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3.4 Dilatancy The strict adherence of the stability postulations of Drucker usually requires an associated yield constitutive law (e.g. dilatancy angle = friction angle). But in reality, for some materials, the calculated volume strains are significantly larger than those, determined by experiments. In that cases, a deformation behaviour closer to reality can be described by using non-associated flow rules. The dilatancy angle describes the ratio of normal and shear translation in the Mohr-Coulomb shear criterion. It has two limits: Dilatancy angle = friction angle => maximum plastic normal strain at shear strain, associated plasticity Dilatancy angle = 0.0 => no plastic normal strain at shear (not recommended limit case because of resulting numerical problems) By replacing the friction angle ϕ by the dilatancy angle ψ within the yield condition (rsp. plastic potential function), a non-associated flow rule is obtained. In addition to that it has to be considered, that the dilatancy angle is only physically reasonable for dilatancy angle ψ ≤ friction angle ϕ. A dilatancy angle larger than the friction angle leads to generation of energy within the system. For the Drucker-Prager yield condition, the plastic deformation behaviour can be controlled via a nonassociated flow rule by manipulating the dilatancy factor δ. Then the plastic potential is modified according to the equations ( Q = σS + β δσ m (3-18) and ( (3-21). Thereby: dilatancy factor δ = 1 => associated plasticity dilatancy factor δ ≤ 1 => non-associated plasticity For the compressive domain 0 ≤ δc ≤ 1 is true. In the tensile domain of the Drucker-Prager, a yield condition of δt = 0,1 ... 0,25 is recommended. In case of prevalent shear strain, the dilatancy factor δ can be calculated via the ratio of the beta values from Fig. 3-8 with the help of the friction angle ϕ and the dilatancy angle ψ. From equation (4.1), this could calculated by: β ( ϕ) = 3 6 ⋅ sinϕ ( 3 + sinϕ) β ( ψ) = 3 6 ⋅ sinψ ( 3 + sinψ) β β ( ϕ) ( ψ ) 28 δ = (3-32) Please note that a non-associated flow rule however lead to asymmetric deformation matrices and may result in pure convergence behaviour. USER’S MANUAL, January, 2013
4 COMMANDS 4.1 Material Models LAW Material Model 1 Mohr-Coulomb / Tresca (isotropic), tension cut off (isotropic) Mohr-Coulomb (anisotropic), tension cut off (anisotropic) for up to 4 joint sets 2 Drucker-Prager / modified Drucker-Prager (ideal elastic-plastic) 5 Drucker-Prager / modified Drucker-Prager, temperature dependent 8 Mortar / Cement (modified Drucker-Prager, stress dependent, nonlinear hardening / softening) 9 Concrete (nonlinear hardening / softening, Temperature Dependency) 10 Mohr-Coulomb (anisotropic), tension cut off (anisotropic) for up to 4 joints 11 fixed crack model (x-direction) 20 Masnory_Ganz (linear hardening /softening, Temperature Dependency) 22 Masonry_Ganz (nonlinear hardening / softening) 33 boxed value (orthotropic) 40 Drucker-Prager-Geo 41 Coupling Mohr-Coulomb and Drucker-Prager 99 usermpls The material library <strong>multiPlas</strong> was implemented within the ANSYS-user-interface “userpl”. The activation is realized by using the tb-commands: tb,user,mat,,80 mat – material number tbda,1,LAW, , , allocation of the data field with the selected material model (LAW) and the material parameters (see the following sections 4.2) 29 USER’S MANUAL, January, 2013
Page 1 and 2: User’s Manual multiPlas Release 4
Page 3 and 4: CONTENT 1 INTRODUCTION.............
Page 5 and 6: 1 INTRODUCTION This manual describe
Page 7 and 8: 3 THEORY OF THE MULTIPLAS MATERIAL
Page 9 and 10: 3.3 Computed yield surfaces 3.3.1 I
Page 11 and 12: Necessary material parameters in th
Page 13 and 14: Residual strength can be defined. T
Page 15 and 16: interim values or blending with Moh
Page 17 and 18: -σm a) b) Fig. 3-10 Singular Druck
Page 19 and 20: This model guaranties a consistent
Page 21 and 22: Tab. 3-1 Temperature dependency of
Page 23 and 24: F1 (F11) Tension failure brick F2 (
Page 25 and 26: 3.3.8 Wood modelling using a boxed-
Page 27: Fig. 3-24 Stress-strain relation -
Page 31 and 32: 4.2.2 LAW = 2 - Modified Drucker-Pr
Page 33 and 34: 4.2.4 LAW = 8 - Modified Drucker-Pr
Page 35 and 36: 4.2.5 LAW = 9 - Concrete 1 2 3 4 5
Page 37 and 38: 4.2.6 LAW = 11 - Fixed Crack Model
Page 39 and 40: tempd switch for temperature depend
Page 41 and 42: Overview input parameter of the rel
Page 43 and 44: 4.2.10 LAW = 40 - Geological Drucke
Page 45 and 46: 4.3 Numerical control variables eps
Page 47 and 48: The global load step bisection can
Page 49 and 50: Output for LAW 33: scale active yie
Page 51 and 52: Elements: Solid45 Load history: 1st
Page 53 and 54: Reference solution: Example 2 - Cal
Page 59 and 60: Equivalent plastic strain 59 USER
Page 61 and 62: Total deformation usum (mm) Equival
Page 63 and 64: 5.5 Example 10 - Concrete-model DRU
Page 65 and 66: 5.6 Example 11 - Concrete-model DRU
Page 67 and 68: 5.7 Example 12 - Masonry-model with
Page 69 and 70: 5.9 Example 14 - Masonry-model with
Page 71 and 72: 5.11 Example 16 - Masonry-model wit
Page 73 and 74: 5.13 Example 18 - Masonry-model (LA
Page 75 and 76: 5.15 Example 20 - Wood-model (LAW=3
Page 77 and 78: 5.16 Example 21 - Wood-model (LAW=3
Page 79 and 80:
5.17 Example 22 - Single Joint Shea
Page 81 and 82:
6 REFERENCES [6-1] ANSYS Users Manu
Page 83 and 84:
7 APENDIX USER INFERFACE - USERMPLS
Page 85 and 86:
85 USER’S MANUAL, January, 2013
Page 87:
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multiPlas - Dynardo GmbH

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