Structural Mechanics Module - COMSOL Multiphysics

1 Structural Mechanics ModuleUser s GuideContact InformationVisit the Contact COMSOL page at to submit general inquiries, contact Technical Support, or search for an address and phone number. You can also visit the Worldwide Sales Offices page at for address and contact you need to contact Support, an online request form is located at the COMSOL Access page at Other useful links include: Support Center: Product Download: Product Updates: COMSOL Blog: Discussion Forum: Events: COMSOL Video Gallery: Support Knowledge Base: number: CM021101 Structural Mechanics Module User s Guide 1998 2018 COMSOLP rotected by patents listed on , and Patents 7,519,518; 7,596,474; 7,623,991; 8,457,932; 8,954,302; 9,098,106; 9,146,652; 9,323,503; 9,372,673; and 9,454,625. Patents Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement ( ) and may be used or copied only under the terms of the license , the COMSOL logo, COMSOL Multiphysics , COMSOL Desktop, COMSOL Server, and LiveLink are either registered trademarks or trademarks of COMSOL AB.

2 All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see : COMSOL | 3 Contents Chapter 1: IntroductionAbout the Structural Mechanics Module 22 Why Structural Mechanics is Important for Modeling .. 22 What Problems Can It Solve? .. 23 The Structural Mechanics Module Physics Interface Guide .. 26 Common Physics Interface and Feature Settings and Nodes .. 30 Geometry Levels for Study Capabilities .. 30 Where Do I Access the Documentation and Application Libraries? .. 32 Overview of the User s Guide 36 Chapter 2: Structural Mechanics ModelingStudy Types 41 Introduction .. 41 Stationary Analysis .. 41 Eigenfrequency Analysis.

3 42 Mode Analysis .. 46 Time Domain Analysis .. 47 Frequency Domain Analysis .. 48 Modal Superposition .. 51 Harmonic Perturbation .. 53 Modal Reduced Order .. 56 Linearized Buckling Analysis .. 61 Bolt Pretension Study .. 62 Response Spectrum Analysis Study .. 63 Selecting the Physics Interface 65 Solid Mechanics .. 65 Shell and Plate .. 68 Membrane .. 684 | CONTENTSBeam .. 69 Truss .. 69 Selecting Discretization 70 Shape Function Order .. 70 Lagrange and Serendipity Shape Functions .. 71 Choosing Shape Functions in Multiphysics Models .. 71 Implicit Shape Function Orders .. 72 Coupling Different Element Types 74 Introduction to the Element Types .. 74 Coupling Techniques .. 74 Applying Loads 81 Units, Orientation, and Visualization .. 81 Load Cases .. 83 Singular Loads.

4 84 Moments in the Solid Mechanics Interface .. 85 Pressure .. 86 Acceleration Loads .. 86 Temperature Loads Thermal Expansion .. 86 Hygroscopic Swelling .. 87 Total Loads .. 87 Defining Constraints 89 Rigid Body Motion .. 89 Orientation .. 90 Prescribed Displacements, Velocities, and Accelerations .. 91 Symmetry Constraints .. 92 Elemental and Nodal Constraints.. 94 Suppressing Constraints on Lower Dimensions .. 96 Kinematic Constraints .. 97 Rotational Joints .. 98 Calculating Reaction Forces 99 Using Predefined Variables to Evaluate Reaction Forces .. 99 Using Weak Constraints to Evaluate Reaction Forces .. 100 Using Surface Traction to Evaluate Reaction Forces.. 101 CONTENTS | 5 Evaluating Surface Traction Forces on Internal Boundaries .. 102 Introduction to Material Models 103 Material Models for Structural Mechanics .

5 103 Combination of Material Models .. 104 Entering material data .. 105 Introduction to Linear Elastic Materials .. 105 Introduction to Viscoelastic Materials .. 106 Mixed Formulation .. 106 Modeling Damage .. 107 About the Material Databases for the Structural Mechanics Module .. 108 Using External Materials .. 109 Modeling Piezoelectric Problems 122 About Piezoelectric Materials .. 122 Piezoelectric Material Orientation .. 123 Piezoelectric Losses.. 131 References for Piezoelectric Damping .. 136 Piezoelectric Coupling .. 137 Create the Piezoelectric Effect Interface and Define Domains .. 137 Complete Settings of Piezoelectric Materials .. 139 Add Damping and Loss .. 140 Define Material Properties .. 140 Coupling Piezoelectric Devices with Acoustics.

6 141 Modeling Magnetostrictive Materials 143 Magnetostriction Coupling .. 143 Create the Magnetostriction Interface and Define Domains.. 143 Linear vs Nonlinear Magnetostriction .. 145 Mechanical Damping and Losses 146 Damping Sources.. 146 About Damping .. 147 Rayleigh Damping .. 149 Loss Factor Damping .. 151 Viscous Damping .. 152 Equivalence Between Loss Factor, Rayleigh, and Viscous Damping .. 152 Explicit Complex Valued Damping .. 1536 | CONTENTSV iscoelastic Damping .. 153 Piezoelectric Damping .. 153 Adding Damping in the Modal Solver .. 153 Modeling Geometric Nonlinearity 155 Geometric Nonlinearity, Frames, and the ALE Method .. 155 Geometric Nonlinearity for the Solid Mechanics Interface.

7 163 Geometric Nonlinearity for the Shell, Plate, Membrane, Beam and Truss Interfaces .. 164 Solving Geometrically Nonlinear Problems .. 164 Prestressed Structures.. 165 Geometric Nonlinearity for the Piezoelectric Material.. 167 References .. 170 Contact Modeling 171 General .. 171 Setting up a contact problem .. 171 Contact Pairs .. 174 Meshing for Contact Analysis .. 175 Constraints .. 176 Settings for Contact Nodes .. 177 Time- dependent Contact Analysis .. 182 Multiphysics Contact .. 182 Fallback Nodes for Contact .. 183 Solver Settings for Contact Analysis.. 183 Monitoring the Solution .. 185 dependent Variables in Contact Analysis .. 185 Important Contact Variables .. 188 Activating and Deactivating Material 190 Springs and Dampers 193 Defining Multiphysics Models 195 Thermal-Structure Interaction.

8 195 Acoustic-Structure Interaction.. 196 Thermal-Electric- Structural Interaction .. 196 CONTENTS | 7 Thermally Coupled Problems 198 Temperature- dependent Material Data .. 198 Thermal Expansion .. 200 Constraints and Thermal Expansion.. 206 Thermoelastic Damping .. 207 Fluid-Structure Interaction 209 Deforming Fluid Domains .. 209 Union or Assembly .. 210 Contact and FSI .. 211 Computing Mass Properties 212 Effective Properties of Periodic Structures 215 RVE Modeling Using the Cell Periodicity Node .. 215 Pretensioned Bolts 217 Simplified Modeling of Bolt Threads 223 Performing a Response Spectrum Analysis 225 Stress Linearization 233 Solver Settings 239 Symmetric Matrices .. 239 Selecting Iterative Solvers .. 240 Solver Settings for Viscoelasticity, Creep, and Viscoplasticity.

9 241 Specifying Tolerances and Scaling for the Solution Components .. 242 Solver Settings .. 2428 | CONTENTSPart Libraries 244 Chapter 3: Structural Mechanics TheorySolid Mechanics Theory 248 Introduction .. 248 Frames and Coordinate Systems 250 Material and Spatial Coordinates .. 250 Coordinate Systems.. 251 Analysis of Deformation 253 Lagrangian Formulation .. 253 Deformation Measures .. 256 Invariants of Strain .. 259 Inelastic Strain Contributions .. 263 Axial Symmetry and Deformation .. 266 Generalized Plane Strain .. 269 Out-of-plane and Circumferential Modes .. 271 Stresses 274 Defining Stress.

10 274 Invariants of the Stress Tensor .. 275 Plane Strain and Plane Stress Cases .. 278 Initial Stresses and Strains .. 279 External Stress.. 280 Axial Symmetry and Stresses .. 281 Equation of Motion 282 Material Models 285 Linear Elastic Material .. 288 Mixed Formulation .. 296 Nonlinear Elastic Materials .. 298 Linear Viscoelastic Materials .. 308 Large Strain Viscoelasticity .. 317 CONTENTS | 9 Hyperelastic Material Models .. 319 Elastoplastic Material Models .. 340 Failure Criteria for Concrete, Rocks, and Other Brittle Material .. 372 Elastoplastic Soil Models .. 377 Creep and Viscoplasticity.. 389 Shape Memory Alloy .. 403 Piezoelectric Material .. 407 Magnetostrictive Material.. 412 Rigid Domain Model .. 419 Damage Models.