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

#include <material.h>

Inheritance diagram for material::PdState:

Collaboration diagram for material::PdState:

Public Member Functions
	PdState (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.

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

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.

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

double	getCriticalStretchDensity (const size_t &dim) const
	Returns Gc / s0^2 for the state-based model.

Private Attributes
double	d_horizon
	Horizon.

double	d_density
	Density.

Material parameters
double	d_K
	Bulk modulus.

double	d_G
	Shear modulus.

double	d_kappa
	Bulk modulus used by the model (K in 3D, in-plane in 2D)

double	d_s0
	Critical stretch.

double	d_dim
	Dimension, as a double.

double	d_alphaFactor
	d(d+2): 15 in 3D, 8 in 2D

Detailed Description

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

Definition at line 1429 of file material.h.

Constructor & Destructor Documentation

◆ PdState()

material::PdState::PdState	(	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 1438 of file material.h.

      : Material("PDState"), d_horizon(horizon), d_density(deck.d_density),
        d_K(0.), d_G(0.), d_kappa(0.), d_s0(0.), d_dim(double(dim)),
        d_alphaFactor(dim == 2 ? 8. : 15.) {
 
    // 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_K = deck.d_bondPotentialParams[0];
      d_G = deck.d_bondPotentialParams[1];
      d_s0 = deck.d_bondPotentialParams[2];
      d_kappa = getModelBulkModulus(dim, is_plane_strain, d_K, d_G);
    }
  };

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

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Member Function Documentation

◆ computeMaterialProperties()

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

inlineoverridevirtual

Computes elastic and fracture material properties and returns the data.

Parameters

dim	Dimension of the problem

Returns: Data Material data

Implements material::Material.

Definition at line 1626 of file material.h.

                                                                         {
 
    auto data = inp::MatData();
 
    // we already have G and K
    data.d_G = d_G;
    data.d_K = d_K;
 
    // get Poisson ratio and Young's modulus
    data.d_nu = (3. * d_K - 2. * d_G) / (2. * (3. * d_K + d_G));
    data.d_E = data.toE(d_K, data.d_nu);
 
    // get lame parameters
    data.d_lambda = data.toLambdaE(data.d_E, data.d_nu);
    data.d_mu = d_G;
 
    // get Gc from s0 (inverse of computeParameters)
    data.d_Gc = d_s0 * d_s0 * getCriticalStretchDensity(dim);
 
    // KIc
    data.d_KIc = data.toKIc(
        data.d_Gc, data.d_nu, data.d_E);
 
    return data;
  };

References d_G, d_K, d_s0, and getCriticalStretchDensity().

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◆ computeParameters()

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

inlineprivate

Compute material model parameters.

Parameters

deck	MaterialDeck
dim	Dimension of the domain

Definition at line 1699 of file material.h.

                                                                   {
    //
    // Need following elastic and fracture properties
    // 1. E or K
    // 2. Poisson ratio or shear modulus
    // 3. Gc or KIc
    //
    bool found_E = false;
    bool found_K = false;
    bool found_G = false;
    bool found_nu = false;
    size_t num_props = 0;
 
    found_E = util::isGreater(deck.d_matData.d_E, 0.);
    if (found_E)
      num_props++;
 
    found_K = util::isGreater(deck.d_matData.d_K, 0.);
    if (found_K)
      num_props++;
 
    found_G = util::isGreater(deck.d_matData.d_G, 0.);
    if (found_G)
      num_props++;
 
    found_nu = util::isGreater(deck.d_matData.d_nu, 0.);
    if (found_nu)
      num_props++;
 
    if (num_props != 2) {
      std::ostringstream oss;
      oss << "Error: Require two different elastic properties for the "
                   "PdState material. Pairs supported are (E, K), (E, G), "
                   "(E, nu), (K, G).\n";
      oss << deck.printStr(0, 0) << "\n";
      throw std::runtime_error(
          util::io::Msg()
          << oss.str());
    }
 
    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 RNP "
          "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 critical energy release rate Gc and critical "
                   "stress intensity factor KIc are provided.\n";
      std::cout << "Warning: To compute the RNP bond-based peridynamic "
                   "parameters, we only require one of those.\n";
      std::cout << "Warning: Selecting critical energy release rate Gc to "
                   "compute parameters.\n";
    }
 
    // compute nu if not provided
    if (!found_nu) {
      if (found_E and found_G)
        deck.d_matData.d_nu =
            (0.5 * deck.d_matData.d_E / deck.d_matData.d_G) - 1.;
 
      if (found_E and found_K)
        deck.d_matData.d_nu =
            (3. * deck.d_matData.d_K - deck.d_matData.d_E) /
            (6. * deck.d_matData.d_K);
 
      if (found_G and found_K)
        deck.d_matData.d_nu =
            (3. * deck.d_matData.d_K - 2. * deck.d_matData.d_G) /
            (2. * (3. * deck.d_matData.d_K + deck.d_matData.d_G));
    }
    found_nu = true;
 
    // compute E if not provided
    if (!found_E) {
      if (found_K)
        deck.d_matData.d_E =
            deck.d_matData.toE(deck.d_matData.d_K, deck.d_matData.d_nu);
 
      if (found_G)
        deck.d_matData.d_E =
            2. * deck.d_matData.d_G * (1. + deck.d_matData.d_nu);
    }
    found_E = true;
 
    // compute K if not provided
    if (!found_K)
      deck.d_matData.d_K =
          deck.d_matData.toK(deck.d_matData.d_E, deck.d_matData.d_nu);
 
    found_K = true;
 
 
    // compute G if not provided
    if (!found_G)
      deck.d_matData.d_G =
          deck.d_matData.toGE(deck.d_matData.d_E, deck.d_matData.d_nu);
 
    found_G = true;
 
    // compute Gc (if not provided) and KIc (if not provided)
    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);
 
    // compute lame parameter
    deck.d_matData.d_lambda =
        deck.d_matData.toLambdaE(deck.d_matData.d_E, deck.d_matData.d_nu);
    deck.d_matData.d_mu = deck.d_matData.d_G;
 
    // compute peridynamic parameters
    d_K = deck.d_matData.d_K;
    d_G = deck.d_matData.d_G;
    d_kappa = getModelBulkModulus(dim, is_plane_strain, d_K, d_G);
 
    // The closed form for s0 holds for a constant influence function.
    if (deck.d_influenceFnType != 0) {
      throw std::runtime_error(
          util::io::Msg()
          << "Error: PDState critical stretch from Gc needs a constant "
             "influence function. Set Influence_Function Type = 0.\n");
    }
    if (dim != 2 && dim != 3) {
      throw std::runtime_error(
          util::io::Msg()
          << "Error: PdState computeParameters: unsupported dim=" << dim
          << "\n");
    }
    d_s0 = std::sqrt(deck.d_matData.d_Gc / getCriticalStretchDensity(dim));
  };

References inp::MatData::d_E, inp::MatData::d_G, d_G, inp::MatData::d_Gc, inp::MaterialDeck::d_influenceFnType, inp::MatData::d_K, d_K, d_kappa, inp::MatData::d_KIc, inp::MatData::d_lambda, inp::MaterialDeck::d_matData, inp::MatData::d_mu, inp::MatData::d_nu, d_s0, getCriticalStretchDensity(), util::isGreater(), util::isLess(), inp::MaterialDeck::printStr(), util::io::Msg::str(), inp::MatData::toE(), inp::MatData::toGc(), inp::MatData::toGE(), inp::MatData::toK(), inp::MatData::toKIc(), and inp::MatData::toLambdaE().

Referenced by PdState().

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◆ getBondEF() [1/2]

std::pair< double, double > material::PdState::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.

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 1500 of file material.h.

                                                                              {
 
    return {0., 0.};
  };

◆ getBondEF() [2/2]

std::pair< double, double > material::PdState::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.

Linear peridynamic solid in dimension d (Silling 2010 for 3D; Yang et al. 2024, JMPS 191, eqs. 5-11 for 2D): \( t = J [ r \theta (d \kappa / m - \alpha / d) + \alpha e ] \) with \( \alpha = d(d+2) G / m \) and \( e^d = e - \theta r / d \). The returned energy is the deviatoric part at x, \( \frac{\alpha}{2} J (e^d)^2 \); the dilatational part is getDilatationEnergyDensity().

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 1526 of file material.h.

                                            {
 
    if (fs)
      return {0., 0.};
 
    double J = getInfFn(r);
    double change_length = s * r;
 
    double alpha = d_alphaFactor * d_G / mx;
    double factor = (d_dim * d_kappa / mx) - alpha / d_dim;
    double e_dev = change_length - thetax * r / d_dim;
 
    return {0.5 * alpha * J * e_dev * e_dev,
            J * (r * thetax * factor + change_length * alpha)};
  };

References d_alphaFactor, d_dim, d_G, d_kappa, and getInfFn().

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◆ getBondForceDirection()

util::Point material::PdState::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 1560 of file material.h.

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

◆ getCriticalStretchDensity()

double material::PdState::getCriticalStretchDensity ( const size_t & dim ) const

inlineprivate

Returns Gc / s0^2 for the state-based model.

Madenci and Oterkus 2014 (constant influence function), with the model bulk modulus in 2D.

Parameters

dim Dimension

Returns: value Gc / s0^2

Definition at line 1845 of file material.h.

                                                            {
    if (dim == 2)
      return (6.0 * d_G / M_PI +
              16.0 * (d_kappa - 2.0 * d_G) / (9.0 * M_PI * M_PI)) *
             d_horizon;
    return (3. * d_G + std::pow(3. / 4., 4) * (d_K - 5. * d_G / 3.)) *
           d_horizon;
  };

References d_G, d_horizon, d_K, and d_kappa.

Referenced by computeMaterialProperties(), and computeParameters().

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◆ getDensity()

double material::PdState::getDensity ( ) const

inlineoverridevirtual

Returns the density of the material.

Returns: density Density of the material

Implements material::Material.

Definition at line 1587 of file material.h.

1587{ return d_density; };

References d_density.

◆ getDilatationEnergyDensity()

double material::PdState::getDilatationEnergyDensity ( const double & thetax ) const

inlineoverridevirtual

Returns the dilatational part of the strain energy density.

Parameters

thetax Dilatation at node

Returns: energy \( \frac{1}{2} \kappa \theta^2 \)

Reimplemented from material::Material.

Definition at line 1549 of file material.h.

                                                                         {
    return 0.5 * d_kappa * thetax * thetax;
  };

References d_kappa.

◆ getHorizon()

double material::PdState::getHorizon ( ) const

inlineoverridevirtual

Returns horizon.

Returns: horizon Horizon

Implements material::Material.

Definition at line 1617 of file material.h.

1617{ return d_horizon; };

References d_horizon.

◆ getInfFn()

double material::PdState::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 1595 of file material.h.

                                                  {
    return getGlobalInfFn(r / d_horizon);
  };

References d_horizon.

Referenced by getBondEF().

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◆ getMoment()

double material::PdState::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 1608 of file material.h.

                                                   {
    return getGlobalMoment(i);
  };

◆ getS()

double material::PdState::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 1571 of file material.h.

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

References util::Point::length().

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◆ getSc()

double material::PdState::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 1581 of file material.h.

1581{ return d_s0; };

References d_s0.

◆ isStateActive()

bool material::PdState::isStateActive ( ) const

inlineoverridevirtual

Returns true if state-based potential is active.

Returns: bool True/false

Implements material::Material.

Definition at line 1489 of file material.h.

1489{ return true; };

◆ print() [1/2]

void material::PdState::print ( ) const

inlineoverridevirtual

Prints the information about the object.

Reimplemented from material::Material.

Definition at line 1690 of file material.h.

1690{ print(0, 0); };

material::PdState::print

void print() const override

Prints the information about the object.

Definition material.h:1690

References print().

Referenced by print().

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◆ print() [2/2]

void material::PdState::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 1685 of file material.h.

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

References printStr().

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◆ printStr()

std::string material::PdState::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 1659 of file material.h.

                                                     {
 
    auto tabS = util::io::getTabS(nt);
    std::ostringstream oss;
    oss << tabS << "------- particle::PdState --------" << std::endl
        << std::endl;
    oss << tabS << "State active = " << 1 << 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 << "  K = " << d_K << std::endl;
    oss << tabS << "  G = " << d_G << std::endl;
    oss << tabS << "  s0 = " << d_s0 << std::endl;
    oss << tabS << std::endl;
 
    return oss.str();
  };

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

Referenced by print().

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Field Documentation

◆ d_alphaFactor

double material::PdState::d_alphaFactor

private

d(d+2): 15 in 3D, 8 in 2D

Definition at line 1882 of file material.h.

Referenced by getBondEF().

◆ d_density

double material::PdState::d_density

private

Density.

Definition at line 1859 of file material.h.

Referenced by getDensity().

◆ d_dim

double material::PdState::d_dim

private

Dimension, as a double.

Definition at line 1879 of file material.h.

Referenced by getBondEF().

◆ d_G

double material::PdState::d_G

private

Shear modulus.

Definition at line 1870 of file material.h.

Referenced by computeMaterialProperties(), computeParameters(), getBondEF(), getCriticalStretchDensity(), PdState(), and printStr().

◆ d_horizon

double material::PdState::d_horizon

private

Horizon.

Definition at line 1856 of file material.h.

Referenced by getCriticalStretchDensity(), getHorizon(), getInfFn(), and printStr().

◆ d_K

double material::PdState::d_K

private

Bulk modulus.

Definition at line 1867 of file material.h.

Referenced by computeMaterialProperties(), computeParameters(), getCriticalStretchDensity(), PdState(), and printStr().

◆ d_kappa

double material::PdState::d_kappa

private

Bulk modulus used by the model (K in 3D, in-plane in 2D)

Definition at line 1873 of file material.h.

Referenced by computeParameters(), getBondEF(), getCriticalStretchDensity(), getDilatationEnergyDensity(), and PdState().

◆ d_s0

double material::PdState::d_s0

private

Critical stretch.

Definition at line 1876 of file material.h.

Referenced by computeMaterialProperties(), computeParameters(), getSc(), PdState(), 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

◆ PdState()

Member Function Documentation

◆ computeMaterialProperties()

◆ computeParameters()

◆ getBondEF() [1/2]

◆ getBondEF() [2/2]

◆ getBondForceDirection()

◆ getCriticalStretchDensity()

◆ getDensity()

◆ getDilatationEnergyDensity()

◆ getHorizon()

◆ getInfFn()

◆ getMoment()

◆ getS()

◆ getSc()

◆ isStateActive()

◆ print() [1/2]

◆ print() [2/2]

◆ printStr()

Field Documentation

◆ d_alphaFactor

◆ d_density

◆ d_dim

◆ d_G

◆ d_horizon

◆ d_K

◆ d_kappa

◆ d_s0