level set method has been widely applied in topology optimization of mechanical structures, primarily for linear materials, but its application to nonlinear hyperelastic materials, particularly for compliant mechanisms, remains largely unexplored. This paper addresses this gap by developing a comprehensive level set-based topology optimization framework specifically for designing compliant mechanisms using neo-Hookean hyperelastic materials. A key advantage of hyperelastic materials is their ability to undergo large, reversible deformations, making them well-suited for soft robotics and biomedical applications. However, existing nonlinear topology optimization studies using the level set method mainly focus on stiffness optimization and often rely on linear results as preliminary approximations. Our framework rigorously derives the shape sensitivity analysis using the adjoint method, including crucial higher-order displacement gradient terms often neglected in simplified approaches. By retaining these terms, we achieve more accurate boundary evolution during optimization, leading to improved convergence behavior and more effective structural designs. The proposed approach is first validated with a mean compliance problem as a benchmark, demonstrating its ability to generate optimized structural configurations while addressing the nonlinear behavior of hyperelastic materials. Subsequently, we extend the method to design a displacement inverter compliant mechanism that fully exploits the advantages of hyperelastic materials in achieving controlled large deformations. The resulting designs feature smooth boundaries and clear structural features that effectively leverage the material's nonlinear properties. This work provides a robust foundation for designing advanced compliant mechanisms with large deformation capabilities, extending the reach of topology optimization into new application domains where traditional linear approaches are insufficient. The developed methodology is expected to provide a timely solution to computational design for soft robotics, flexible mechanisms, and other emerging technologies that benefit from hyperelastic material properties.more » « less
-
The deformations of several slender structures at nano-scale are conceivably sensitive to their non-homogenous elasticity. Owing to their small scale, it is not feasible to discern their elasticity parameter fields accurately using observations from physical experiments. Molecular dynamics simulations can provide an alternative or additional source of data. However, the challenges still lie in developing computationally efficient and robust methods to solve inverse problems to infer the elasticity parameter field from the deformations. In this paper, we formulate an inverse problem governed by a linear elastic model in a Bayesian inference framework. To make the problem tractable, we use a Gaussian approximation of the posterior probability distribution that results from the Bayesian solution of the inverse problem of inferring Young’s modulus parameter fields from available data. The performance of the computational framework is demonstrated using two representative loading scenarios, one involving cantilever bending and the other involving stretching of a helical rod (an intrinsically curved structure). The results show that smoothly varying parameter fields can be reconstructed satisfactorily from noisy data. We also quantify the uncertainty in the inferred parameters and discuss the effect of the quality of the data on the reconstructions.more » « less
-
Geometry projection-based topology optimization has attracted a great deal of attention because it enables the design of structures consisting of a combination of geometric primitives and simplifies the integration with computer-aided design (CAD) systems. While the approach has undergone substantial development under the assumption of linear theory, it remains to be developed for non-linear hyperelastic problems. In this study, a geometrically non-linear explicit topology optimization approach is proposed in the framework of the geometry projection method. The energy transition strategy is adopted to mitigate excessive distortion in low-stiffness regions that might cause the equilibrium iterations to diverge. A neo-Hookean hyperelastic strain energy potential is used to model the material behavior. Design sensitivities of the functions passed to the gradient-based optimizer are detailed and verified. The proposed method is used to solve benchmark problems for which the output displacement in a compliant mechanism is maximized and the structural compliance is minimized.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- The DOI is not currently available.
