Is it permissible for them to get married and stipulate that they will not have intercourse?
Question

                If a married couple is living together without any marital/physical realation (not even once) and they are just like friends, is it halal in islam? and what is the position of such wife according to islam?.
Praise be to Allah.
    Firstly: 

    It is not permissible according to sharee’ah for a man and 
    woman who are non-mahrams to live together in the same house. Hence likening 
    a couple living together without having intercourse to friends living 
    together is not proper. 

    Both spouses must understand that one of the most important 
    aims of marriage is guarding and maintaining chastity and producing 
    offspring. This cannot be done without having intercourse. 

    The Prophet  (peace and blessings of Allaah be upon him) 
    encouraged marrying the woman who is fertile, and he told some of his 
    companions not to marry women who could not bear children. 

    It was narrated that Ma’qil ibn Yasaar (may Allaah be pleased 
    with him) said: A man came to the Messenger of Allaah  (peace and 
    blessings of Allaah be upon him) and said: I have found a woman who is of 
    good lineage and high status, but she cannot bear children; should I marry 
    her? And he told him not to (marry her). Then he came to him a second time 
    and he told him not to (marry her). Then he came to him a third time and he 
    told him not to (marry her) and said; “Marry the one who is loving and 
    fertile, for I will be proud of your great numbers.” 

    Narrated by al-Nasaa’i (3227) and Abu Dawood (2050); classed 
    as saheeh by al-Albaani in Saheeh al-Targheeb (1921). 

    See also the commentary on the hadeeth in the answer to 
    question no. 32668, and question no. 
    13492. 

    But if the two spouses in the marital home agree not to have 
    intercourse, then this is something that could happen and it may be said 
    that it is permissible, in the case of spouses who are sick or elderly and 
    have no desire for intercourse. But if they have the desire for intercourse, 
    then how can they live together without being able to keep themselves 
    chaste? Where will each of them fulfil his or her desire if not with the one 
    with whom Allaah has permitted that?! 

    It may also be possible and it may be said that it is 
    permissible if the woman is young and has desire, and she agrees to marry a 
    man who is impotent, has had his penis cut off or is elderly. The opposite 
    may also be said, which is that a man may marry a woman who is sick and has 
    no desire, or is physically incapable of intercourse, if he is able to be 
    patient and seek reward for that, or he has other wives with whom he may 
    fulfill his desires. 

    Thirdly: 

    The fuqaha’ distinguished between two issues with regard to 
    this matter: 

    1 – When it is stipulated in the marriage contract that it is 
    not permissible for them to have intercourse. In this case the condition is 
    invalid, and the contract is invalid according to the majority of scholars. 

    2 – When it is stipulated in the marriage contract that they 
    will not have intercourse. In this case it depends, but the most correct 
    view is that the contract is valid and the condition is invalid and carries 
    no weight and has no value, regardless of whether the condition is 
    stipulated by the husband, the wife or both. 

    It says in al-Mawsoo’ah al-Fiqhiyyah (44/45): 

    The fuqaha’ differentiated in the ruling on this stipulation 
    between two cases, when the condition denies that intercourse is 
    permissible, and when it stipulates that it will not be done. 

    This is explained as follows:  

    If it is stipulated in the marriage contract that intercourse 
    is not permissible, and that he married her on the basis that it is not 
    permissible for him, then there is no difference of opinion among the 
    scholars concerning the fact that this condition is invalid, but they did 
    differ as to its effect on the validity of the marriage contract. There are 
    two opinions: 

    1 – The majority of Shaafa’i, Maaliki and Hanbali fuqaha’ are 
    of the view that both the condition and the marriage contract are invalid, 
    because this condition cancels out the purpose of the contract, and because 
    it contradicts it, because the marriage no longer makes any sense, rather it 
    is an unrealistic contract. 

    2 –The Hanafi view is that the condition is invalid, but the 
    contract is valid, because the basic principle according to the Hanafis is 
    that marriage is not invalidated by an invalid condition, rather the 
    condition alone is invalid. 

    But if it is stipulated in the marriage contract that there 
    will be no intercourse, the fuqaha’ differed concerning the ruling on that 
    and there are three views: 

    1 – The Hanafis and Hanbalis are of the view that the 
    contract is valid but the condition is invalid. As for the invalidity of the 
    condition, it is contrary to the purpose of the contract, and it implies 
    waiving rights that would be binding according to the contract if this 
    condition were not stipulated. As for the contract remaining valid, that is 
    because this condition is something additional to the contract so it does 
    not invalidate it.  

    The basic principle according to the Hanafis is that marriage 
    is not invalidated by an invalid condition, rather the condition alone is 
    invalid. 

    2 –The Maalikis are of the view that the condition is 
    invalid, and the contract is invalid, because it has been done in a way that 
    is forbidden in sharee’ah. 

    Then the Maalikis differed as to the consequences after the 
    contract is done. It was said that the marriage may be annulled before and 
    after consummation, or it was said that it may be annulled before 
    consummation and confirmed afterwards, and this condition is to be waived.  
    This is the well known view of the (Maaliki) madhhab. 

    3 – The Shaafa’is are of the view that if he marries her on 
    condition that he will not have intercourse with her, or he will only have 
    intercourse with her by day, or only once, for example, the marriage is 
    invalid if the condition was stipulated by her, because it is contrary to 
    the purpose of the contract. If it was stipulated by him, then it does not 
    matter, because intercourse is his right, and he may forsake it, and 
    enabling him to have intercourse with her is her duty, and she has no right 
    to forsake it. End quote.  

    Fourthly: 

    The woman should not agree to this marriage, and the man 
    should not agree with the woman if she does not want there to be any 
    intercourse between them. They should both understand that this is contrary 
    to sound fitrah (human nature). Allaah has created in men an inclination 
    towards women, and He has created in women an inclination towards men. There 
    are some people who direct their desires in haraam ways, and some who direct 
    them in halaal ways. Marriage is one of the laws of Allaah in which He has 
    permitted the man and woman to come together and has created affection and 
    compassion between them, and has brought forth children and offspring from 
    them. 

    Allaah says (interpretation of the meaning): 

    “And Allaah has made for you Azwaaj (mates or wives) of 
    your own kind, and has made for you, from your wives, sons and grandsons, 
    and has bestowed on you good provision. Do they then believe in false 
    deities and deny the Favour of Allaah (by not worshipping Allaah Alone)”

    [al-Nahl 16:72]

    “And among His Signs is this, that He created for you 
    wives from among yourselves, that you may find repose in them, and He has 
    put between you affection and mercy. Verily, in that are indeed signs for a 
    people who reflect”

    [al-Room 30:21]

    Marriage is the way of the Messengers (peace and blessings of 
    Allaah be upon them), and they are the best of mankind. Allaah says 
    (interpretation of the meaning): 

    “And indeed We sent Messengers before you (O Muhammad
    صلى الله عليه وسلم), and made for them 
    wives and offspring”

    [al-Ra’d 13:38]

    “At that time Zakariyya (Zachariya) invoked his Lord, 
    saying: ‘O my Lord! Grant me from You, a good offspring. You are indeed the 
    All-Hearer of invocation’”

    [Aal ‘Imraan 3:38]

    And Allaah knows best.