ANSYS12.0官方培训教程 Explicit_Dynamics_Chapter 9_Material_Models.ppt

1、Chapter 9Material Models,ANSYS Explicit Dynamics,Material Behavior Under Dynamic Loading,In general, materials have a complex response to dynamic loading The following phenomena may need to be modelled Non-linear pressure response Strain hardening Strain rate hardening Thermal softening Compaction (

2、porous materials) Orthotropic behavior (e.g. composites) Crushing damage (e.g. ceramics, glass, geological materials, concrete) Chemical energy deposition (e.g. explosives) Tensile failure Phase changes (solid-liquid-gas) No single material model incorporates all of these effects Engineering Data of

3、fers a selection of models from which you can choose based on the material(s) present in your simulation,Modeling Provided By Engineering Data,Material deformation can be split into two independent parts Volumetric Response - changes in volume (pressure) Equation of state (EOS) Deviatoric Response -

4、 changes in shape Strength model Also, it is often necessary to specify a Failure model as materials can only sustain limited amount of stress / deformation before they break / crack / cavitate (fluids).,Material Deformation,Principal Stresses,A stress state in 3D can be described by a tensor with s

5、ix stress components Components depend on the orientation of the coordinate system used. The stress tensor itself is a physical quantity Independent of the coordinate system used When the coordinate system is chosen to coincide with the eigenvectors of the stress tensor, the stress tensor is represe

6、nted by a diagonal matrix where 1, 2 , and 3, are the principal stresses (eigenvalues). The principal stresses may be combined to form the first, second and third stress invariants, respectively. Because of its simplicity, working and thinking in the principal coordinate system is often used in the

7、formulation of material models.,Elastic Response,For linear elasticity, stresses are given by Hookes law : where l and G are the Lame constants (G is also known as the Shear Modulus) The principal stresses can be decomposed into a hydrostatic and a deviatoric component : where P is the pressure and

8、si are the stress deviators Then :,Hookes Law,Generalized Non-Linear Response,Equation of State,Strength Model,Non-linear Response,Many applications involve stresses considerably beyond the elastic limit and so require more complex material models,Failure Model,i (max,min) = f,Models Available for E

9、xplicit Dynamics,Elastic Constants,Physical and Thermal Properties,Density All material must have a valid density defined for Explicit Dynamics simulations. The density property defines the initial Mass / unit volume of a material at time zero This property is automatically included in all models Sp

10、ecific Heat This is required to calculate the temperature used in material models that include thermal softening This property is automatically included in thermal softening models,Linear Elastic,Isotropic Elasticity Used to define linear elastic material behavior suitable for most materials subject

11、ed to low compressions. Properties defined Youngs Modulus (E) Poissons Ratio () From the defined properties, Bulk modulus and Shear modulus are derived for use in the material solutions. Temperature dependence of the linear elastic properties is not available for explicit dynamics,Linear Elastic,Ort

12、hotropic Elasticity Used to define linear orthotropic elastic material behavior suitable for most orthotropic materials subjected to low compressions. Properties defined Youngs Modulii (Ex, Ey, Ez) Poissons Ratios (xy, yz, xz) Shear Modulii (Gxy, Gyz, Gxz) Temperature dependence of the properties is

13、 not available for explicit dynamics,Linear Elastic,Viscoelastic Represents strain rate dependent elastic behavior Long term behavior is described by a Long Term Shear Modulus, G. Specified via an Isotropic Elasticity model or Equation OF State Viscoelastic behavior is introduced via an Instantaneou

14、s Shear Modulus, G0 and a Viscoelastic Decay Constant . The deviatoric viscoelastic stress at time n+1 is calculated from the viscoelastic stress at time n and the shear strain increments at time n: Deviatoric viscoelastic stress is added to the elastic stress to give the total stress,Viscoelastic,L

15、inear Elastic,Hyperelastic,Several forms of strain energy potential () are provided for the simulation of nearly incompressible hyperelastic materials. Forms are generally applicable over different ranges of strain. Need to verify the applicability of the model chosen prior to use. Currently hyperel

16、astic materials may only be used for solid elements,Tensile tests on vulcanised rubber,Examples of Hyperelasticity,Hyperelastic,Plasticity,If a material is loaded elastically and subsequently unloaded, all the distortion energy is recovered and the material reverts to its initial configuration. If t

17、he distortion is too great a material will reach its elastic limit and begin to distort plastically. In Explicit Dynamics, plastic deformation is computed by reference to the Von Mises yield criterion (also known as PrandtlReuss yield criterion) . This states that the local yield condition is where

18、Y is the yield stress in simple tension. It can be also written as or (since ) Thus the onset of yielding (plastic flow), is purely a function of the deviatoric stresses (distortion) and does not depend upon the value of the local hydrostatic pressure unless the yield stress itself is a function of

19、pressure (as is the case for some of the strength models).,Plasticity,If an incremental change in the stresses violates the Von Mises criterion then each of the principal stress deviators must be adjusted such that the criterion is satisfied. If a new stress state n + 1 is calculated from a state n

20、and found to fall outside the yield surface, it is brought back to the yield surface along a line normal to the yield surface by multiplying each of the stress deviators by the factor By adjusting the stresses perpendicular to the yield circle only the plastic components of the stresses are affected

21、. Effects such as work hardening, strain rate hardening, thermal softening, e.t.c. can be considered by making Y a dynamic function of these,Plasticity,Bilinear Isotropic / Kinematic Hardening Used to define the yield stress (Y) as a linear function of plastic strain, p Properties defined Yield Stre

22、ngth (Y0) Tangent Modulus (A) Isotropic Hardening Total stress range is twice the maximum yield stress, Y Kinematic Hardening Total stress range is twice the starting yield stress, Y0 Models Bauschinger effect Often required to accurately predict response of thin structure (shells),Plasticity,Isotro

23、pic vs Kinematic Hardening,Plasticity,Multilinear Isotropic / Kinematic Hardening Used to define the yield stress (Y) as a piecewise linear function of plastic strain, p Properties defined Up to ten stress-strain pairs Isotropic Hardening Total stress range is twice the maximum yield stress, Y Kinem

24、atic Hardening Can only be used with solid elements,Plasticity,Johnson Cook Strength Used to model materials, typically metals, subjected to large strains, high strain rates and high temperatures. Defines the yield stress, Y, as a function of strain, strain rate and temperature p = effective plastic

25、 strain p* = normalized effective plastic strain rate (1.0 sec-1) TH = homologous temperature = (T - Troom) / (Tmelt - Troom) The plastic flow algorithm used with this model has an option to reduce high frequency oscillations that are sometimes observed in the yield surface under high strain rates.

26、A first order rate correction is applied by default. A specific heat capacity must also be defined to enable the calculation of temperature for thermal softening effects,Normal impact of tungsten sphere on thick steel plate at 10 kms-1 Lagrange Parts used with erosion Johnson-Cook strength model use

27、d to model effects of strain hardening, strain-rate hardening and thermal softening including melting,Effects of Strain Hardening (Johnson-Cook Model) Hypervelocity Impact,Plasticity,Plasticity,Cowper Symonds Strength Used to define the yield strength of isotropic strain hardening, strain rate depen

28、dant materials. Hardening term is same as that used in the Johnson Cook Model Strain rate dependent term has different form No thermal softening term The plastic flow algorithm used with this model has an option to reduce high frequency oscillations that are sometimes observed in the yield surface u

29、nder high strain rates. A first order rate correction is applied by default. Strain rate properties should be input assuming that the units of strain rate are 1/second.,Plasticity,Steinberg Guinan Strength Computes the shear modulus and yield strength as functions of effective plastic strain, pressu

30、re and internal energy (temperature) Fits experimental data on shock-induced free surface velocities Yield Stress and Shear modulus increase with increasing pressure and decreases with increasing temperature Yield stress reaches a maximum value which is subsequently strain rate independent. subject

31、to Y0 1 + n Ymax = effective plastic strain t = temperature (degrees K) = compression = v0 / v Primed parameters (with subscripts P and ) are derivatives with respect to pressure and temperature Constants for 14 metals in the library.,Plasticity,Zerilli Armstrong Strength Used to model materials sub

32、jected to large strains, high strain rates and high temperatures. Based on dislocation dynamics. Applicable to a wide range of bcc (body centered cubic) and fcc (face centered cubic) metals. For fcc metals (e.g. Copper, Nickel, Platinum ), set C1 = 0 For bcc metals (e.g. Iron, Chromium, Tungsten, Va

33、nadium), set C2 = 0 A specific heat capacity must also be defined to enable the calculation of temperature for thermal softening effects,bcc fcc,Brittle / Granular,Drucker-Prager Strength Yield stress is a function of Pressure Used for dry soils, rocks, concrete and ceramics where cohesion and compa

34、ction cause increasing resistance to shear up to a limiting value of the yield stress. Three forms Linear Original Drucker-Prager model Stassi Constructed from yield strengths in uniaxial compresion and tension Piecewise Yield stress is a piecewise linear function of pressure,Brittle / Granular,John

35、son-Holmquist Strength Use to model brittle materials (glass, ceramics) subjected to large pressures, shear strain and high strain rates Combined plasticity and damage model Yielding is based on micro-crack growth instead of dislocation movement (metallic plasticity) Fully cracked material still ret

36、ains some strength in compression due to frictional effects in crushed grains Yield reduced from intact value to fractured value via a Damage function Damage accumulates due to effective plastic strain,Brittle / Granular,Johnson-Holmquist Strength Continuous (JH2) Strength is modeled as smoothly var

37、ying functions of intact strength, fractured strength, strain rate and damage via dimensionless analytic functions Damage is accumulated as ratio of incremental plastic strain over a pressure-dependant fracture strain Two methods for application of damage Gradual (default) Damage is incrementally ap

38、plied as it accumulates Instantaneous Damage accumulates over time, but is only applied to failure when it reaches 1.0 Can be used with a Linear or Polynomial Equation of State,Brittle / Granular,Johnson-Holmquist Strength Segmented (JH1) Strength is modeled using piecewise linear segments Damage is

39、 always applied instantaneously Damage accumulates over time, but is only applied to failure when it reaches 1.0 Can be used with a Linear or Polynomial Equation of State The gradual softening in the more recent continuous model (JH2) has not been supported by experimental data, so this earlier vari

40、ant is still commonly used,Brittle / Granular,Johnson-Holmquist Strength Segmented Example: Penetrator dwell,Brittle / Granular,RHT Concrete Strength Advanced plasticity model for brittle materials developed by Riedel, Hiermaier and Thoma at the Ernst Mach Institute (EMI) Models dynamic loading of c

41、oncrete and other brittle materials such as rock and ceramic. Combined plasticity and shear damage model in which the deviatoric stress in the material is limited by a generalised failure surface of the form: Represents the following response of geological materials Pressure hardening Strain hardeni

42、ng Strain rate hardening in tension and compression Third invariant dependence for compressive and tensile meridians Strain softening (shear induced damage) Coupling of damage due to porous collapse Input can be scaled with compressive strength, fc Data for 35MPa and 140MPa in the distributed materi

43、al library,Impact onto plain concrete,Impact onto reinforced concrete,Brittle / Granular,RHT Concrete Strength Examples,Brittle / Granular,MO Granular Extension of the Drucker-Prager model Takes into account effects associated with granular materials such as powders, soil, and sand. In addition to p

44、ressure hardening, the model also represents density hardening and variations in the shear modulus with density. Yield stress has two components, one dependent on the density and one dependent of the pressure Where Y , p , and denote the total yield stress, the pressure yield stress and the density

45、yield stress respectively. The un-load / re-load slope is defined by the shear modulus which is defined as a function of the density of the material at zero pressure The yield stress is defined by a yield stress pressure and a yield stress density curve with up to 10 points in each curve. The shear

46、modulus is defined by a shear modulus density curve with up to 10 points. All three curves must be defined.,Equation of State,Equation of State Properties Bulk Modulus A bulk modulus can be used to define a linear, energy independent equation of state Combined with a Shear modulus property, this mat

47、erial definition is equivalent to using an Isotropic Linear Elastic, model Shear Modulus A shear modulus must be used when a solid or porous equation of state are selected. To represent fluids, specify a small value.,Equation Of State,Mei-Gruneisen form of Equation of State Covers entire (p,v=1/,e)

48、space using a 1st order Taylor expansion from a reference curve Reference Curves The shock Hugoniot A standard adiabat The 0 K isotherm The isobar p = 0 The curve e = 0 The saturation curve,Equation of State,Polynomial EOS A Mie-Gruneisen form of equation of state that expresses pressure as a polyno

49、mial function of compression (density) 0 (compression): 0 (tension): Commonly found in early papers Shock EOS is more commonly used today,Equation of State,Shock EOS A Mie-Gruneisen form of EOS that uses the shock Hugoniot as a reference curve The Rankine-Hugoniot equations for the shock jump condit

50、ions defining a relation between any pair of the variables (density), p (pressure), e (energy), up (particle velocity) and Us (shock velocity). Us - up space is used to define the Hugoniot In many dynamic experiments, measuring up and Us, it has been found that for most solids and many liquids over

51、a wide range of pressure there is an empirical linear relationship between these two variables: Us = C1 + S1up Gruneisen Coefficient, G, is often approximated using G = 2s1 - 1,Equation of State,Shock EOS Linear Lets you define a linear or a quadratic relationship Us = C1 + S1Up Us = C1 + S1Up + S2U

52、p2 Shock EOS Bilinear Lets you define a bilinear relationship,Porosity,Some materials exhibit irreversible compaction due to pore collapse Examples Foam Powders Concrete Soils Porous materials are extremely effective in attenuating shocks and mitigating impact pressures. Compact to solid density at

53、relatively low stress levels Volume change is large Significant amount of energy is irreversibly absorbed Four models are available in Explicit Dynamics,Porosity,Crushable Foam Relatively simple strength model designed to represent the crush characteristics of foam materials under impact loading con

54、ditions (non-cyclic loading). Must be used with Isotropic Elasticity automatically included Compaction curve is defined as a piecewise linear principal stress vs volumetric strain curve. Youngs Modulus, E, is used for unloading / re-loading Maximum Tensile Stress provides a tension cutoff,Porosity,C

55、ompaction EOS Linear Plastic compaction path is defined as a piecewise linear function of Pressure vs Density The elastic unloading / reloading path is defined via a piecewise linear function of Sound Speed vs Density The Bulk Modulus of the material is calculated from Model can be combined with a v

56、ariety of strength and failure models,Porosity,Compaction EOS Non-Linear Plastic compaction path is defined as a piecewise linear function of Pressure vs Density Elastic unloading / reloading path is defined via a piecewise linear function of Bulk Modulus vs Density For non-linear unloading, if the

57、current pressure is less than the current compaction pressure, the pressure is obtained from the bulk modulus using:,Porosity,P-alpha EOS Crushable Foam and Compaction EOS give good results for low stress levels and for materials with low initial porosities, but they may not do well for highly porou

58、s materials over a wide stress range Herrmanns P- alpha EOS is a phenomenological model which gives the correct behavior at high stresses but at the same time provides a reasonably detailed description of the compaction process at low stress levels. Principal assumption is that specific internal ene

59、rgy is the same for a porous material as for the same material at solid density at identical conditions of pressure and temperature. Solid EOS Porous EOS where V is the specific volume of the porous material and Vs is the specific volume of the solid material = g (p,e) (fitted to experimental data),Failure,Material failure has two components Failure initiation When specified criteria are met within a material, a post failure response is activated Post failure response After failure initiation, subsequent strength characte