1
|
Liu Z, Hui CY, Jagota A, Gong JP, Kiyama R. A surface flattening method for characterizing the surface stress, drained Poisson's ratio and diffusivity of poroelastic gels. SOFT MATTER 2021; 17:7332-7340. [PMID: 34286785 DOI: 10.1039/d1sm00513h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
When a poroelastic gel is released from a patterned mold, surface stress drives deformation and solvent migration in the gel and flattens its surface profile in a time-dependent manner. Specifically, the gel behaves like an incompressible solid immediately after removal from the mold, and becomes compressible as the solvent is able to squeeze out of the polymer network. In this work, we use the finite element method (FEM) to simulate this transient surface flattening process. We assume that the surface stress is isotropic and constant, the polymer network is linearly elastic and isotropic, and that solvent flow obeys Darcy's law. The short-time and long-time surface profiles can be used to determine the surface stress and drained Poisson's ratio of the gel. Our analysis shows that the drained Poisson's ratio and the diffusivity of the gel can be obtained using interferometry and high-speed video microscopy, without mechanical measurement.
Collapse
Affiliation(s)
- Zezhou Liu
- Field of Theoretical and Applied Mechanics, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA.
| | | | | | | | | |
Collapse
|
2
|
Zafar MR, Basu S. Calibrating surface hyperelastic constitutive models in soft solids. Phys Rev E 2021; 103:063003. [PMID: 34271667 DOI: 10.1103/physreve.103.063003] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2021] [Accepted: 05/25/2021] [Indexed: 11/07/2022]
Abstract
Soft solids such as silicone gels, with bulk shear modulus ranging from ∼10 to 1000kPa, exhibit strongly strain-dependent surface stresses. Moreover, unlike conventional stiffer materials, the effects of surface stress in these materials manifest at length scales of tens of micrometers rather than nanometers. However, the calibration of constitutive parameters for surface hyperelasticity has proved to be challenging. Using a reasonably general surface constitutive model, we explore the possibility of obtaining its parameters from force-twist, torque-twist, and force-extension (force-compression) responses of a soft cylinder held between two inert, rigid plates. The motivation behind using these responses is derived from the fact that the roles of the surface constitutive parameters, under suitably ideal conditions, are neatly separated from each other and the three responses easily yield values of the three parameters. Moreover, through large deformation finite-element simulations with coupled bulk and surface hyperelasticity, we delineate the extent to which deviation from the ideal conditions may be tolerated. Using an example with previously reported material parameters, we estimate that, for cylindrical specimens with a radius of the order of 100μm, the capability to measure forces and torques of the order of 1-100μN and 10^{3}-10^{5}μN-μm, respectively, will be required to determine the parameters accurately.
Collapse
Affiliation(s)
- M Rashid Zafar
- Department of Mechanical Engineering, IIT Kanpur, Kanpur 208016, Uttar Pradesh, India
| | - Sumit Basu
- Department of Mechanical Engineering, IIT Kanpur, Kanpur 208016, Uttar Pradesh, India
| |
Collapse
|
3
|
Hui CY, Liu Z, Bain N, Jagota A, Dufresne ER, Style RW, Kiyama R, Gong JP. How surface stress transforms surface profiles and adhesion of rough elastic bodies. Proc Math Phys Eng Sci 2020; 476:20200477. [PMID: 33362416 DOI: 10.1098/rspa.2020.0477] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2020] [Accepted: 10/06/2020] [Indexed: 01/07/2023] Open
Abstract
The surface of soft solids carries a surface stress that tends to flatten surface profiles. For example, surface features on a soft solid, fabricated by moulding against a stiff-patterned substrate, tend to flatten upon removal from the mould. In this work, we derive a transfer function in an explicit form that, given any initial surface profile, shows how to compute the shape of the corresponding flattened profile. We provide analytical results for several applications including flattening of one-dimensional and two-dimensional periodic structures, qualitative changes to the surface roughness spectrum, and how that strongly influences adhesion.
Collapse
Affiliation(s)
- Chung-Yuen Hui
- Field of Theoretical and Applied Mechanics, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA.,Global Station for Soft Matter, GI-CoRE, Hokkaido University, Sapporo, Japan
| | - Zezhou Liu
- Field of Theoretical and Applied Mechanics, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
| | - Nicolas Bain
- Laboratory of Soft and Living Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Anand Jagota
- Departments of Bioengineering and of Chemical and Biomolecular Engineering, Lehigh University, 111 Research Drive, Bethlehem, PA 18015, USA
| | - Eric R Dufresne
- Laboratory of Soft and Living Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Robert W Style
- Laboratory of Soft and Living Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Ryuji Kiyama
- Graduate School of Life Science, Hokkaido University, Sapporo 001-0021, Japan
| | - Jian Ping Gong
- Global Station for Soft Matter, GI-CoRE, Hokkaido University, Sapporo, Japan.,Faculty of Advanced Life Science, Hokkaido University, Sapporo 001-0021, Japan.,WPI-ICReDD, Hokkaido University, Sapporo 001-0021, Japan
| |
Collapse
|
4
|
Liu Z, Jagota A, Hui CY. Modeling of surface mechanical behaviors of soft elastic solids: theory and examples. SOFT MATTER 2020; 16:6875-6889. [PMID: 32642744 DOI: 10.1039/d0sm00556h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Surfaces of soft solids can have significant surface stress, extensional modulus and bending stiffness. Previous theoretical studies have usually examined cases in which both the surface stress and bending stiffness are constant, assuming small deformation. In this work we consider a general formulation in which the surface can support large deformation and carry both surface stresses and surface bending moments. We demonstrate that the large deformation theory can be reduced to the classical linear theory (Shuttleworth equation). We obtain exact solutions for problems of an inflated cylindrical shell and bending of a plate with a finite thickness. Our analysis illustrates the different manners in which surface stiffening and surface bending stabilize these structures. We discuss how the complex surface constitutive behaviors affect the stress field of the bulk. Our calculation provides insights into effects of strain-dependent surface stress and surface bending in the large deformation regime, and can be used as a model to implement surface finite elements to study large deformation of complex structures.
Collapse
Affiliation(s)
- Zezhou Liu
- Department of Mechanical and Aerospace Engineering, Field of Theoretical and Applied Mechanics, Cornell University, 322 Kimball Hall, Ithaca, NY 14853, USA.
| | - Anand Jagota
- Departments of Bioengineering and of Chemical & Biomolecular Engineering, Lehigh University, 111 Research Drive, Bethlehem, PA 18015, USA
| | - Chung-Yuen Hui
- Department of Mechanical and Aerospace Engineering, Field of Theoretical and Applied Mechanics, Cornell University, 322 Kimball Hall, Ithaca, NY 14853, USA.
| |
Collapse
|
5
|
Liu Z, Bouklas N, Hui CY. Coupled flow and deformation fields due to a line load on a poroelastic half space: effect of surface stress and surface bending. Proc Math Phys Eng Sci 2020; 476:20190761. [PMID: 32082069 PMCID: PMC7016556 DOI: 10.1098/rspa.2019.0761] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2019] [Accepted: 12/19/2019] [Indexed: 11/12/2022] Open
Abstract
In the past decade, many experiments have indicated that the surfaces of soft elastic solids can resist deformation by surface stresses. A common soft elastic solid is a hydrogel which consists of a polymer network swollen in water. Although experiments suggest that solvent flow in gels can be affected by surface stress, there is no theoretical analysis on this subject. Here we study the solvent flow near a line load acting on a linear poroelastic half space. The surface of this half space resists deformation by a constant, isotropic surface stress. It can also resist deformation by surface bending. The time-dependent displacement, stress and flow fields are determined using transform methods. Our solution indicates that the stress field underneath the line load is completely regularized by surface bending-it is bounded and continuous. For small surface bending stiffness, the line force is balanced by surface stresses; these forces form what is commonly known as 'Neumann's triangle'. We show that surface stress reduces local pore pressure and inhibits solvent flow. We use our line load solution to simulate the relaxation of the peak which is formed by applying and then removing a line force on the poroelastic half space.
Collapse
Affiliation(s)
- Zezhou Liu
- Sibley School of Mechanical and Aerospace Engineering, Field of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA
| | - Nikolaos Bouklas
- Sibley School of Mechanical and Aerospace Engineering, Field of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA
| | - Chung-Yuen Hui
- Sibley School of Mechanical and Aerospace Engineering, Field of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA
- Global Station for Soft Matter, GI-CoRE, Hokkaido University, Sapporo, Japan
| |
Collapse
|