1. Material Definitions Chapter 4

2. Training Manual March 15, 2001 Inventory #001458 4-2 Chapter Objectives Upon completion of this chapter, students will be able to define a wide range of Material Models within the ANSYS/LS-DYNA Program 1. Give an overview of the material models available in ANSYS/LS-DYNA 2. Introduce the GUI material model groupings and input procedure 3. Give guidelines on when specific material models should be used 4. Given step-by-step guidance, material properties will be used in an explicit analysis

3. Training Manual March 15, 2001 Inventory #001458 4-3 Overview - Material Models ANSYS/LS-DYNA contains a wide range of material models for nearly any application Compared to ANSYS implicit, ANSYS/LS-DYNA offers a significantly larger material library ANSYS/LS-DYNA materials offer several unique features not all of which are available in ANSYS implicit: –Strain rate dependent plasticity models –Temperature sensitive plasticity model –Stress and strain failure criterion models –Null models (used in bird-strike) –Equation of state models

4. Training Manual March 15, 2001 Inventory #001458 4-4 (continued) Overview - Material Models Linear Elastic –Isotropic (with Fluid Option) –Orthotropic –Anisotropic Plasticity –Rate Independent –Rate Sensitive Composite Damage Concrete Other –Rigid bodies - Discrete –Cables –Fluid Nonlinear Elastic –Blatz-Ko Rubber –Mooney-Rivlin –Viscoelastic Foam –Isotropic –Orthotropic Equation of State –Temp. & strain rate dependent plasticity –Null materials

5. Training Manual March 15, 2001 Inventory #001458 4-5 GUI Material Input - Description All supported material models are available in the GUI format New GUI allows for optimum material model selection Filtered GUI menus prompt for only the relevant material data Appropriate MP and TBDATA commands are automatically issued MPMOD command associates batch material data into GUI format

6. Training Manual March 15, 2001 Inventory #001458 4-6 GUI Material Input - Procedure STEP 1: Add a new material model Preprocessor: Material Props > Define MAT Model > Add STEP 2: Choose the desired material model –Make sure that the correct Material Number is input –Select the family for which the model belongs (e.g., Plasticity) –Choose the specific model desired and choose the OK button

7. Training Manual March 15, 2001 Inventory #001458 4-7 (continued) GUI Material Input - Procedure STEP 3: Enter the required values For nearly all of the material models DENS, EX, and NUXY are required Make sure that material stress/strain data is in true stress/strain format After all of the data has been input, choose the OK button

8. Training Manual March 15, 2001 Inventory #001458 4-8 (continued) GUI Material Input - Procedure For several of the material models within the ANSYS/LS-DYNA program, load curves are required. They are used to define the dependence of two variables within a material model, such as the variation of yield stress with plastic strain. Load curves are defined using two existing array parameters and the EDCURVE command: –Preprocessor: Material props > Curve Options... The Curve ID Number is directly referenced when defining a specific material model, such as LCID 1 - LCID 4 in the rate dependent plasticity dialogue box shown.

9. Training Manual March 15, 2001 Inventory #001458 4-9 Material Models - Linear Elastic There are three different material models available in the linear elastic family: –Elastic (Isotropic) : Material properties are the same in all directions –Orthotropic : Properties have 3 mutually orthogonal planes of symmetry –Anisotropic : Properties are independent of position at a point within a material Linear elastic materials do not undergo any plastic deformations and are fully defined by generalized Hooke’s law: Elastic (Isotropic) Materials: –Most engineering metals (e.g., steel) are isotropic –Simply defined by DENS, EX, and NUXY

10. Training Manual March 15, 2001 Inventory #001458 4-10 (continued) Material Models - Linear Elastic Orthotropic: –General orthotropic materials are defined with 9 independent constants and DENS –Transversely Isotropic (a special case of orthotropy) materials are defined with five independent constants (EXX, EZZ, NUXY, NUXZ, GXY) and DENS –Orthotropic materials are defined with respect to a specified coordinate system ID 1. Select Linear Elastic >Orthotropic 2. Enter required material constants and density 3. Enter coordinate system ID as defined by the EDLCS command which is found at the following menu path: Preprocessor: Material Props > Local CS > Create Local CS

11. Training Manual March 15, 2001 Inventory #001458 4-11 (continued) Material Models - Linear Elastic Anisotropic: –Anisotropic materials are defined with 21 independent material constants and DENS 1. Select Linear Elastic > Anisotropic 2. Enter required material constants and density 3. Enter coordinate system ID as defined by the EDLCS command

12. Training Manual March 15, 2001 Inventory #001458 4-12 Material Models - Nonlinear Elastic There are three different material models available in the non-linear elastic family: –Blatz-Ko : Used for compressible foam-type materials such as polyurethane rubbers –Mooney Rivlin : Used to define behavior of incompressible rubber materials –Viscoelastic : Defines the behavior of glass and glass-like materials Non-linear elastic materials can undergo large recoverable elastic deformations Blatz-Ko rubber materials are only for rubber materials under compression Poisson’s ratio (NUXY) automatically set to.463 by ANSYS, so only DENS and GXY required Material response is defined through the strain energy density function (W): Blatz-Ko Rubber:

13. Training Manual March 15, 2001 Inventory #001458 4-13 (continued) Material Models - Nonlinear Elastic –Used to define the material response of incompressible rubbers –Mooney-Rivlin model is nearly identical to the 2-parameter model existing in ANSYS implicit. –DENS, NUXY, and constants C 10 and C 01 are required for input –To ensure incompressible behavior, NUXY must be between.49 and.5 –Mooney-Rivlin coefficients can be input directly (TBOPT=0) or calculated automatically from test data (TBOPT=2) –Material response defined through the strain energy density function (W): –where  1,  2, and  3 are the strain invariants and K is the bulk modulus. Mooney-Rivlin:

14. Training Manual March 15, 2001 Inventory #001458 4-14 (continued) Material Models - Nonlinear Elastic –The shear relation behavior is described by the expression: –With DENS, the required input parameters for the model are: G o = The short term (origin) elastic shear modulus G  = The long term (infinity) elastic shear modulus K = elastic bulk modulus 1/  = decay constant Viscoelastic:

15. Training Manual March 15, 2001 Inventory #001458 4-15 (continued) Material Models - Discrete –Discrete material properties must be defined for COMBIN165 elements –Several different spring and damper types can be selected –A damping or stiffness constant must then be entered. Discrete:

16. Training Manual March 15, 2001 Inventory #001458 4-16 (continued) Material Models - Cable –Cable material properties must be defined for LINK167 elements –The density, elastic modulus, and load curve for load-deflection properties must be specified. Note: Rigid Body Definition is explained in Chapter 5. Other > Cable:

17. Training Manual March 15, 2001 Inventory #001458 4-17 Material Models – Plasticity There are 12 different plasticity models available in the ANSYS/LS- DYNA program. The selection of a specific model depends on the type of material being analyzed and the availability of material constants. The accuracy of most highly nonlinear finite element analyses hinges upon the quality of the material constants used. For best results, obtain constants from material suppliers or pay to have the material specially analyzed. The plasticity models can be separated into three distinct categories –Category 1: Strain rate independent plasticity for isotropic materials –Category 2: Strain rate dependent plasticity for isotropic materials –Category 3: Strain rate dependent plasticity for anisotropic materials It is very important to select the correct category for the material being analyzed. It is less important to select the specific model within a category, which is usually controlled by the material data available.

18. Training Manual March 15, 2001 Inventory #001458 4-18 Material Models – Plasticity: Category 1 Category 1: Strain rate independent plasticity for isotropic materials There are three basic strain rate independent plasticity models available: –a. Classical bilinear kinematic hardening (BKIN) –b. Classical bilinear isotropic hardening (BISO) –c. Elastic plastic Hydrodynamic (HYDRO) Both models use two slopes, the elastic modulus (EX) and tangent modulus (ETAN) to represent the stress-strain behavior of the material Strain rate independent models are most typically used in processes such as sheet metal stamping where the overall forming duration is relatively long. All three models can be used for most engineering metals (steel, aluminum, cast iron, etc.) The only differences between the BKIN and BISO models is the hardening assumption, where kinematic hardening assumes secondary yield to occur at 2  y while isotropic hardening occurs at 2  max

19. Training Manual March 15, 2001 Inventory #001458 4-19 (continued) Material Models – Plasticity: Category 1 The required input parameters for the BKIN and BISO models are identical: DENS, EX, NUXY, Yield Stress (  y ), and Tangent Modulus (E tan )

20. Training Manual March 15, 2001 Inventory #001458 4-20 The stress strain behavior can also be defined using up to 16 data points. A linear polynomial equation of state is required to be specified. Material Models – Plasticity: Category 1 Elastic-Plastic Hydrodynamic –Good for materials undergoing large amounts of strain that may encounter failure. –If effective true stress and strain data not specified, isotropic hardening is assumed and sy and Etan must be specified to define the yield strength, where the plastic hardening modulus Eh is defined in terms of E and Etan.

21. Training Manual March 15, 2001 Inventory #001458 4-21 Category 2: Strain rate dependent plasticity for isotropic materials There are five strain rate models available for isotropic materials: –a. Plastic Kinematic: Cowper-Symonds model with failure strain –b. Rate Sensitive: Cowper-Symonds with strength and hardening coefficients –c. Piecewise Linear: Cowper-Symonds with multilinear curve and failure strain –d. Rate Dependent: Strain rate defined with load curves and failure stress –e. Power Law: Ramburgh-Osgood model for superplastic forming Models 2a - 2c utilize the Cowper-Symonds model which scales the yield stress based on the strain rate factor : where C and P are the Cowper-Symonds strain rate parameters. Model 2d is the most general strain rate model because the elastic modulus, yield stress, tangent modulus, and failure stress can all be input as a function of strain. All of the models 2a-2d can be used for general metal and plastic forming analyses of isotropic materials Model 2e is a specialized model used specifically for superplastic forming. Material Models – Plasticity: Category 2

22. Training Manual March 15, 2001 Inventory #001458 4-22 2a. Plastic Kinematic: (continued) Material Models - Plasticity: Category 2 Bilinear hardening plasticity (  y and E tan ) Hardening parameter  between 0 (kinematic) and 1 (isotropic) Failure strain can be input for which elements will be eliminated. The yield function is given by: where  0 is the initial yield stress,  p eff is the effective plastic strain, E p is the plastic hardening modulus which is given by:

23. Training Manual March 15, 2001 Inventory #001458 4-23 2b. Rate Sensitive: (continued) Material Models – Plasticity: Category 2 Plastic behavior with bilinear isotropic hardening Power law hardening defined with strength coefficient k and hardening coefficient n The yield function is given by: where  e is the elastic strain.

24. Training Manual March 15, 2001 Inventory #001458 4-24 2c. Piecewise Linear: (continued) Material Models – Plasticity: Category 2 Stress strain behavior defined with effective stress vs effective strain Load Curve ID (1) Similar to the TB, MISO model in ANSYS implicit Failure strain can be input for which elements will be eliminated Model is very efficient in solution and is most commonly used in crash simulations. Yield surface scaled for rate dependence by the Cowper-Symonds model.

25. Training Manual March 15, 2001 Inventory #001458 4-25 2d. Rate Dependent: (continued) Material Models – Plasticity: Category 2 –Most general strain rate plasticity model –  y, E, E tan, and  fail can all be rate dependent –The yield stress at a given plastic strain rate is defined by: where LCID 1 = defines  y as a function of LCID 2 = defines E as a function of LCID 3 = defines Etan as function of LCID 4 = defines effective von Mises stress at failure as a function of

26. Training Manual March 15, 2001 Inventory #001458 4-26 2e. Power Law: (continued) Material Models – Plasticity: Category 2 Rate sensitive powerlaw plasticity model used specifically for superplastic forming analyses Ramburgh-Osgood constitutive relationship for the yield stress: where k is the material coefficient, m is the hardening coefficient, n is the strain rate parameter, and is the strain rate.

27. Training Manual March 15, 2001 Inventory #001458 4-27 Material Models – Plasticity: Category 3 Category 3: Strain rate dependent plasticity for anisotropic materials –There are four strain rate models available for anisotropic materials: a. Transversely Isotropic: Hills yield criterion with strain rate dependence b. 3 Parameter Barlat: Orthotropic model for sheet metal forming of aluminum c. Barlat Anisotropic: Anisotropic model for forming of 3-D continuum problems d. Transversely anisotropic Forming Limit Diagram –Model 3a is for modeling high strain rate forming processes of general anisotropic materials –Models 3b and 3c were developed at ALCOA for specialized aluminum processes –Model 3d is used specifically for sheet metal forming

28. Training Manual March 15, 2001 Inventory #001458 4-28 (continued) Material Models – Plasticity: Category 3 –Most commonly used for sheet metal forming of anisotropic materials –Optional load curve parameter can be defined for the relationship between the effective yield stress and the effective plastic strain –The yield function is defined by: –The anisotropic hardening parameter, R, is defined by the ratio of the in-plane plastic strain rate to the out-of-plane plastic strain rate: 3a. Transversely Isotropic:

29. Training Manual March 15, 2001 Inventory #001458 4-29 (continued) Material Models – Plasticity: Category 3 Developed for sheet metal forming of aluminum Linear (1) and Exponential (2) hardening rules For the linear rule,  y and E tan input For the exponential rule, n and m input The Barlat exponent m=6 is recommended for BCC metals and M = 8 for FCC metals The orthotropic Lankford coefficients for the length to thickness ratios An orthotropic material coordinate system can be input as specified with the EDMP command. 3b. 3-Parameter Barlat:

30. Training Manual March 15, 2001 Inventory #001458 4-30 (continued) Material Models – Plasticity: Category 3 Model useful for metal forming processes of 3-D continuum materials, especially aluminum Mostly used for solid and not sheet materials There are 6 anisotropic parameters to be determined from experiments a,b,c,f,g,h The Barlat exponent m = 6 is recommended for BCC metals and m = 8 for FCC metals The yield strength is given by:  y =k(  o +  p ) n, where  o and  p are initial yield and plastic strains 3c. Barlat Anisotropic:

31. Training Manual March 15, 2001 Inventory #001458 4-31 (continued) Material Models – Plasticity: Category 3 Model is used for simulating sheet forming processes with transversely isotropic metals. Available only for shell elements Yield behavior can be defined using  y and E tan or a load curve of the effective stress vs plastic strain. Flow Limit Diagram can also be input using load curves to compute maximum strain ratio 3d. Transversely Anisotropic FLD:

32. Training Manual March 15, 2001 Inventory #001458 4-32 Material Models - Foam There are five different foam models available in the ANSYS/LS- DYNA program. The selection of a specific model depends on the type of material being analyzed. There are four options available for isotropic foams: –Closed cell foam: used most often for low density polyurethane –Low density foam: highly compressible for padded materials such as seat cushions –Viscous foam: energy absorbing foam used in crash simulations –Crushable foam: permanent crush materials such as polystyrene There is one option for Honeycomb (orthotropic crushable) foams All of the foam models in ANSYS/LS-DYNA are primarily used in automotive impact applications

33. Training Manual March 15, 2001 Inventory #001458 4-33 Closed Cell Foam: where a, b, and c are experimental parameters, and  = V/ V o +  o - 1, where V is the current volume, V o is the initial volume, and  o is the initial volumetric strain. Material Models - Foam (continued) –Developed for low density polyurethane (often used for modeling impact limiters in shipping containers and automobile design) –DENS, EX, the initial foam pressure, Po, and the Ratio of foam to polymer density, , are required –Includes the effect of confined air pressure –NUXY taken to be approximately zero –The yield condition is defined by:  y = a + b(1+c  ),

34. Training Manual March 15, 2001 Inventory #001458 4-34 (continued) Material Models - Foam Low Density Foam: –Used primarily for seat cushions in automobiles –Both DENS and EX are required –Stress-strain behavior input using a load curve ID (LCID) –In compression, model assumes hysteretic behavior with possible energy dissipation –In tension, model behaves linearly until tension cut-off stress is attained (optional) –NUXY approximately set to zero –When hysteretic unloading is used the reloading will follow the unloading curve if the decay constant,  =0. –If  is nonzero, the original loading is governed by 1-e-  t A viscous coefficient (.05-.5) can be used to model damping effects. –Bulk viscosity can be activated by setting the flag to 1 –A shape unloading factor is used for hysteretic unloading. Values less than one reduce energy dissipation. –A hysteretic unloading (HU) factor between 0 and 1 is input. If HU=1, there is no energy dissipation.

35. Training Manual March 15, 2001 Inventory #001458 4-35 (continued) Material Models - Foam Energy absorbing foam used to model energy absorbing materials (e.g., dummies) in crash- simulations Model should only be used for solids in compressive loading Consists of a nonlinear elastic spring in parallel with a viscous damper DENS, EX (initial Young’s modulus, E1) and NUXY required The elastic stiffness, E’ is defined by: E’ = E 1 V -n 1, where n 1 is the elastic stiffness powerlaw. The viscous coefficient, V’, is given by: V’ = V 2 |1-V| n 2, where V 2 is the initial viscous coefficient and n 2 is the viscous coefficient powerlaw Viscous Foam:

36. Training Manual March 15, 2001 Inventory #001458 4-36 (continued) Material Models - Foam For materials with permanent crush, such as expanded polystyrene solids Optional viscous damping and tension cut-off (tearing) Unloading is considered to be fully elastic Tension is treated as completely elastic-plastic DENS, EX, NUXY required Load curve ID used to define the yield stress versus the volumetric strain,  The volumetric strain  is defined to be:  = 1 - V, where V is defined to be the ratio of the current to initial volume. Crushable Foam:

37. Training Manual March 15, 2001 Inventory #001458 4-37 Honeycomb : (continued) Material Models - Foam Orthotropic crushable foam model developed for the front end material of a side impact bumper and for aerospace structures A nonlinear behavior can be defined separately for normal and shear stresses DENS, EX, and NUXY, Viscosity Coef. Required Yield stress and volume of the fully compacted honeycomb also required Elastic Moduli and Load Curve ID’s for stresses vs relative volume or volumetric strain in each of the orthotropic directions

38. Training Manual March 15, 2001 Inventory #001458 4-38 Composite Damage: Material Models - Composites Developed for failure of composite materials used for energy absorption Elastic moduli, shear moduli, and Poisson’s ratio must be input for each direction Bulk modulus of failed material is required for compressive failure Shear, longitudinal tensile, transverse tensile, and transverse compressive strengths can all be input to define failure

39. Training Manual March 15, 2001 Inventory #001458 4-39 Material Models - Concrete Concrete Damage : Developed to analyze buried steel reinforced cable subject to impact loads. Along with density and Poisson’s ratio, this model requires constants for the concrete and reinforced cable The concrete damage model also requires that a tabulated equation of state also be specified.

40. Training Manual March 15, 2001 Inventory #001458 4-40 Material Model - Fluid Elastic Fluid –This option is used to model fluid-filled containers that will undergo impact loading. –The fluid model only requires that the bulk modulus be specified. The bulk modulus can be input with either the EDMP command or automatically calculated from E x and NUXY values:

41. Training Manual March 15, 2001 Inventory #001458 4-41 Material Models - Equations of State (EOS) There are some material models in ANSYS/LS-DYNA that require an additional equation of state to be defined with them: –Johnson-Cook Plasticity: high strain rate and temperature dependent problems –Null Material: used primarily in bird strike analyses –Zerilli-Armstrong: high speed impact and some metal forming processes –Bamman: Complex material model used with internal equation of state variables. –Steinberg: Modeling Materials deforming at very high strain rates (>105) There are three different EOS types in the ANSYS/LS-DYNA program that can be used with the above material models: –1. Linear Polynomial –2. Gruneisen –3. Tabulated

42. Training Manual March 15, 2001 Inventory #001458 4-42 Material Models - Equations of State (EOS) There are three different EOS types in the ANSYS/LS-DYNA program: –1. Linear Polynomial : EOS is linear in internal energy. The pressure is defined in terms of  and the linear coefficients Ci: P = Co + C1  + C2  2 + C3  3 + (C4 + C5  +C6  2) E where  =  /  o - 1, where  and  o are the current and initial densities. –2. Gruneisen: equation of state with cubic shock - particle velocity. The pressure is defined in terms of  and the Gruneisen coefficients C, a, S1, S2, S3, and  0: –3. Tabulated: EOS is also linear in internal energy. The pressure is defined by: P = Ci(evi) + gTi(evi)E where Ci and Ti are respectively volumetric pressure and temperature values and evi are volumetric strain values.

43. Training Manual March 15, 2001 Inventory #001458 4-43 A,B,C, m, and n are experimentally determined constants and  p is the effective plastic strain The effective plastic strain rate is given by: Johnson-Cook: Material Models - EOS Johnson-Cook Johnson-Cook model used primarily for high strain rate processes such as machining where there are large temperature increases Model originally developed for ballistics DENS, EX, and NUXY required for input The yield stress is defined by:

44. Training Manual March 15, 2001 Inventory #001458 4-44 For temperature calculations, the specific heat, melt temperature, and room temperature are required The effective plastic strain rate is also required A failure strain can be incorporated into the model by the implementation of the failure constants D 1 -D 5 as described by: where After the Johnson-Cook parameters are entered, the equation of state constants must be entered for either the linear polynomial or Gruneisen models. (continued) Material Models - EOS - Johnson-Cook

45. Training Manual March 15, 2001 Inventory #001458 4-45 Material Models - EOS - Null Material Null materials allow equations of state to be considered without computing deviatoric stresses. Null materials are most often utilized in bird strike analyses. The required input are DENS and the pressure cut-off. EX and NUXY are only required for null beams and shells. Viscosity and erosion in tension and compression can optionally also be defined. Null Material:

46. Training Manual March 15, 2001 Inventory #001458 4-46 Material Models - EOS Zerilli-Armstrong The Zerilli-Armstrong Model is used in metal forming processes and high speed impact applications where the stress depends on strain, strain rate, and temperature. One of the three EOS types must be used with this model. The Zerilli-Armstrong Model requires the input of flow stress (C i ), temperature (B i ) and heat capacity (G i ) coefficients. Zerilli-Armstrong:

47. Training Manual March 15, 2001 Inventory #001458 4-47 Bamman: Material Models - EOS Bamman Model Complex material model used in metal forming processes with strain rate and temperature dependence. Model does not require an additional EOS to be specified as internal equation of state variables are input directly into the model through constants (Ai) The Bamman model requires the input of flow stress parameters Ci.

48. Training Manual March 15, 2001 Inventory #001458 4-48 Material Models - EOS Steinberg Model –Deformations of solids at high strain rates (>10 5 ) with failure. Well suited for machining operations and high-speed impact applications. –Yield strength a function of temperature and pressure –Equation of State (EOS) used to determine pressure Steinberg:

49. Training Manual March 15, 2001 Inventory #001458 4-49 Material Models - Guidelines 1. Not all material models are available for every element type. Check the Elements Manual to see which models can be used. 2. For each material model, not all constants and options are required for input. For example, failure strains can be incorporated into a material that does not have strain rate effects by setting the Cowper-Symonds constants to zero. 3. Make sure to use consistent units when defining your material properties. Incorrect units will not only effect the material response, but will also effect the contact stiffness. 4. Don’t underestimate the importance of having accurate material data. Spend the extra time and money to obtain accurate material data.

50. Training Manual March 15, 2001 Inventory #001458 4-50 Material Model Exercise The exercise for this chapter begins on page E4-1 of Volume II. A strain rate dependent plasticity material model with failure is demonstrated with a ceramic bar impacting a metal plate.