A class providing methods to compute energy density and force of peridynamic material. More...

#include <material.h>

Inheritance diagram for material::PmbMaterial:

Collaboration diagram for material::PmbMaterial:

Public Member Functions
	PmbMaterial (inp::MaterialDeck &deck, const size_t &dim, const double &horizon)
	Constructor.

bool	isStateActive () const override
	Returns true if state-based potential is active.

std::pair< double, double >	getBondEF (const double &r, const double &s, bool &fs, const bool &break_bonds) const override
	Returns energy and force between bond due to pairwise interaction.

std::pair< double, double >	getBondEF (const double &r, const double &s, bool &fs, const double &mx, const double &thetax) const override
	Returns energy and force between bond due to state-based model.

util::Point	getBondForceDirection (const util::Point &dx, const util::Point &du) const override
	Returns the unit vector along which bond-force acts.

double	getS (const util::Point &dx, const util::Point &du) const override
	Returns the bond strain.

double	getSc (const double &r) const override
	Returns critical bond strain.

double	getDensity () const override
	Returns the density of the material.

double	getInfFn (const double &r) const override
	Returns the value of influence function.

double	getMoment (const size_t &i) const override
	Returns the moment of influence function.

double	getHorizon () const override
	Returns horizon.

inp::MatData	computeMaterialProperties (const size_t &dim) const override
	Computes elastic and fracture material properties and returns the data.

std::string	printStr (int nt, int lvl) const override
	Returns the string containing printable information about the object.

void	print (int nt, int lvl) const override
	Prints the information about the object.

void	print () const override
	Prints the information about the object.

Public Member Functions inherited from material::Material
	Material (std::string name="")
	Constructor.

virtual	~Material ()
	Destructor.

std::string	name ()
	Returns name of the material.

size_t	getDimension () const
	Returns dimension of the problem.

bool	isPlaneStrain () const
	Returns plane-strain condition.

virtual double	getBreakSc (const double &r) const
	Returns bond strain beyond which the bond is marked broken.

virtual double	getDilatationEnergyDensity (const double &thetax) const
	Returns the dilatational part of the strain energy density.

Private Member Functions
void	computeParameters (inp::MaterialDeck &deck, const size_t &dim)
	Compute material model parameters.

Private Attributes
double	d_horizon
	Horizon.

double	d_density
	Density.

Material parameters
double	d_c
	Micromodulus c (divided by the constant influence value)

double	d_s0
	Critical stretch.

double	d_Jscale
	Constant influence value a0 that c was divided by.

Detailed Description

A class providing methods to compute energy density and force of peridynamic material.

Definition at line 731 of file material.h.

Constructor & Destructor Documentation

◆ PmbMaterial()

material::PmbMaterial::PmbMaterial	(	inp::MaterialDeck &	deck,
		const size_t &	dim,
		const double &	horizon
	)

inline

Constructor.

Parameters

deck	Input deck which contains user-specified information
dim	Dimension
horizon	Horizon

Definition at line 740 of file material.h.

      : Material("PMBBond"), d_horizon(horizon), d_density(deck.d_density),
        d_c(0.), d_s0(0.), d_Jscale(1.) {
 
    // set global fields
    if (dimension != dim)
      dimension = dim;
 
    if (is_plane_strain != deck.d_isPlaneStrain)
      is_plane_strain = deck.d_isPlaneStrain;
 
    // create influence function
    if (deck.d_influenceFnType == 0) {
      if (influence_fn == nullptr)
        influence_fn = std::make_shared<material::ConstInfluenceFn>(
            deck.d_influenceFnParams, dim);
    }
    else if (deck.d_influenceFnType == 1) {
      if (influence_fn == nullptr)
        influence_fn = std::make_shared<material::LinearInfluenceFn>(
            deck.d_influenceFnParams, dim);
    }
    else if (deck.d_influenceFnType == 2) {
      if (influence_fn == nullptr)
        influence_fn = std::make_shared<material::GaussianInfluenceFn>(
            deck.d_influenceFnParams, dim);
    }
    else {
      throw std::runtime_error(
          util::io::Msg()
          << "Error: Influence function type = "
          << deck.d_influenceFnType
          << " is invalid.\n");
    }
 
    // check if we need to compute the material parameters
    if (deck.d_computeParamsFromElastic)
      computeParameters(deck, dim);
    else {
      d_c = deck.d_bondPotentialParams[0];
      d_s0 = deck.d_bondPotentialParams[1];
    }
  };

References computeParameters(), inp::MaterialDeck::d_bondPotentialParams, d_c, inp::MaterialDeck::d_computeParamsFromElastic, inp::MaterialDeck::d_influenceFnParams, inp::MaterialDeck::d_influenceFnType, inp::MaterialDeck::d_isPlaneStrain, and d_s0.

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Member Function Documentation

◆ computeMaterialProperties()

inp::MatData material::PmbMaterial::computeMaterialProperties ( const size_t & dim ) const

inlineoverridevirtual

Computes elastic and fracture material properties and returns the data.

Parameters

dim	Dimension of the problem

Returns: inp::MatData Material data

Implements material::Material.

Definition at line 919 of file material.h.

                                                                         {
 
    auto data = inp::MatData();
    data.d_nu = (dim == 2 && !is_plane_strain) ? 1. / 3. : 0.25;
 
    // inverse of computeParameters, with c for J = 1
    const double h = d_horizon;
    const double c = d_c * d_Jscale;
    if (dim == 2) {
      data.d_E = is_plane_strain ? 5. * M_PI * std::pow(h, 3) * c / 48.
                                 : M_PI * std::pow(h, 3) * c / 9.;
      data.d_K = data.toK(data.d_E, data.d_nu);
      data.d_Gc = c * d_s0 * d_s0 * std::pow(h, 4) / 4.;
    } else if (dim == 3) {
      data.d_K = M_PI * std::pow(h, 4) * c / 18.;
      data.d_E = data.toE(data.d_K, data.d_nu);
      data.d_Gc = M_PI * c * d_s0 * d_s0 * std::pow(h, 5) / 10.;
    }
    data.d_G = data.toGE(data.d_E, data.d_nu);
    data.d_lambda = data.toLambdaE(data.d_E, data.d_nu);
    data.d_mu = data.d_G;
    data.d_KIc = data.toKIc(data.d_Gc, data.d_nu, data.d_E);
    return data;
  };

References d_c, d_horizon, d_Jscale, and d_s0.

◆ computeParameters()

void material::PmbMaterial::computeParameters	(	inp::MaterialDeck &	deck,
		const size_t &	dim
	)

inlineprivate

Compute material model parameters.

Parameters

deck	MaterialDeck
dim	Dimension of the domain

Definition at line 990 of file material.h.

                                                                   {
    //
    // Need following elastic and fracture properties
    // 1. E or K
    // 2. Gc or KIc
    // Bond-based Poisson ratio is locked by dimension / plane-strain flag
    // (Silling & Askari 2005; Madenci & Oterkus 2014; Ha & Bobaru 2010).
    //
    if (util::isLess(deck.d_matData.d_E, 0.) &&
        util::isLess(deck.d_matData.d_K, 0.)) {
      throw std::runtime_error(
          util::io::Msg()
          << "Error: Require either Young's modulus E or Bulk modulus K"
          " to compute the PMB bond-based peridynamic parameters.\n");
    }
    if (util::isGreater(deck.d_matData.d_E, 0.) &&
        util::isGreater(deck.d_matData.d_K, 0.)) {
      std::cout << "Warning: Both Young's modulus E and Bulk modulus K are "
                   "provided.\n";
      std::cout << "Warning: Selecting Young's modulus E for PMB calibration.\n";
    }
 
    if (util::isLess(deck.d_matData.d_Gc, 0.) &&
        util::isLess(deck.d_matData.d_KIc, 0.)) {
      throw std::runtime_error(
          util::io::Msg()
          << "Error: Require either critical energy release rate Gc or "
          "critical stress intensity factor KIc to compute the PMB "
          "bond-based peridynamic parameters.\n");
    } else if (util::isGreater(deck.d_matData.d_Gc, 0.) &&
               util::isGreater(deck.d_matData.d_KIc, 0.)) {
      std::cout << "Warning: Both Gc and KIc provided; selecting Gc.\n";
    }
 
    // Bond-based PMB fixes nu: 1/4 in 3D and plane strain, 1/3 in plane
    // stress. E is matched.
    const double nu_pmb = (dim == 2 && !is_plane_strain) ? 1. / 3. : 0.25;
    if (util::isGreater(deck.d_matData.d_nu, 0.) &&
        std::abs(deck.d_matData.d_nu - nu_pmb) > 1.0e-12)
      std::cout << "Warning: PMB bond-based model fixes nu = " << nu_pmb
                << "; ignoring nu = " << deck.d_matData.d_nu << ".\n";
    deck.d_matData.d_nu = nu_pmb;
 
    // Prefer E; else recover E from K with the fixed nu.
    if (deck.d_matData.d_E < 0. && deck.d_matData.d_K > 0.)
      deck.d_matData.d_E =
          deck.d_matData.toE(deck.d_matData.d_K, deck.d_matData.d_nu);
    if (deck.d_matData.d_E > 0.)
      deck.d_matData.d_K =
          deck.d_matData.toK(deck.d_matData.d_E, deck.d_matData.d_nu);
 
    if (deck.d_matData.d_Gc > 0.)
      deck.d_matData.d_KIc = deck.d_matData.toKIc(
          deck.d_matData.d_Gc, deck.d_matData.d_nu, deck.d_matData.d_E);
 
    if (deck.d_matData.d_KIc > 0. && deck.d_matData.d_Gc < 0.)
      deck.d_matData.d_Gc = deck.d_matData.toGc(
          deck.d_matData.d_KIc, deck.d_matData.d_nu, deck.d_matData.d_E);
 
    deck.d_matData.d_lambda =
        deck.d_matData.toLambdaE(deck.d_matData.d_E, deck.d_matData.d_nu);
    deck.d_matData.d_G =
        deck.d_matData.toGE(deck.d_matData.d_E, deck.d_matData.d_nu);
    deck.d_matData.d_mu = deck.d_matData.d_G;
 
    // The closed forms for c and s0 hold for a constant influence function.
    if (deck.d_influenceFnType != 0) {
      throw std::runtime_error(
          util::io::Msg()
          << "Error: PMB parameters from E and Gc need a constant influence "
             "function. Set Influence_Function Type = 0.\n");
    }
    d_Jscale = deck.d_influenceFnParams.empty() ? double(dim + 1)
                                                : deck.d_influenceFnParams[0];
    if (!(d_Jscale > 0.)) {
      throw std::runtime_error(
          util::io::Msg()
          << "Error: PMB influence scale must be > 0.\n");
    }
 
    // c and s0 for J = 1: Silling and Askari 2005 (3D), Ha and Bobaru 2010
    // (2D plane stress); plane strain uses the same energy match with
    // nu = 1/4. Then J = a0 is absorbed into c.
    const double Gc = deck.d_matData.d_Gc;
    const double E = deck.d_matData.d_E;
    const double h = d_horizon;
    if (dim == 2) {
      d_c = is_plane_strain ? 48. * E / (5. * M_PI * std::pow(h, 3))
                            : 9. * E / (M_PI * std::pow(h, 3));
      d_s0 = std::sqrt(4. * Gc / (d_c * std::pow(h, 4)));
    } else if (dim == 3) {
      d_c = 18. * deck.d_matData.d_K / (M_PI * std::pow(h, 4));
      d_s0 = std::sqrt(10. * Gc / (M_PI * d_c * std::pow(h, 5)));
    } else {
      throw std::runtime_error(
          util::io::Msg()
          << "Error: PMB computeParameters: unsupported dim=" << dim
          << "\n");
    }
    d_c /= d_Jscale;
  };

References d_c, inp::MatData::d_E, inp::MatData::d_G, inp::MatData::d_Gc, d_horizon, inp::MaterialDeck::d_influenceFnParams, inp::MaterialDeck::d_influenceFnType, d_Jscale, inp::MatData::d_K, inp::MatData::d_KIc, inp::MatData::d_lambda, inp::MaterialDeck::d_matData, inp::MatData::d_mu, inp::MatData::d_nu, d_s0, util::isGreater(), util::isLess(), inp::MatData::toE(), inp::MatData::toGc(), inp::MatData::toGE(), inp::MatData::toK(), inp::MatData::toKIc(), and inp::MatData::toLambdaE().

Referenced by PmbMaterial().

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◆ getBondEF() [1/2]

std::pair< double, double > material::PmbMaterial::getBondEF	(	const double &	r,
		const double &	s,
		bool &	fs,
		const bool &	break_bonds
	)		const

inlineoverridevirtual

Returns energy and force between bond due to pairwise interaction.

Micropotential \( w = \frac{1}{2} c s^2 r \) and pair force \( c s \) (Silling and Askari 2005), both times \( J(r/\delta) \). The returned energy is the bond's share of the strain energy density at x, \( W(x) = \frac{1}{2} \int w \, dy \), i.e. \( w/2 \).

Parameters

r	Reference (initial) bond length
s	Bond strain
fs	Bond fracture state
break_bonds	Flag to specify whether bonds are allowed to break or not

Returns: value Pair of energy and force

Implements material::Material.

Definition at line 804 of file material.h.

                                                                              {
 
    if (!break_bonds)
      return std::make_pair(getInfFn(r) * 0.25 * d_c * s *
                                s * r,
                            getInfFn(r) * d_c * s);
 
    // Fracture: literature PMB is tension-only (s > s0). Absolute stretch is
    // applied in pdForce when Model.Bond_Break = absolute_stretch.
    if (!fs && util::isGreater(s, d_s0 + 1.0e-10))
      fs = true;
 
    // if bond is not fractured, return energy and force from nonlinear
    // potential otherwise return energy of fractured bond, and zero force
    if (!fs)
      return std::make_pair(getInfFn(r) * 0.25 * d_c * s *
                                s * r,
                            getInfFn(r) * d_c * s);
    else
      return std::make_pair(
          getInfFn(r) * 0.25 * d_c * d_s0 * d_s0 * r, 0.);
  };

References d_c, d_s0, getInfFn(), and util::isGreater().

Referenced by getBondEF().

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◆ getBondEF() [2/2]

std::pair< double, double > material::PmbMaterial::getBondEF	(	const double &	r,
		const double &	s,
		bool &	fs,
		const double &	mx,
		const double &	thetax
	)		const

inlineoverridevirtual

Returns energy and force between bond due to state-based model.

Parameters

r	Reference (initial) bond length
s	Bond strain
fs	Bond fracture state
mx	Weighted volume at node
thetax	Dilation

Returns: value Pair of energy and force

Implements material::Material.

Definition at line 840 of file material.h.

                                            {
 
    return this->getBondEF(r, s, fs, true);
  };

References getBondEF().

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◆ getBondForceDirection()

util::Point material::PmbMaterial::getBondForceDirection	(	const util::Point &	dx,
		const util::Point &	du
	)		const

inlineoverridevirtual

Returns the unit vector along which bond-force acts.

Parameters

dx	Reference bond vector
du	Difference of displacement

Returns: vector Unit vector

Implements material::Material.

Definition at line 853 of file material.h.

                                                                         {
    return (dx + du) / (dx + du).length();
  };

◆ getDensity()

double material::PmbMaterial::getDensity ( ) const

inlineoverridevirtual

Returns the density of the material.

Returns: density Density of the material

Implements material::Material.

Definition at line 880 of file material.h.

880{ return d_density; };

References d_density.

◆ getHorizon()

double material::PmbMaterial::getHorizon ( ) const

inlineoverridevirtual

Returns horizon.

Returns: horizon Horizon

Implements material::Material.

Definition at line 910 of file material.h.

910{ return d_horizon; };

References d_horizon.

◆ getInfFn()

double material::PmbMaterial::getInfFn ( const double & r ) const

inlineoverridevirtual

Returns the value of influence function.

Parameters

r	Reference (initial) bond length

Returns: value Influence function at r

Implements material::Material.

Definition at line 888 of file material.h.

                                                  {
    return getGlobalInfFn(r / d_horizon);
  };

References d_horizon.

Referenced by getBondEF().

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◆ getMoment()

double material::PmbMaterial::getMoment ( const size_t & i ) const

inlineoverridevirtual

Returns the moment of influence function.

If \( J(r) \) is the influence function for \( r\in [0,1)\) then \( i^{th}\) moment is given by

\[ M_i = \int_0^1 J(r) r^i dr. \]

Parameters

i	ith moment

Returns: value Moment

Implements material::Material.

Definition at line 901 of file material.h.

                                                   {
    return getGlobalMoment(i);
  };

◆ getS()

double material::PmbMaterial::getS	(	const util::Point &	dx,
		const util::Point &	du
	)		const

inlineoverridevirtual

Returns the bond strain.

Parameters

dx	Reference bond vector
du	Difference of displacement

Returns: strain Bond strain \( S = \frac{du \cdot dx}{|dx|^2} \)

Implements material::Material.

Definition at line 864 of file material.h.

                                                                       {
    return ((dx + du).length() - dx.length()) / dx.length();
  };

References util::Point::length().

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◆ getSc()

double material::PmbMaterial::getSc ( const double & r ) const

inlineoverridevirtual

Returns critical bond strain.

Parameters

r	Reference length of bond

Returns: strain Critical strain

Implements material::Material.

Definition at line 874 of file material.h.

874{ return d_s0; };

References d_s0.

◆ isStateActive()

bool material::PmbMaterial::isStateActive ( ) const

inlineoverridevirtual

Returns true if state-based potential is active.

Returns: bool True/false

Implements material::Material.

Definition at line 788 of file material.h.

788{ return false; };

◆ print() [1/2]

void material::PmbMaterial::print ( ) const

inlineoverridevirtual

Prints the information about the object.

Reimplemented from material::Material.

Definition at line 981 of file material.h.

981{ print(0, 0); };

material::PmbMaterial::print

void print() const override

Prints the information about the object.

Definition material.h:981

References print().

Referenced by print().

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◆ print() [2/2]

void material::PmbMaterial::print	(	int	nt,
		int	lvl
	)		const

inlineoverridevirtual

Prints the information about the object.

Parameters

nt	Number of tabs to append before printing
lvl	Information level (higher means more information)

Reimplemented from material::Material.

Definition at line 976 of file material.h.

                                             {
    std::cout << printStr(nt, lvl);
  };

References printStr().

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◆ printStr()

std::string material::PmbMaterial::printStr	(	int	nt,
		int	lvl
	)		const

inlineoverridevirtual

Returns the string containing printable information about the object.

Parameters

nt	Number of tabs to append before printing
lvl	Information level (higher means more information)

Returns: string String containing printable information about the object

Reimplemented from material::Material.

Definition at line 951 of file material.h.

                                                     {
 
    auto tabS = util::io::getTabS(nt);
    std::ostringstream oss;
    oss << tabS << "------- particle::PmbMaterial --------" << std::endl
        << std::endl;
    oss << tabS << "State active = " << 0 << std::endl;
    oss << tabS << "Horizon = " << d_horizon << std::endl;
    oss << tabS << "Influence fn address = " << influence_fn.get() << std::endl;
    oss << tabS << "Influence fn info: " << std::endl;
    oss << influence_fn->printStr(nt + 1, lvl);
    oss << tabS << "Peridynamic parameters: " << std::endl;
    oss << tabS << "  c = " << d_c << std::endl;
    oss << tabS << "  s0 = " << d_s0 << std::endl;
    oss << tabS << std::endl;
 
    return oss.str();
  };

References d_c, d_horizon, d_s0, and util::io::getTabS().

Referenced by print().

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Field Documentation

◆ d_c

double material::PmbMaterial::d_c

private

Micromodulus c (divided by the constant influence value)

Definition at line 1105 of file material.h.

Referenced by computeMaterialProperties(), computeParameters(), getBondEF(), PmbMaterial(), and printStr().

◆ d_density

double material::PmbMaterial::d_density

private

Density.

Definition at line 1097 of file material.h.

Referenced by getDensity().

◆ d_horizon

double material::PmbMaterial::d_horizon

private

Horizon.

Definition at line 1094 of file material.h.

Referenced by computeMaterialProperties(), computeParameters(), getHorizon(), getInfFn(), and printStr().

◆ d_Jscale

double material::PmbMaterial::d_Jscale

private

Constant influence value a0 that c was divided by.

Definition at line 1111 of file material.h.

Referenced by computeMaterialProperties(), and computeParameters().

◆ d_s0

double material::PmbMaterial::d_s0

private

Critical stretch.

Definition at line 1108 of file material.h.

Referenced by computeMaterialProperties(), computeParameters(), getBondEF(), getSc(), PmbMaterial(), and printStr().

The documentation for this class was generated from the following file:

/home/user/project/src/material/mparticle/material.h

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ PmbMaterial()

Member Function Documentation

◆ computeMaterialProperties()

◆ computeParameters()

◆ getBondEF() [1/2]

◆ getBondEF() [2/2]

◆ getBondForceDirection()

◆ getDensity()

◆ getHorizon()

◆ getInfFn()

◆ getMoment()

◆ getS()

◆ getSc()

◆ isStateActive()

◆ print() [1/2]

◆ print() [2/2]

◆ printStr()

Field Documentation

◆ d_c

◆ d_density

◆ d_horizon

◆ d_Jscale

◆ d_s0